Physics Wiki - User contributions [en]

Main Page/PHYS 4210/Bell's Inequalities

2026-02-03T22:04:06Z

Mgeorge:

<h1>Bell's Inequalities and Quantum Entanglement</h1>

<p> Deep at the root of the underlying principles of quantum mechanics lies shadowy principles based on probability which never sit well with some people. This experiment is meant to shine some (laser)light on these principles, and see if we can't come to some deeper understanding of the underlying framework of Quantum Dynamics.</p>
<p>No better introduction can be given than the following set of famous papers, commonly referred to today by their author lists.</p>
<ul>
<li>Einstein, Podolsky, Rosen<ref>A. Einstein, B. Podolsky & N. Rosen, <i>"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"</i> [http://prola.aps.org/abstract/PR/v47/i10/p777_1 Phys. Rev., '''47''', 777-780 (1935)]</ref></li>
<li>Bell<ref><i>J.S. Bell, "On the Einstein Podolsky Rosen Paradox"</i> [[Media:Bell1964.pdf| Physics, '''1''', 195 (1964)]]</ref> </li>
<li>CHSH (Clauser, Horne, Shimony, & Holt)<ref>J.F. Clauser, M.A. Horne, A. Shimony, & R.A. Holt, <i>"Proposed Experiment to Test Local Hidden-Variable Theories"</i> [http://prl.aps.org/abstract/PRL/v23/i15/p880_1 Phys. Rev. Lett., '''23''', 880 (1969)]</ref></li>
</ul>
<p>Another useful resource, more directly relevant to our experiment and summarizing the information in the above papers is from Dehlinger and Mitchell <ref name="Dehlinger">D. Dehlinger & M.W. Mitchell. <i>"Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory."</i> [http://scitation.aip.org/content/aapt/journal/ajp/70/9/10.1119/1.1498860 Am. J. Phys. '''70''', 903 (2002)]</ref>.</p>
<p>It is imperative that you read and understand these papers ''before'' you attempt to perform this experiment.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Entanglement</li>
<li>Parametric down conversion</li>
<li>Nonlocality</li>
<li>Coincidence</li>
<li>Correlation</li>

</ul>
</td>
<td width=250>
<ul>
<li>Logic Analyzer</li>
<li>Avalanche Photodiode</li>
<li></li>
<li></li>
</ul>
</td>
</table>

<h2> Method </h2>
<p> All optical components have to be precisely aligned in order for your data to yield the expected results. Please take time to understand fully what is described below, and to diligently follow the directions.</p>
<b> Laser Safety goggles are provided, and are mandatory to be worn when the laser is on. THERE ARE NO EXCEPTIONS. If you are noticed not wearing the goggles, you will be forbidden from continuing.</b>
<p><b>Question: </b> What is the relative sensitivity of the human eye to 405nm? Does this make it more or less dangerous than green light?</p>

<table width=400 align=center>
<tr>
<td>
<p align=justify>[[File:BE-LaserRegion.png|400px|border|center]]
<b>Figure 1 -</b> Laser Region.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-MainRegionv2.png|600px|border|center]]
<b>Figure 1 -</b> Experiment setup.
<br clear=right>
</p>
</td>
</tr></table>

<h3>Step 1: Align the laser and BBO crystal</h3>
<ol>
<li>Remove the mounts containing the half-wave plate, quarter-wave plate and BBO crystal.</li>
<li>Put on your safety goggles, and turn on the 405nm laser by plugging in the power supply. Using the two mirrors, adjust the path of the beam to follow at a constant height and consistently directly above one line of holes in the optics table. </li>
<li>Insert the BBO crystal into position above the vertex of the rails. Adjust the mounting so the laser is passing through the crystal without clipping. Fine adjust the angle of the crystal so the retro-reflected beam off of the face of the crystal is directly back onto the incoming beam.</li>
<li>Shut off the laser.</li>
</ol>
<h3>Step 2: Align the 810nm-photon collection optics</h3>
<ol>
<li>For Detector Assembly A, remove the linear polarizer and unscrew the 810nm filter from the front of the photon collection optics.</li>
<table width=400 align=center>
<tr>
<td>
<p align=justify>[[File:BE-RemovePolarizer1.png|260px|border|center]]
<b>Figure 2a -</b> Remove Linear Polarizer.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-RemovePolarizer2.png|230px|border|center]]
<b>Figure 2b -</b> Remove Linear Polarizer.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-Remove810Filter1.png|245px|border|center]]
<b>Figure 2c -</b>Unscrew 810nm Filter.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-Remove810Filter2.png|250px|border|center]]
<b>Figure 2d -</b>Filter and Polarizer Removed.
<br clear=right>
</p>
</td>
</tr></table>
<li>Adjust (if necessary) the height of the detector assembly to be the same height as the 405nm laser beam.</li>
<li>Adjust the angle of rail containing the detector assembly to 3º.</li>
<li>Remove the optical fiber attached to the single photon detector corresponding to that detector assembly. Attach the Fiber Checker to this free end of the optical fiber. This will send a beam of red light backwards through the system.</li>
<li>Adjust the mount of the detector assembly so the red beam is aligned onto the back of the BBO crystal at the point where the 405nm passes through.</li>
<li>The reflection of the red beam off of the back of the BBO crystal should reflect back into the other detector system. If not, your detectors are not symmetric about the 405nm beam path, or the BBO crystal pair is not perpendicular to the incoming 405nm beam.</li>
<li>Replace the 810nm filter, linear polarizer, and fiber connection to the single photon detector.</li>
<li>Repeat above for Detector Assembly B.</li>
</ol>
<h3>Step 3: Power up the Electronics</h3>
<p>The single photon detectors are extremely sensitive pieces of equipment. Special care must be taken to minimize stray photons from entering and overloading the internal electronics.<b>The overhead room lights must be turned off before the power supply for the single photon detectors are turned on.</b> The acceptable ambient light sources are the desk lamp shining on the electronics rack, and a handheld red led keychain (particularly useful since your laser safety goggles transmit red light well.).</p>
<table width=400 align=center><td>
<p align=justify>[[File:BE-Electronicsv2.png|500px|border|center]]
<b>Figure 3 -</b> Electronics Rack.
<br clear=right>
</p>
</td></table>
<ol>
<li>Turn on the desk lamp so it shines onto the electronics rack.</li>
<li>Turn the room lights off.</li>
<li>Turn on the power to the electronics rack</li>
<li>Turn on the power supply for the single photon counting modules. The modules take 5.0V as input voltage, but are very sensitive to overvoltage. There, the power supply (under the workbench) which powers these devices passes through a dc voltage regulator. The give an output of 5.0V, set a voltage output on the power supply of 7.0 V- the regulator will take it down to 5.0V.</li>
<li>Connect the outputs of each of the single photon counting modules to an Integral Discriminator. This device will look for an input signal greater than a user-set threshhold value and output a 1-microsecond-long TTL pulse. The discriminator value should be set to the lowest setting.</li>
<li>Connect the outputs of the Discriminators each to a ratemeter. The [http://www.nuclearphysicslab.com/npl/wp-content/uploads/Ortec_441_Ratemeter.pdf user manual] for the Ortec 441 ratemeter contains information on how to understand the integration time setting. This needs to be understood to properly compute the uncertainties. Observe and record the number of counts on each detectors (will be around 10,000 per second).</li>
</ol>
<h3>Step 4: Insert and align the half-wave and quarter-wave plates</h3>
<ol>
<li>Insert the quarter-wave plate mount. Ensure the fast axis of the quarter-wave plate is vertical. The fine adjustment of the rotation will be done later.</li>
<li>Disconnect the output of the Discriminators from the Ratemeters and attach them to the inputs of the Coincidence unit. Have the output of the Coincidence unit go to one of the Ratemeters. Note how you can ''enable'' and ''disable'' the various inputs of the Coincidence unit. Does it give the expected output when only one channel is enabled?</li>
<li>Insert the half-wave plate rotational mount. Ensure the 405nm beam is not clipping. The correct rotational setting of the half-wave plate is when the coincidence rates are equal when having the detector assembly linear polarizers both at 0º and both at 90º. </li>
<li> Set both linear polarizers to 0º. Fine adjust the detectors assembly mounts to maximize this rate of the output from the Coincidence unit.</li>
<li>Set the linear polarizers to 45º. Rotate the post of the quarter-wave plate so that the coincidence rate is a maximum.</li>
</ol>
<h3>Step 5: Fine Adjust</h3>
<ol>
<li>Patiently cycle through adjusting the mounts of the detector assemblies, and the rail angle to maximize coincidence.</li>
</ol>
<h3>Step 6: Take Data!</h3>
<ol>
<li>Following the scheme described in Dehlinger and Mitchell <ref name="Dehlinger"/>, collect the data required to test a Bell's Inequality.</li>
<li>''Note:'' If your coincidence count rate for the first set of angles in Table I of <ref name="Dehlinger"/> is not at least 300 cps (though ideally 600+), then you have not set up the experiment properly.</li>
<li>''Note:'' You must subtract off the background coincidence counts from each of your readings. (see <ref name="Dehlinger"/>).</li>

</ol>

<h2> Core Experiment </h2>
<p>To setup the experiment as described in the Method section and to take one complete set of data required to test a Bell's Inequality as described in <ref name="Dehlinger"/> using the readings from the ratemeter. A full analysis of the data with proper treatment of uncertainties is required.</p>

<p><b>You are required to complete the core experiment along with your choice of one of the modules listed below. </b></p>

<h2> Module 1: Purity of Correlation</h2>
<p>In this module, you will try to improve on the purity of the correlation by reducing the acceptance angle of the single-photon detectors by placing adjustable collimating slits into each path before the single photon detectors. You have to determine(research) how purity of correlation can be measured in this experiment.</p>

<h2> Module 2: Computer Analysis </h2>
<p> In this module, you will use a Logic Analyzer to collect the raw outputs from the individual single photon detectors, then create an analysis program to calculate coincidence. Once this is accomplished, you can take data for longer periods of time, reduce the statistical uncertainty of the Bell's Inequality, and really put nail in the coffin of Hidden Variable Theories. Be sure to motivate your choice of coincidence window.</p>

<h2> Module 3: Pump Laser Power </h2>
<p>In this module, you will vary the power of the 405nm pump laser beam using neutral density filters in order to study the rate of coincident photon as a function of pump laser power. Does this trend follow expectations?</p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Bell's Inequalities

2026-02-03T21:58:22Z

Mgeorge:

<h1>Bell's Inequalities and Quantum Entanglement</h1>

<p> Deep at the root of the underlying principles of quantum mechanics lies shadowy principles based on probability which never sit well with some people. This experiment is meant to shine some (laser)light on these principles, and see if we can't come to some deeper understanding of the underlying framework of Quantum Dynamics.</p>
<p>No better introduction can be given than the following set of famous papers, commonly referred to today by their author lists.</p>
<ul>
<li>Einstein, Podolsky, Rosen<ref>A. Einstein, B. Podolsky & N. Rosen, <i>"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"</i> [http://prola.aps.org/abstract/PR/v47/i10/p777_1 Phys. Rev., '''47''', 777-780 (1935)]</ref></li>
<li>Bell<ref><i>J.S. Bell, "On the Einstein Podolsky Rosen Paradox"</i> [[Media:Bell1964.pdf| Physics, '''1''', 195 (1964)]]</ref> </li>
<li>CHSH (Clauser, Horne, Shimony, & Holt)<ref>J.F. Clauser, M.A. Horne, A. Shimony, & R.A. Holt, <i>"Proposed Experiment to Test Local Hidden-Variable Theories"</i> [http://prl.aps.org/abstract/PRL/v23/i15/p880_1 Phys. Rev. Lett., '''23''', 880 (1969)]</ref></li>
</ul>
<p>Another useful resource, more directly relevant to our experiment and summarizing the information in the above papers is from Dehlinger and Mitchell <ref name="Dehlinger">D. Dehlinger & M.W. Mitchell. <i>"Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory."</i> [http://scitation.aip.org/content/aapt/journal/ajp/70/9/10.1119/1.1498860 Am. J. Phys. '''70''', 903 (2002)]</ref>.</p>
<p>It is imperative that you read and understand these papers ''before'' you attempt to perform this experiment.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Entanglement</li>
<li>Parametric down conversion</li>
<li>Nonlocality</li>
<li>Coincidence</li>
<li>Correlation</li>

</ul>
</td>
<td width=250>
<ul>
<li>Logic Analyzer</li>
<li>Avalanche Photodiode</li>
<li></li>
<li></li>
</ul>
</td>
</table>

<h2> Method </h2>
<p> All optical components have to be precisely aligned in order for your data to yield the expected results. Please take time to understand fully what is described below, and to diligently follow the directions.</p>
<b> Laser Safety goggles are provided, and are mandatory to be worn when the laser is on. THERE ARE NO EXCEPTIONS. If you are noticed not wearing the goggles, you will be forbidden from continuing.</b>
<p><b>Question: </b> What is the relative sensitivity of the human eye to 405nm? Does this make it more or less dangerous than green light?</p>

<table width=400 align=center>
<tr>
<td>
<p align=justify>[[File:BE-LaserRegion.png|400px|border|center]]
<b>Figure 1 -</b> Laser Region.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-MainRegionv2.png|600px|border|center]]
<b>Figure 1 -</b> Experiment setup.
<br clear=right>
</p>
</td>
</tr></table>

<h3>Step 1: Align the laser and BBO crystal</h3>
<ol>
<li>Remove the mounts containing the half-wave plate, quarter-wave plate and BBO crystal.</li>
<li>Put on your safety goggles, and turn on the 405nm laser by plugging in the power supply. Using the two mirrors, adjust the path of the beam to follow at a constant height and consistently directly above one line of holes in the optics table. </li>
<li>Insert the BBO crystal into position above the vertex of the rails. Adjust the mounting so the laser is passing through the crystal without clipping. Fine adjust the angle of the crystal so the retro-reflected beam off of the face of the crystal is directly back onto the incoming beam.</li>
<li>Shut off the laser.</li>
</ol>
<h3>Step 2: Align the 810nm-photon collection optics</h3>
<ol>
<li>For Detector Assembly A, remove the linear polarizer and unscrew the 810nm filter from the front of the photon collection optics.</li>
<table width=400 align=center>
<tr>
<td>
<p align=justify>[[File:BE-RemovePolarizer1.png|260px|border|center]]
<b>Figure 2a -</b> Remove Linear Polarizer.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-RemovePolarizer2.png|230px|border|center]]
<b>Figure 2b -</b> Remove Linear Polarizer.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-Remove810Filter1.png|245px|border|center]]
<b>Figure 2c -</b>Unscrew 810nm Filter.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-Remove810Filter2.png|250px|border|center]]
<b>Figure 2d -</b>Filter and Polarizer Removed.
<br clear=right>
</p>
</td>
</tr></table>
<li>Adjust (if necessary) the height of the detector assembly to be the same height as the 405nm laser beam.</li>
<li>Adjust the angle of rail containing the detector assembly to 3º.</li>
<li>Remove the optical fiber attached to the single photon detector corresponding to that detector assembly. Attach the Fiber Checker to this free end of the optical fiber. This will send a beam of red light backwards through the system.</li>
<li>Adjust the mount of the detector assembly so the red beam is aligned onto the back of the BBO crystal at the point where the 405nm passes through.</li>
<li>The reflection of the red beam off of the back of the BBO crystal should reflect back into the other detector system. If not, your detectors are not symmetric about the 405nm beam path, or the BBO crystal pair is not perpendicular to the incoming 405nm beam.</li>
<li>Replace the 810nm filter, linear polarizer, and fiber connection to the single photon detector.</li>
<li>Repeat above for Detector Assembly B.</li>
</ol>
<h3>Step 3: Power up the Electronics</h3>
<p>The single photon detectors are extremely sensitive pieces of equipment. Special care must be taken to minimize stray photons from entering and overloading the internal electronics.<b>The overhead room lights must be turned off before the power supply for the single photon detectors are turned on.</b> The acceptable ambient light sources are the desk lamp shining on the electronics rack, and a handheld red led keychain (particularly useful since your laser safety goggles transmit red light well.).</p>
<table width=400 align=center><td>
<p align=justify>[[File:BE-Electronicsv2.png|500px|border|center]]
<b>Figure 3 -</b> Electronics Rack.
<br clear=right>
</p>
</td></table>
<ol>
<li>Turn on the desk lamp so it shines onto the electronics rack.</li>
<li>Turn the room lights off.</li>
<li>Turn on the power to the electronics rack</li>
<li>Turn on the power supply for the single photon counting modules. The voltage on this supply must be set greater than 5 volts. This is subsequently limited to precisely 5 volts by use of a voltage regulator downstream.</li>
<li>Connect the outputs of each of the single photon counting modules to an Integral Discriminator. This device will look for an input signal greater than a user-set threshhold value and output a 1-microsecond-long TTL pulse. The discriminator value should be set to the lowest setting.</li>
<li>Connect the outputs of the Discriminators each to a ratemeter. The [http://www.nuclearphysicslab.com/npl/wp-content/uploads/Ortec_441_Ratemeter.pdf user manual] for the ratemeter in the binder in the lab contains information on how to understand the integration time it used for various settings. This needs to be understood to properly compute the uncertainties. Observe and record the number of counts on each detectors (will be around 10,000 per second).</li>
</ol>
<h3>Step 4: Insert and align the half-wave and quarter-wave plates</h3>
<ol>
<li>Insert the quarter-wave plate mount. Ensure the fast axis of the quarter-wave plate is vertical. The fine adjustment of the rotation will be done later.</li>
<li>Disconnect the output of the Discriminators from the Ratemeters and attach them to the inputs of the Coincidence unit. Have the output of the Coincidence unit go to one of the Ratemeters. Note how you can ''enable'' and ''disable'' the various inputs of the Coincidence unit. Does it give the expected output when only one channel is enabled?</li>
<li>Insert the half-wave plate rotational mount. Ensure the 405nm beam is not clipping. The correct rotational setting of the half-wave plate is when the coincidence rates are equal when having the detector assembly linear polarizers both at 0º and both at 90º. </li>
<li> Set both linear polarizers to 0º. Fine adjust the detectors assembly mounts to maximize this rate of the output from the Coincidence unit.</li>
<li>Set the linear polarizers to 45º. Rotate the post of the quarter-wave plate so that the coincidence rate is a maximum.</li>
</ol>
<h3>Step 5: Fine Adjust</h3>
<ol>
<li>Patiently cycle through adjusting the mounts of the detector assemblies, and the rail angle to maximize coincidence.</li>
</ol>
<h3>Step 6: Take Data!</h3>
<ol>
<li>Following the scheme described in Dehlinger and Mitchell <ref name="Dehlinger"/>, collect the data required to test a Bell's Inequality.</li>
<li>''Note:'' If your coincidence count rate for the first set of angles in Table I of <ref name="Dehlinger"/> is not at least 300 cps (though ideally 600+), then you have not set up the experiment properly.</li>
<li>''Note:'' You must subtract off the background coincidence counts from each of your readings. (see <ref name="Dehlinger"/>).</li>

</ol>

<h2> Core Experiment </h2>
<p>To setup the experiment as described in the Method section and to take one complete set of data required to test a Bell's Inequality as described in <ref name="Dehlinger"/> using the readings from the ratemeter. A full analysis of the data with proper treatment of uncertainties is required.</p>

<p><b>You are required to complete the core experiment along with your choice of one of the modules listed below. </b></p>

<h2> Module 1: Purity of Correlation</h2>
<p>In this module, you will try to improve on the purity of the correlation by reducing the acceptance angle of the single-photon detectors by placing adjustable collimating slits into each path before the single photon detectors. You have to determine(research) how purity of correlation can be measured in this experiment.</p>

<h2> Module 2: Computer Analysis </h2>
<p> In this module, you will use a Logic Analyzer to collect the raw outputs from the individual single photon detectors, then create an analysis program to calculate coincidence. Once this is accomplished, you can take data for longer periods of time, reduce the statistical uncertainty of the Bell's Inequality, and really put nail in the coffin of Hidden Variable Theories. Be sure to motivate your choice of coincidence window.</p>

<h2> Module 3: Pump Laser Power </h2>
<p>In this module, you will vary the power of the 405nm pump laser beam using neutral density filters in order to study the rate of coincident photon as a function of pump laser power. Does this trend follow expectations?</p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-28T19:32:31Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[:File:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the ([https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D Electron spin resonance at DPPH (P6.2.6.2)]) Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-28T15:37:25Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[Media:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the ([https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D Electron spin resonance at DPPH (P6.2.6.2)]) Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-28T15:36:58Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[Media:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the ([https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D target="_blank" rel="noopener noreferrer" Electron spin resonance at DPPH (P6.2.6.2)]) Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-28T15:36:14Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[Media:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the (<a href="https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D" target="_blank" rel="noopener noreferrer"> Electron spin resonance at DPPH (P6.2.6.2)</a>) Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-28T15:35:08Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[Media:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the (<a href="https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D" " target="_blank" rel="noopener noreferrer"> Electron spin resonance at DPPH (P6.2.6.2)</a>) Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-27T21:46:41Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[Media:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the ([https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D Electron spin resonance at DPPH (P6.2.6.2)]) Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Electron Spin Resonance

2026-01-27T21:45:52Z

Mgeorge:

<h1>Electron Spin Resonance</h1>

<p>The objective of this experiment is to investigate the electron's internal angular momentum called spin. <b>A sample containing a substance with a 'free' electron in an s-state</b> is placed in a homogeneous magnetic field of strength B, which splits the energy levels for electrons with spin projections aligned with the field compared to the counter-aligned ones. A radio-frequency generator is used to resonantly pump electrons from the spin state with lower energy to the upper state. Tracing the resonance as a function of B provides the means for determining the gyro-magnetic ratio of the electron.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Free Electron</li>
<li>S-state</li>
<li>Spin ½</li>
<li>Fermions</li>
<li>Angular momentum</li>
<li>Lande-g factor</li>

</ul>
</td>
<td width=250>
<ul>
<li>Helmholtz Coils</li>
<li>Gyromagnetic Ratio</li>
<li>Anomalous Zeeman Effect</li>
<li>Normal Zeeman Effect</li>
<li>Magnetic Dipole</li>
<li>Axis of Quantization</li>
</ul>
</td>
</table>

<h1>Introduction</h1>
<p>In this experiment we obtain direct evidence for the unusual property of electrons, namely that while being point particles they exhibit the property of having two spin states. Most introductory texts on modern physics contain discussions of the historical developments leading to the discovery of this intrinsic angular momentum variable by Goudsmit and Uhlenbeck. Today we know that all elementary particles are spin - 1/2 objects called fermions, while the mediators of interactions are spin-1 objects called bosons (photons, gluons, W and Z gauge bosons for weak interactions). This experiment is also related to the study of electronic structure in magnetic and disordered systems; the 1977 Nobel Prize in physics went to P.W. Anderson, N.F. Mott, and J.H. Van Vleck for a number of achievements in this area. In chemistry ESR is applied as an important analysis technique to determine the properties of outer electrons responsible for covalent bonding in molecules. The twin concept to ESR is NMR - nuclear magnetic resonance - a technique known commonly as a non-intrusive medical diagnostic tool: it detects proton densities via their spin. It is also closely related to FMR – ferromagnetic resonance, and the Zeeman effect.</p>
<p>ESR is also known as EPR – electron paramagnetic resonance, since it deals only with paramagnetic materials. The atoms in a paramagnetic material have unpaired electrons, and therefore a net magnetic moment, but the internal interactions are not strong enough and do not create areas of similarly oriented magnetic moments, or ferromagnetism. The paramagnetic material is therefore a collection of randomly directed magnetic moments, all of which align the same direction due to the torque created by an external magnetic field. The paramagnetic material used in this experiment is an organic chemical called a free radical: diphnyl picryl hydrazyl ([http://en.wikipedia.org/wiki/DPPH DPPH]). The outer shell electron of this substance acts as though it was free, or almost so, resulting in a g-factor of 2.0023, which has a fractional difference of less than one part in a thousand from a perfectly free electron .</p>
<p>The idea in the spin resonance experiment is the following: if we place a macroscopic sample of material containing appropriate electrons in the vicinity of a radiating antenna, while an external magnetic field is present to make the energy splitting of the spin-up and spin-down states coincide with the energy of the radio wave quanta, we should be able to observe the fact that energy gets absorbed by the electrons in the sample. This observation is possible by detecting a change in a receiver placed in the vicinity, but also by observing the current that the radio generator passes through the coil (which acts as the antenna). In the microwave case one uses the former technique, while in the radiofrequency case (our experiment) the latter is preferred. The presence of the sample with resonating electrons (electrons in spin states of lower energy get transferred to the less favourable state, and decay later spontaneously) leads not only to a measurable change in the DC current through the coil, but also to a detuning of the frequency (the inductivity of the coil changes). For a discussion of both the radio wave and microwave methods read the descriptions of nuclear magnetic resonance and electron spin resonance in <ref>A.C. Melissinos , [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press, (2003). </ref>.</p>

<p>According to Quantum theory, an electron has ‘spin’, a property which behaves like angular motion, resulting in an angular momentum and consequently, as any ‘moving’ charge, a magnetic moment:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where ''µ<sub>B</sub>'' is the Bohr magneton and ''g'' is the Landé factor. But since quantum theory permits only two values for the spin ''S<sub>z</sub>''= ± hbar/2 , the magnetic moment results in only two possible projections:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>and the resulting energy levels are then:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn3.png|110px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Since the coupling of a magnetic moment with an external magnetic field B results in a torque aligning the magnetic moment with the field. The application of electromagnetic radiation to such a system, with a carefully set energy to match the splitting between the + and – values, results in the absorption of energy from the field, which is observable and therefore of interest to us:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn4.png|200px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>here ω is the frequency of the applied electromagnetic field (What is the expected energy scale?). Since this result is for only a single free electron, while we’re dealing with a macroscopic sample, a statistical correction has to be made. Using the Boltzmann distribution for the energy levels N<sub>+</sub> and N<sub>-</sub>:</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn5.png|170px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>where ''k'' is the Boltzmann constant and ''T'' is the temperature. It is important to note that a long natural lifetime of the upper state in a magnetic field is shortened at room temperature (''kT''=0.025eV), resulting in an equilibration of the spin level populations in a fraction of a second.</p>

<p>For most transition lines a fractional value of ''g'' was observed, a phenomenon highly important for the development of quantum theory. To unravel the complicated behavior of fractional ''g'' values in atomic spectroscopy, physicists had to figure out (before the advent of modern quantum mechanics) that the electron must have an internal angular momentum with an unusual value of ''g''=2 (all classical charge distributions have ''g''=1), and that this internal angular momentum when coupled to the orbital angular momentum (which has the classical value of ''g''=1) leads to fractional ''g'' values for most optical transitions. Thus quantum mechanics was subject to tough testing with the Schrödinger-Pauli theory incorporating spin in an ad-hoc way, and explaining atomic spectroscopy to a high degree of accuracy. Later Dirac showed how the marriage of quantum mechanics and special relativity leads to a prediction of ''g''=2 for fermions. Today the g value of the electron is one of the best-known quantities in physics (measured to 14 decimal places)<ref>D. Hanneke, S. Fogwell & G. Gabrielse, ''New Measurement of the Electron Magnetic Moment and the Fine Structure Constant'' [http://prl.aps.org/abstract/PRL/v100/i12/e120801 Phys. Rev. Lett. '''100''',120801 (2008)]</ref>. The correction of the value of ''g''=2 is fully explained by quantum field theory. </p>

<p>In the present experiment we investigate this internal angular momentum of the electron without the added complication of orbital angular momentum. The spin degree of freedom - in contrast to orbital angular momentum - has nothing to do with the orbiting motion of the electrons. The classical analogy of a spinning particle is also inappropriate, since there is not much meaning to a spinning point particle. As explained above, for the intrinsic spin angular momentum variable the interaction energy with a magnetic field requires a special choice for the gyro-magnetic ratio, namely ''g''=2. For magnetic fields that can be created in the laboratory (sub-Tesla range) the interaction energies given by eq. (4) correspond to radiofrequencies ranging up to microwaves as ''B'' is increased (verify this. i.e. calculate frequencies and wavelengths for a few examples). Thus, we need a mechanism to perform the excitation, and a way to measure the relationship between the transition frequency and the magnetic field strength. Electron spin resonance solves both problems in an elegant way, we measure the energy splitting between the two spin levels in the ground state of the spatial motion directly.</p>

<p>To make the experiment work one modulates the external magnetic field with a low-frequency AC signal component (60 cycles). For a fixed radiofrequency one is then able to sweep through a range of B values, such that at a particular phase (time) the resonance condition is met, and this condition will happen periodically. By observing the DC current through the transmitting coil in coincidence with the voltage used to generate the external magnetic field one can find out at what strength of the magnetic field the resonance condition is met. For this technique to work, one has to know that the relaxation times for the electrons are shorter than the time constant of the modulating field. If this is not the case, then less than half of the electrons in the sample would be available for excitation, and the signal might deteriorate too rapidly for detection to occur. </p>

<p> A note about the directions of fields and polarizations used in this experiment; The transition that we are driving in this experiment is a magnetic-dipole transition- meaning that it is the magnetic field component of the radio-frequency radiation which is driving the transition. Also, note that we are transitioning from an m<sub>s</sub>=-1/2 to m<sub>s</sub>=+1/2 state. This type of transition (Δm<sub>s</sub>=1) requires a circularly polarized driving field. The axis of quantization in this experiment is defined by the DC magnetic field created by the Helmholtz coils, so we need an RF magnetic field circularly polarized with respect to the DC magnetic field. The RF-coil used generates a linearly-polarized magnetic field along its axis. If the coil were aligned such that the RF-coil was along the axis of the DC-magnetic field from the Helmholtz coil, we would never drive the transition of interest. However, if the RF-coil was perpendicular to the DC magnetic field, then it can be shown that the a linearly-polarized field aligned perpendicularly to an axis of quantization is equivalent to a circularly-polarized field with respect to the axis of quantization. Therefore, in this experiment, the RF-coil is aligned perpendicular to the axis of the DC-magnetic field. (Be sure you understand this concept).</p>

<h1>Procedure</h1>

<p>To prepare for the experimental setup read through [[Media:514571e.pdf|ESR Control Unit]], [[Media:P6262_e.pdf|Electron spin resonance at DPPH]] and [[Media:P6263_e.pdf|Passive RF Oscillator]].

<h2>Part I: Verify the detection technique for the resonance condition. </h2>

<p>A radiofrequency generator is connected to a probe with an inductance (three exchangeable coils with different inductances) ''L'', and a variable capacitor ''C''. Changing the capacitance results in an adjustable frequency range for each coil allowing us to scan between approximately 20 and 100 MHz. A digital frequency meter is built into the control box that contains the radio-oscillator, as well as the power supply for the Helmholtz coils for the magnetic field. Note that the oscillator is split into two parts with the electronics residing in the control box, and the frequency-determining components ''L'' and ''C'' (and an amplitude control potentiometer) residing in the probe. </p>

<p>A receiver circuit made up of a coil and a variable capacitance is brought close to the radiating coil. It is connected to an AC voltmeter that indicates the strength of the received signal. For fixed transmitter frequency one varies the receiver's capacitor until the receiver circuit matches the transmitter (i.e. achieve resonance). Observe how the receiver shows a strong signal on resonance, how the DC current through the transmitting coil drops on resonance, and how the frequency of the transmitting circuit detunes. Compare this to the resonance problem of classical mechanics (damped driven harmonic oscillator). Detuning is related to the fact that the resonance condition has a slight dependence on the damping constant. Describe your observations in the write-up. This part demonstrates that a transmitter (oscillator) reacts to the conditions of the space surrounding it (mathematically speaking: you are changing the boundary conditions in the Maxwell equations, and creating a load that affects the transmitting coil). The damping effect is not much different from the one obtained by putting an iron core into a coil, thereby forcing the alternating B field to do work on the electron spins in the iron core which would introduce damping in the oscillator circuit.</p>

<h2>Part II: Calibrate the magnetic field produced by the Helmholtz coils for a known DC current. </h2>

<p>Note that you have to place the two coils accurately at a separation a that corresponds to their radius ''R''. Use the result from Biot-Savart's law for a single coil for the magnetic field strength for a given current along its axis as a function of the separation from the coil ''d'':</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Esr-eqn6.png|200px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>To obtain the field generated by two coils separated at distance ''a''=''R'' (many first-year physics texts have this problem, e.g., Fishbane, Gasiorowicz, Thornton 2nd ed. Q 65 on p. 835). <b> Here ''μ<sub>0</sub>'' is not the same ''μ'' as in eq. (1)</b>! Note that the current in Biot-Savart law is the current through each coil and not necessarily the total current in the circuit (You can use the Leybold manual to check whether your numbers are in the right range). Check the homogeneity of the field for a=R. How does your calibration compare to the Biot-Savart result? The number of turns is noted on the coils as n=320. Calibrate the Gaussmeter to zero for zero current. Does the Earth's magnetic field come into play in this experiment?</p>

<h2>Part III: Perform the electron spin resonance experiment. </h2>

<p><b>Read through the ([https://labdocs.leylab.de/doc/en/EXP/P/P6/P6262_e.pdf?hash=+FNytC8D Electron spin resonance at DPPH (P6.2.6.2)]) [[Media:P6262_e.pdf|<i>Electron spin resonance at DPPH (P6.2.6.2)</i>]] Physics Leaflet provided by Leybold. Connect the control box to the oscilloscope as outlined in the instructions provided by Leybold using the dual-channel set-up while triggering on the channel displaying the driving voltage for the Helmholtz coils.</b> Understand the function of the controls of the DC current through the Helmholtz coils and the AC modulation by observing the voltage applied to the coil displayed on trace 1 (used to trigger the scope). This voltage is not coincident in time with the strength of the magnetic field. To adjust for that, one can shift the phase with a third control. This will be a one-time adjustment once the resonance condition is met. A phase adjustment is necessary since AC current and voltage are out of phase by about 90 degrees for an inductance. The second trace displays a voltage that is proportional to the DC current passing through the transmitting coil. Without a sample the trace should be a straight line.</p>

<p>Set the oscillator to a given frequency, set the DC current to some value (e.g. total current = 1A), pick a midrange value for the modulating magnetic field. Place the DPPH sample inside the transmitting coil. Vary the magnetic field modulation until dips in the trace representing the DC current through the transmitting coil appear. Due to the modulation in the field two resonant points should occur as the magnetic field passes through a maximum in its sinusoidal shape. Use the phase delay control in the control box to adjust the signal such that the resonant points occur symmetrically with respect to the maximum. This adjustment should be performed only once. <b>It would not be necessary if we used a Gauss probe to measure the magnetic field in AC mode </b>(try this out).</p>

<p>Now reduce the magnetic field modulation to a small value (you will need to decrease the DC component to maintain resonance). You can adjust the DC current through the Helmholtz coils so that the resonance occurs at those points in time where the AC component vanishes. Record the DC current through the Helmholtz coils at this point, since the resonance now occurs at the magnetic field strength corresponding to the DC current alone. Observe the frequency change (detuning) as you remove and re-insert the sample, and record it.</p>

<p>Repeat this measurement for about 15 settings of frequency in 5 MHz intervals. This requires a change in coils. Notice the different amount of detuning for the different coils. Perform a linear least squares fit with estimate of uncertainties. Does the fit pass through zero energy splitting (frequency) at zero current? If not, why not? Determine your value of the gyromagnetic ratio for the 'free' electron in DPPH. </p>

<h1>References</h1>
<references/>

Main Page/BPHS 4090

2017-10-20T15:08:28Z

Mgeorge:

<table width=400 align=right><td>
[[File:Raman_logo2.png|350px|border|center]]

</td></table>

<h1>PHYS 4090 4.0 BioPhysics II</h1>
<br clear=right>
<h2>Course Director</h2>
<p>Dr. Christopher Bergevin</p>
<p>240 PSE</p>
<p>cberge@yorku.ca</p>
<p></p>
<p></p>

<h2>Laboratory Technologist</h2>
<table width=400>
<tr><td> </td> </tr>
<tr><td> </td> </tr>
<tr><td> </td> </tr>
</table>

<h2>Prerequisite</h2>
<ul>
<li>BPHS 2090 2.0</li>
<li>PHYS 2020 3.0</li>
<li>PHYS 2060 3.0</li>
</ul>

<h1>Laboratory Manual</h1>
<ul>
<li> [[Main Page/BPHS 4090/microscopy I|Transmitted Light Microscopy]] <b> </b> </li>
<li> [[Main Page/BPHS 4090/microscopy II|Contrast Modes in Microscopy]] <b> </b> </li>
<li> [[Main Page/BPHS 4090/Optical Tweezers of Onions|Optical Tweezers of Onion Cells]] <b></b> </li>
<li> [[Main Page/BPHS 4090/Choloplast Translocation|Light Induced Chloroplast Translocation]] <b> </b> </li>
<li> [[Main Page/BPHS 4090/Lysozyme Crystallization|Lysozyme Crystallization]]<b> </b> </li>
<li> [[Main Page/BPHS 4090/In-Vivo Spectrocopy|In-Vivo Spectroscopy]]<b></b></li>

<li> [[Main Page/BPHS 4090/ElectroPhysiology of Chara revised|The Electrical Properties of ''Chara'']]<b> </b> </li>
<li> [[Main Page/BPHS 4090/Mapping a binding site using NMR spectroscopy|Mapping a binding site using NMR spectroscopy]]<b> </b> </li>
<li> Otoacoustic Emissions<b> </b> </li>
<li> Student Project Presentations<b> </b> </li>
</ul>

Main Page/PHYS 3220/Radioactive Decays

2016-10-26T14:18:09Z

Mgeorge:

<h1>Radioactive Decays</h1>

<h1>Learning Outcomes</h1>
<ol>
<li>Three types of radioactivity
<li>Poisson statistics
<li>Radiation detection technology
</ol>

<h1>Introduction</h1>

<h2>Radioactive Decays</h2>
<p>Radioactive nuclear decays can be classified according to their decay mechanism: </p>

<ol style="list-style-type:lower-roman">
<li><p><b>α-decay:</b> heavy radionucleides often decay via the emission of a cluster composed of 2 protons and 2 neutrons, i.e., a <sub>2</sub>He<sup>4</sup> nucleus.</p></li>
<li><p><b>β-decay:</b> nuclei away from the line of stability N = Z, where N is the total number of neutrons, and Z the total number of protons, can lower their energy, and hence become more stable, by emitting either an electron or a positron. In the case of neutron-rich nuclei, a neutron converts into a proton, electron and antineutrino. The fast electron is emitted from the nucleus, corresponding to the β<sup>-</sup> decay of free neutrons (half-life 10.6 min.). For proton-rich nuclei, a proton is converted into a neutron, positron and a neutrino (β<sup>+</sup> decay). The fast positron emerges from the nucleus. This latter process may seem counterintuitive as it cannot occur for free protons (why?). The rest of the nuclear system supplies the energy necessary for the reaction to take place.</p></li>

<li><p><b>γ-decay:</b> the emission of photons with energies higher than X-rays (MeV-range) is the result of a nuclear transition from an excited to a lower state in complete analogy with photon emission from excited atoms (eV to keV-range). This decay almost always accompanies α- and β-decays, since these processes usually leave the daughter nucleus in an excited state.</p></li>

<li><p><b>spontaneous fission:</b>the emission of nuclear clusters bigger than α-particles is a rare process that has been studied recently in a systematic way at heavy ion facilities. It represents an alternative but rare decay mechanism, which provides insight into the nature of nuclear forces.</p></li>
</ol>

<p>All modern physics texts contain a chapter that describes nuclear phenomenology as well as a table of isotopes. Understand the basic principles (there will be no need to understand previous chapters of the book for this!). See, e.g., refs. 1-3. </p>

<h2>Detection of radiation</h2>

<p>The detection of nuclear radiation relies on the property that it ionizes the surrounding matter through which it passes. This statement is obvious for the charged α, and β particles. For γ particles the ionization arises through the photoeffect and Compton scattering (refs. 1-3). This ionization can be detected through the electric spark induced between condenser plates that are biased with a high voltage, resulting in a short burst of current. This is the principle of a Geiger-Müller (GM) tube. The efficiency of detection depends on the voltage applied to the gas-filled tube (why can’t one use a vacuum tube?). It is important to realize that the detector has a finite efficiency, i.e., it does not detect every single α, β, or γ particle entering the detector. In particular, the efficiency depends on the voltage applied with a threshold behaviour (around 900 V) followed by saturation. In small hand-held radiation counters the high voltage is produced by a DC-DC converter as used in electronic flashlights. Read the description of GM counters available in many texts (e.g., refs. 1,2,6), and include a concise description in your own words in your report.</p>
<p>Other detection mechanisms used for monitoring are: (i) exposure blackening of photographic film, e.g., in personal total dose monitors; (ii) scintillator counters; (iii) triggering of semiconductor devices; etc. </p>

<h2>Absorption of radiation</h2>
<p>Radiation is slowed down and eventually stopped as it passes through matter. This fact is exploited both in shielding and in applications of radiation for energy deposition (e.g., burning of cancer cells in radiation medicine). The absorption of the three different forms of radiation by matter is very different: α particles are heavy and doubly charged, therefore, they give up their energy readily in collisions with the nuclei of the surrounding matter; β particles are lighter and faster (as they emerge from the decay), and therefore pass more readily through matter until they are stopped; γ-rays have the best penetration characteristics, i.e., are the most difficult to shield. α particles, which have typical energies of 5 MeV, are stopped by a few centimeters of air, since they are doubly charged and slow compared to β particles. They are detected by GM counters only if they enter through a specially designed opening (transparent to them provided they are fast enough). </p>

<p>The stopping power and energy deposition is also a function that depends strongly on the kinetic energy of the ionizing particles. In radiation medicine this is exploited, e.g., by having fast particles penetrate healthy tissue with limited damage but sufficient slow-down such that energy deposition becomes efficient when the tissue to be destroyed is reached. Usually physicists with nuclear medicine training are in charge of designing a radiation plan for each patient depending on the location of the tissue to be destroyed, vicinity of vital organs, etc. This is a non-trivial process, since secondary radiation (e.g., production of electrons) contributes to the energy deposition and may diffuse the flux of radiation.</p>

<h2>Lifetimes of radioactive sources</h2>
<p>A proper understanding of nuclear decays on the basis of a nuclear shell model (in analogy to atomic structure of electronic energy levels) enables one to predict the energies of the emitted particles as well as the half-lifes. The lifetime is related to the broadening in energy of the decaying state and can be understood from Heisenberg's uncertainty principle. (As a function of time the number of decaying particles is described by an exponential decay law.) </p>

<p>The radioactive sources that we use in this experiment do not permit a measurement of the decay law, since they have long lifetimes (tens to thousands of years), i.e., it is impossible to observe the decrease in radioactivity over a reasonable time span. However, sources with a short lifetime can be produced by exposure of a sample to a high-flux source, e.g., a reactor, which results in the conversion of stable nuclei into unstable ones.</p>

<h2>Statistics of nuclear counting</h2>
<p>In the early studies of radioactivity it was not understood whether radioactivity was a purely random process, or whether the emission of one particle might effect the emission of others. One can prove that the observation of the number of independent decays per time interval (count rate) as a function of time should result in a Poissonian distribution (ref. 5). In the limit of high count rates the Poissonian distribution can be approximated by a Gaussian distribution. </p>

<p>Rutherford performed experiments that showed that the probability, ''P(n)'', of observing ''n'' counts in a fixed time interval followed the Poisson formula</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Rd-eqn1.png|150px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where the ''average'' number of counts per interval is calculated as </p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn2.png|280px|center]]
</p>
</td></table>

<p>For all the measurements in this experiment that are performed with computerized data acquisition and data analysis, the Poissonian character of the statistical distribution of decay events are to be investigated and verified. Since the computer program "Particle Tracking.vi" performs the statistical analysis automatically, it is crucial that you think through the steps involved in obtaining the histogram (ch. 11 in ref. 5).</p>

<p>To illustrate how one explicitly analyzes the data we include an example for your convenience.</p>

<ol>
<li>Let us say that you record the number of counts heard during 100 five-second intervals by entering a mark in the column appropriate for that number of counts (col. 2 in the table below).
<table width=420 align=center>
<tr><td width=120><b>Number of Counts in interval (n)</b></td><td width=120><b>Number of times Count occurs</b></td><td width=100><b>''P(n)''</b></td><td width=100><b>Total Counts</b></td></tr>
<tr><td>0</td> <td>I(1)</td> <td>0.01</td> <td>0x1=0</td></tr>
<tr><td>1</td> <td>III(3)</td> <td>0.03</td> <td>1x3=3</td></tr>
<tr><td>2</td> <td>IIII I(5)</td> <td>0.05</td> <td>2x5=10</td></tr>
<tr><td>etc..</td><td></td><td></td><td></td></tr>
</table>
</li>

<li><p>Now construct a bar graph for the results, showing ''P(n)'' vs ''n'', where ''P(n)'' is the probability for finding n counts:</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn3.png|260px|center]]
</p>
</td></table>
<p>Then, using the Poisson distribution (Eq. 1) evaluate ''P(n)'' and graph the theoretical distribution over the same range of values. To do this, you require the value of n-bar; this should be the mean number of counts in your measurement:</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn4.png|110px|center]]
</p>
</td></table>
<p>Thus, your theoretical distribution and your experimental results will have the same mean.</p>
</li>
<li><p>Now calculate the standard deviation of your data:</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn5.png|180px|center]]
</p>
</td></table>
</li>

<li><p>Compare this with the expected standard deviation from the theoretical probability distribution, which is (for a Poisson distribution):</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn6.png|140px|center]]
</p>
</td></table>
<p>Note that this simple relation between the '''mean''' and the standard deviation is not a property of all distributions.</p>
</li>

<li><p>To see if the numbers of counts obey Poisson statistics in a quantitative way, we use the Chi-squared (χ<sup>2</sup>) test (ch. 12 in ref. 5; an example is given on pg. 235). From the reduced χ<sup>2</sup> value one infers the agreement.</p>
</li>

</ol>

<h1>Experimental Procedure</h1>

<p>In this experiment a Geiger-Müller counter with a computer interface is used to detect the radiation coming from the natural background, as well as from some weak sources. The statistics of the decays is investigated to confirm the independence of the decay mechanism. The dependence of the count rate on the distance from the source is also investigated. Also, the Geiger-Müller method for detection of radioactivity will be investigated.</p>

<p>Familiarize yourself with the computer-interfaced GM counter and associated computer software.</p>

<h2>Required Components</h2>
<ol>
<li>[[Media:Radioactive-ACratemeter.JPG|AC Powered Table-Top GM Counter]]</li>
<li>[[Media:RDHandHeldGM.JPG|Hand-held GM Counter]]</li>
<li>[[Media:RDBeigeFiesta.JPG|Beige 'Fiesta' Ceramic Dish]]</li>
<li>[[Media:RDOrangeFiesta.JPG|Orange 'Fiesta' Ceramic Dish]]</li>
<li>[[Media:RDMantles.JPG|α,γ Source: <sub>90</sub>Th<sup>232</sup>, Lantern Mantles]]</li>
</ol>

<h2>Hardware instructions:</h2>
<p>The hand-held GM counter can be operated independent of the computer interface. You should use it in range I (up to 2000? counts per minute - cpm), and turn on the audio monitoring. The background rate should be in the range of up to a few counts per second. For sources we use a bag containing Coleman-type naphta lantern mantles and Fiesta plates. Original Coleman mantles used radioactive elements until 1990; the clones still use a <sub>90</sub>Th<sup>232</sup> α emitter to enhance fluorescence. Radioactive elements were also used in glazing for bathroom tiles and Fiesta plates (no longer on the market). Make sure that the sources are some distance away from the GM counter when measuring the background radiation.</p>

<h2>Computer Instruction</h2>

<p>Data will be collected using a program called "Particle Tracking.vi" located on the desktop.
This program uses the microphone input of the computer to monitor the counts from the "Radiation Alert- Monitor 4" detector. The operation of the program is is described below</p>

<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-vi.png|800px|center]]
</p>
</td></table>

<p>''Note that the program displays a histogram of the results for you to see, but only the raw data of the counts is written to the output file.''</p>

<h2>Required Data</h2>
<ol>
<li>Test the statistics of nuclear background radiation. Note the direction in which the GM counter is pointing. Make sure that it is aiming at free space, and not at a potential radioactive source. Take at least two runs, one of which should be with a larger amount of data to observe an improvement in the fit to a Poissonian distribution. Comment on the χ<sup>2</sup> obtained, and quote the decay rate, with its standard error. Include histograms of the distributions. Repeat the longer run with the GM counter pointing in an orthogonal direction. Are the data consistent with the previous run? Should they be? What are some sources of background radiation? Save the data points for one of the long runs to a data file. Perform the Poisson statistics analysis explicitly as described in the example in the previous section.</li>

<li>Perform measurements similar to (1) while bringing the bag with lantern mantles (<sub>90</sub>Th<sup>232</sup> α,γ source) close to the opening of the GM counter. Comment on the obtained distribution. Use a detailed table of isotopes (with decay schemes) to identify the radionuclide of the thorium family (ref. 6). </li>

<li>Place the orange 'Fiesta' ceramic dish plate on the table. Mount the GM counter centered above the plate using a retort stand. Measure average count rates as a function of distance, e.g., 0.5 cm, 5 cm, 10 cm, 15 cm, 20 cm, 25 cm. Has the count rate at 25 cm reached the background count rate within errors? Plot the count rates after subtraction of the background rate as a function of distance. What functional behaviour do you find? Can you explain why the Geiger counter is responding when exposed to the Fiesta plate? Show relevant decay chain diagrams.</li>

<li>Turn on the AC powered table-top GM counter. Set the knob to HV and dial up an operating voltage not exceeding 1200 Volts. Set the knob to display count rate X1 (in counts per minute) and note the background radiation. Place the beige Fiesta dish close to the exposed GM tube (the aluminium shield can be rotated such that an opening appears). You may need to reduce the sensitivity of the meter by setting the knob to the X10 range. Then measure the count rate as a function of the operating voltage.</li>
</ol>

<p>Incorporate in your report an outline on the three nuclear decay mechanisms. The function of the GM counter should also be explained briefly in the report.</p>

<h1>References</h1>

<ol>
<li>Knoll, G.F., ''Radiation Detection and Measurement'', 2nd ed.</li>
<li>Tsoulfanidis, N., ''Measurement and Detection of Radiation''.</li>
<li>Rohlf, J.W., ''Modern Physics from α to Z<sup>0</sup>'', Wiley 1994</li>
<li>Brehm J.J., Mullin, W.J. ''Modern Physics'', Wiley 1989</li>
<li>Taylor, J.R., ''An Introduction to Error Analysis'', University Science Books, 1997.</li>
<li>Cork, J.M., ''Radioactivity and Nuclear Physics'', D. van Nostrand 195</li>
</ol>

Main Page/PHYS 4210/He-Ne Lasers

2016-01-06T14:23:36Z

Mgeorge:

<h1>He-Ne Lasers</h1>

<p>In this experiment we first align an open-ended laser. Then we set up some transverse mode patterns, and perform further exercises and experiments to understand how a laser works.</p>

<h2> Key Concepts</h2>
<table width=500>
<td width=250><ul>
<li>Stimulated Emission</li>
<li>Spontaneous Emission</li>
<li>Stimulated Emission</li>
<li>Incoherent/Coherent Radiation</li>
<li>Einstein Coefficients</li>
<li>Population Inversion</li>
<li>Forbidden Transitions</li>
<li>Metastable States</li>
<li>LS coupling</li>
<li>Electric dipole selection rules</li>
</ul>
</td>
<td width=250>
<ul>
<li>Axial Modes</li>
<li>TEM modes</li>
<li>Spectral Width</li>
<li>Atomic Lineshape</li>
<li>Loss/Gain Coefficient</li>
<li>Index of Refraction</li>
<li>Brewster’s Angle</li>
<li>Malus’s Law</li>
<li>Fresnel-Arago Law</li>
<li>Q-Switch</li>
</ul>
</td>
</table>

<h1>Reading and Exercises</h1>
<ul>
<li>Read pages 94 to 105 from Preston-Dietz, [https://www.library.yorku.ca/find/Record/1038893 The Art of Experimental Physics], John Wiley and Sons,1991. Carry out '''Exercise 1''' (pg. 100), '''Exercise 2''' (pg. 103), '''Exercise 3''' (pg. 104), and '''Exercise 4''' (pg. 104) and submit them as part of your report, either in the introduction or as an appendix as you deem appropriate.</li>
<li>Read pages 100 to 112, on laser cavity modes.</li>
<li>Do '''Exercise 1''' (pp 111-112). Do not forget to answer the last question of the exercise: Calculate the frequency difference between two adjacent axial modes TEM<sub>oom</sub> & TEM<sub>oo(m+1)</sub>.</li>
</ul>

<h1>Experiments</h1>
<h2>Aligning the laser</h2>
<p>Align the laser until it begins lasing. The TA will discuss techniques to accomplish this.</p>
<p>When you are successful with the aligning process, and lasing is achieved, try varying the distances between the mirrors (using the adjusting screws on the laser mount) that still supports lasing. Record, in your lab book, the aligning process used, maximum, minimum and 'best' distances between the mirrors.</p>
<p>What the radius of curvature of the mirrors which form the optical cavity? </p>
<p>Use the polarizers to determine the polarization of laser.</p>
<p>Assume that the He-Ne produces 3 mW of laser output power and that the electrical data given applies to your gas discharge tube. Compute the efficiency, in percent, for converting electrical energy to red laser light energy with this He-Ne laser. Discuss your results.</p>

<h2>Brewster's Angle</h2>
<p>Using the glass plate provided, find an approximate value for the Brewster's angle. You can determine this by rotating the glass plate until lasing stops. Only at the Brewster's angle does lasing resume.</p>
<p>Knowing that the tangent of the Brewster's angle is the ratio of the refractive indices of the lasing medium to air, determine the refractive index of the glass medium.</p>
<p>Every resonant laser cavity has a characteristic quality factor or Q that measures the internal losses. The higher the Q, the lower the losses.</p>
<p>A Q-switch pulse can be made by blocking one end of the mirror, then exciting the medium and then quickly unblocking the mirror. Stimulated emission will quickly drain the stored laser energy from the cavity in a short pulse with peak power much higher than the laser can produce. One can think of a Q-switch as a device that quickly switches from absorbing to transmitting, suddenly reducing cavity losses.</p>
<p>The Q-switch pulse length is given by</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn1a.png|180px|center]]
</p>
</td></table>
<p>where t is the round trip time (back and forth in the cavity), and R is the output mirror reflectivity ( >98% ).</p>
<p>Therefore</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn2.png|210px|center]]
</p>
</td></table>
<p>where ''L'' is the distance between the mirrors, ''n<sub>1</sub>'' is the refractive index of the medium, and ''c'' is the speed of light. Pulse length can then be written as</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn3.png|180px|center]]
</p>
</td></table>
<p>Using the data from your laser, what is the theoretical value for the pulse length?</p>

<h2>TEM Modes</h2>
<p>Set up a camera with the screen at about 1 to 2 meters from the output mirror. Adjust the output coupler screws (or any other adjustments) to produce the TEM<sub>00m</sub>, TEM<sub>10m</sub>, TEM<sub>01m</sub>, .... modes. Photograph or sketch a few of them.</p>

<h2>Beam Profile of the TEM<sub>oom</sub> and the TEM<sub>10m</sub> modes</h2>
<p>Realign the beam to produce the TEM<sub>oom</sub> mode.</p>
<p>You will use a rotating mirror and a photodiode monitored on an oscilloscope to observe the profile of the laser beam.</p>
<p>Be sure to ensure the photodiode is not saturating when the laser is aligned onto it. If it is, switch the scale of the photodiode amplifier to a lower gain setting.</p>
<p>Repeat your observations for the TEM<sub>o1m</sub> mode. Remember that photodetectors are square-law detectors, i.e., the current density J is proportional to the square of the electric field. (See Preston for details). Sketch the beam profiles for both modes.</p>

<h2>Beam Profile or Shape</h2>
<p>A laser beam has a certain profile with most energy concentrated at the center. The beam has the following form</p>

<table width=400 align=center><td>
<p align=justify>[[File:HeNe-fig1v2.jpg|400px|border|center]]
<b>Figure 1 -</b> Amplitude distribution across laser beam oscillating in the TEM<sub>oo</sub> mode.
<br clear=right>
</p>
</td></table>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn4.png|120px|center]]
</p>
</td></table>

<p>where ''w'' is the radius of the beam. The Gaussian function, exp [- (''r''/''w'')<sup>2</sup> ] falls to 1/e, when ''r'' = ''w'', i.e.,</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn5.png|90px|center]]
</p>
</td></table>
<p>Since the energy is proportional to the square of the amplitude, the beam radius, or SPOT SIZE, ''w'', is defined as that distance from the axis where the power has dropped to 1/e<sup>2</sup> of its value at the center. Twice that distance, 2''w'', is the beam diameter.</p>
<p>The beam radius, ''w'', is the function of distance along the axis. If we call ''x'' the axial distance measured from the midpoint between the two (concave) mirrors, then the parameter ''w'' is given by</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn6.png|160px|center]]
</p>
</td></table>
<p>where λ is the wavelength and ''w<sub>0</sub>'' is the minimum beam radius between mirrors.</p>
<table width=400 align=center><td>
<p align=justify>[[File:HeNe-fig2v2.jpg|400px|border|center]]
<br clear=right>
</p>
</td></table>

<p>Note that from ''w<sub>x</sub>'' above; at ''x'' = 0, ''w<sub>x</sub>'' = ''w<sub>o</sub>''.</p>
<p>From Preston (equation 21, p. 102),</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn7.png|160px|center]]
</p>
</td></table>
<p>Calculate ''w<sub>o</sub>'' and ''w<sub>x</sub>''.</p>
<p>From your observations of the beam profile for the TEM<sub>oom</sub>, determine ''w<sub>x</sub>'', the beam radius. How does your calculated value compare with the experimental value? Explain any differences.</p>

<h2>Malus's Law</h2>
<p>Malus’ law states that when a linearly polarized light beam of intensity ''I<sub>0</sub>'' passes through a linear polarizer with its axis rotated by angle ''A'' from the light beam polarization, the emergent intensity ''I'' is given by</p>
<table width=200 align=center>
<td>
<p align=justify>[[File:HeNe-eqn8.png|90px|center]]
</p>
</td></table>
<p>Use the rotatable polarizer and photodiode detector to verify this law quantitatively. Make detector readings at several values of angle ''A'' and record them in a neat table in your notebook. Graph your data to demonstrate the expected cos<sup>2</sup>''A''dependence.</p>

<h2>Verification of the Fresnel-Arago Law</h2>
<p>Fresnel-Arago law state that two coherent light rays which are polarized right angles to each other will not mutually interfere. </p>
<p>Use the laser to set up the Michelson interferometer as shown below to form an interference pattern. </p>
<p>Insert polarizers P<sub>1</sub> and P<sub>2</sub> such that their axes of polarization is in the same direction. You may have to make slight adjustments to retain the interference pattern. Now, rotate ONE of the polarizers through 90º. Verify that the law is true. Try to take pictures of the resulting effect and include them with your report.</p>

Main Page/PHYS 4210 & 4211

2016-01-04T22:34:43Z

Mgeorge:

<h1>PHYS 4210/11 3.0 Advanced Experimental Physics I/II </h1>

<p>Selected advanced experiments in physics related to
topics in solid state physics, atomic spectroscopy,
microwaves, low-noise measurements,
superconductivity, and nuclear and particle physics.</p>

<p> See the course [http://moodle.yorku.ca Moodle Site] for all adminstrative details. </p>

<h1>Laboratory Manual</h1>

<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<p> Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<p> '''Please submit a request to sign-up at least 24 hours before the time you wish to perform the lab.''' You will receive an email confirmation from the responsible TA confirming the time and date. Please show up prepared for the demo, and on time!</p>

<ul>
<li> [[Main Page/PHYS 4210/How to Choose Experiments|How to Choose Experiments]] </li>
<li> [[Main Page/PHYS 4210/How to Write Reports|How to Write Reports]] </li>
<li> [[Main Page/PHYS 3220/Lab Safety|Lab Safety]] </li>
</ul>

<h2> List of Experiments </h2>
<table width=500>
<tr><td width=250>'''Experiment'''</td><td width=100>'''Location'''</td><td width=150> </td></tr>
<tr><td>'' [[Main Page/PHYS 4210/Rutherford II|Rutherford Scattering II]]''</td><td>'' 111 PSE ''</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Coaxial Cable|Coaxial Cable]]</td><td> 126 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Waveguides|Waveguides]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Optical Fibers|Optical Fibers]] </td><td> 126 PSE</td><td></td></tr>
<tr><td> [[Main Page/PHYS 4210/He-Ne Lasers|He-Ne Lasers]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>''[[Main Page/PHYS 4210/Fourier Optics|Fourier Optics]]'' </td><td>'' 126 PSE''</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Zeeman Effect|Zeeman Effect]] </td><td> 123PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Mass Spectrometer|Mass Spectrometer]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Gamma Ray Spectroscopy|Gamma Ray Spectroscopy]] </td><td> 111 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Johnson Noise|Johnson Noise]] </td><td> 126 PSE</td><td></td></tr>
<tr><td><del>[[Main Page/PHYS 4210/Semiconductors II|Semiconductors II]]</del> </td><td> 111 PSE</td><td>
</td></tr>
<tr><td>[[Main Page/PHYS 4210/Electron Spin Resonance|Electron Spin Resonance]] </td><td> 126 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Sonoluminescence|Sonoluminescence]]</td><td> 126 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Muon Lifetime|Muon Lifetime]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Bell's Inequalities|Bell's Inequalities ]]</td><td>111 PSE</td><td></td></tr>
</table>

<p> </p>

Main Page/PHYS 4210 & 4211

2016-01-04T22:34:25Z

Mgeorge:

<h1>PHYS 4210/11 3.0 Advanced Experimental Physics I/II </h1>

<p>Selected advanced experiments in physics related to
topics in solid state physics, atomic spectroscopy,
microwaves, low-noise measurements,
superconductivity, and nuclear and particle physics.</p>

<p> See the course [http://moodle.yorku.ca Moodle Site] for all adminstrative details. </p>

-->

<h1>Laboratory Manual</h1>

<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<p> Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<p> '''Please submit a request to sign-up at least 24 hours before the time you wish to perform the lab.''' You will receive an email confirmation from the responsible TA confirming the time and date. Please show up prepared for the demo, and on time!</p>

<ul>
<li> [[Main Page/PHYS 4210/How to Choose Experiments|How to Choose Experiments]] </li>
<li> [[Main Page/PHYS 4210/How to Write Reports|How to Write Reports]] </li>
<li> [[Main Page/PHYS 3220/Lab Safety|Lab Safety]] </li>
</ul>

<h2> List of Experiments </h2>
<table width=500>
<tr><td width=250>'''Experiment'''</td><td width=100>'''Location'''</td><td width=150> </td></tr>
<tr><td>'' [[Main Page/PHYS 4210/Rutherford II|Rutherford Scattering II]]''</td><td>'' 111 PSE ''</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Coaxial Cable|Coaxial Cable]]</td><td> 126 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Waveguides|Waveguides]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Optical Fibers|Optical Fibers]] </td><td> 126 PSE</td><td></td></tr>
<tr><td> [[Main Page/PHYS 4210/He-Ne Lasers|He-Ne Lasers]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>''[[Main Page/PHYS 4210/Fourier Optics|Fourier Optics]]'' </td><td>'' 126 PSE''</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Zeeman Effect|Zeeman Effect]] </td><td> 123PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Mass Spectrometer|Mass Spectrometer]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Gamma Ray Spectroscopy|Gamma Ray Spectroscopy]] </td><td> 111 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Johnson Noise|Johnson Noise]] </td><td> 126 PSE</td><td></td></tr>
<tr><td><del>[[Main Page/PHYS 4210/Semiconductors II|Semiconductors II]]</del> </td><td> 111 PSE</td><td>
</td></tr>
<tr><td>[[Main Page/PHYS 4210/Electron Spin Resonance|Electron Spin Resonance]] </td><td> 126 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Sonoluminescence|Sonoluminescence]]</td><td> 126 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Muon Lifetime|Muon Lifetime]]</td><td> 123 PSE</td><td></td></tr>
<tr><td>[[Main Page/PHYS 4210/Bell's Inequalities|Bell's Inequalities ]]</td><td>111 PSE</td><td></td></tr>
</table>

<p> </p>

Main Page/PHYS 3220/Radioactive Decays

2015-10-19T19:50:52Z

Mgeorge:

<h1>Radioactive Decays</h1>

<h1>Learning Outcomes</h1>
<ol>
<li>Three types of radioactivity
<li>Poisson statistics
<li>Radiation detection technology
</ol>

<h1>Introduction</h1>

<h2>Radioactive Decays</h2>
<p>Radioactive nuclear decays can be classified according to their decay mechanism: </p>

<ol style="list-style-type:lower-roman">
<li><p><b>α-decay:</b> heavy radionucleides often decay via the emission of a cluster composed of 2 protons and 2 neutrons, i.e., a <sub>2</sub>He<sup>4</sup> nucleus.</p></li>
<li><p><b>β-decay:</b> nuclei away from the line of stability N = Z, where N is the total number of neutrons, and Z the total number of protons, can lower their energy, and hence become more stable, by emitting either an electron or a positron. In the case of neutron-rich nuclei, a neutron converts into a proton, electron and antineutrino. The fast electron is emitted from the nucleus, corresponding to the β<sup>-</sup> decay of free neutrons (half-life 10.6 min.). For proton-rich nuclei, a proton is converted into a neutron, positron and a neutrino (β<sup>+</sup> decay). The fast positron emerges from the nucleus. This latter process may seem counterintuitive as it cannot occur for free protons (why?). The rest of the nuclear system supplies the energy necessary for the reaction to take place.</p></li>

<li><p><b>γ-decay:</b> the emission of photons with energies higher than X-rays (MeV-range) is the result of a nuclear transition from an excited to a lower state in complete analogy with photon emission from excited atoms (eV to keV-range). This decay almost always accompanies α- and β-decays, since these processes usually leave the daughter nucleus in an excited state.</p></li>

<li><p><b>spontaneous fission:</b>the emission of nuclear clusters bigger than α-particles is a rare process that has been studied recently in a systematic way at heavy ion facilities. It represents an alternative but rare decay mechanism, which provides insight into the nature of nuclear forces.</p></li>
</ol>

<p>All modern physics texts contain a chapter that describes nuclear phenomenology as well as a table of isotopes. Understand the basic principles (there will be no need to understand previous chapters of the book for this!). See, e.g., refs. 1-3. </p>

<h2>Detection of radiation</h2>

<p>The detection of nuclear radiation relies on the property that it ionizes the surrounding matter through which it passes. This statement is obvious for the charged α, and β particles. For γ particles the ionization arises through the photoeffect and Compton scattering (refs. 1-3). This ionization can be detected through the electric spark induced between condenser plates that are biased with a high voltage, resulting in a short burst of current. This is the principle of a Geiger-Müller (GM) tube. The efficiency of detection depends on the voltage applied to the gas-filled tube (why can’t one use a vacuum tube?). It is important to realize that the detector has a finite efficiency, i.e., it does not detect every single α, β, or γ particle entering the detector. In particular, the efficiency depends on the voltage applied with a threshold behaviour (around 900 V) followed by saturation. In small hand-held radiation counters the high voltage is produced by a DC-DC converter as used in electronic flashlights. Read the description of GM counters available in many texts (e.g., refs. 1,2,6), and include a concise description in your own words in your report.</p>
<p>Other detection mechanisms used for monitoring are: (i) exposure blackening of photographic film, e.g., in personal total dose monitors; (ii) scintillator counters; (iii) triggering of semiconductor devices; etc. </p>

<h2>Absorption of radiation</h2>
<p>Radiation is slowed down and eventually stopped as it passes through matter. This fact is exploited both in shielding and in applications of radiation for energy deposition (e.g., burning of cancer cells in radiation medicine). The absorption of the three different forms of radiation by matter is very different: α particles are heavy and doubly charged, therefore, they give up their energy readily in collisions with the nuclei of the surrounding matter; β particles are lighter and faster (as they emerge from the decay), and therefore pass more readily through matter until they are stopped; γ-rays have the best penetration characteristics, i.e., are the most difficult to shield. α particles, which have typical energies of 5 MeV, are stopped by a few centimeters of air, since they are doubly charged and slow compared to β particles. They are detected by GM counters only if they enter through a specially designed opening (transparent to them provided they are fast enough). </p>

<p>The stopping power and energy deposition is also a function that depends strongly on the kinetic energy of the ionizing particles. In radiation medicine this is exploited, e.g., by having fast particles penetrate healthy tissue with limited damage but sufficient slow-down such that energy deposition becomes efficient when the tissue to be destroyed is reached. Usually physicists with nuclear medicine training are in charge of designing a radiation plan for each patient depending on the location of the tissue to be destroyed, vicinity of vital organs, etc. This is a non-trivial process, since secondary radiation (e.g., production of electrons) contributes to the energy deposition and may diffuse the flux of radiation.</p>

<h2>Lifetimes of radioactive sources</h2>
<p>A proper understanding of nuclear decays on the basis of a nuclear shell model (in analogy to atomic structure of electronic energy levels) enables one to predict the energies of the emitted particles as well as the half-lifes. The lifetime is related to the broadening in energy of the decaying state and can be understood from Heisenberg's uncertainty principle. (As a function of time the number of decaying particles is described by an exponential decay law.) </p>

<p>The radioactive sources that we use in this experiment do not permit a measurement of the decay law, since they have long lifetimes (tens to thousands of years), i.e., it is impossible to observe the decrease in radioactivity over a reasonable time span. However, sources with a short lifetime can be produced by exposure of a sample to a high-flux source, e.g., a reactor, which results in the conversion of stable nuclei into unstable ones.</p>

<h2>Statistics of nuclear counting</h2>
<p>In the early studies of radioactivity it was not understood whether radioactivity was a purely random process, or whether the emission of one particle might effect the emission of others. One can prove that the observation of the number of independent decays per time interval (count rate) as a function of time should result in a Poissonian distribution (ref. 5). In the limit of high count rates the Poissonian distribution can be approximated by a Gaussian distribution. </p>

<p>Rutherford performed experiments that showed that the probability, ''P(n)'', of observing ''n'' counts in a fixed time interval followed the Poisson formula</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Rd-eqn1.png|150px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where the ''average'' number of counts per interval is calculated as </p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn2.png|280px|center]]
</p>
</td></table>

<p>For all the measurements in this experiment that are performed with computerized data acquisition and data analysis, the Poissonian character of the statistical distribution of decay events are to be investigated and verified. Since the computer program "Particle Tracking.vi" performs the statistical analysis automatically, it is crucial that you think through the steps involved in obtaining the histogram (ch. 11 in ref. 5).</p>

<p>To illustrate how one explicitly analyzes the data we include an example for your convenience.</p>

<ol>
<li>Let us say that you record the number of counts heard during 100 five-second intervals by entering a mark in the column appropriate for that number of counts (col. 2 in the table below).
<table width=420 align=center>
<tr><td width=120><b>Number of Counts in interval (n)</b></td><td width=120><b>Number of times Count occurs</b></td><td width=100><b>''P(n)''</b></td><td width=100><b>Total Counts</b></td></tr>
<tr><td>0</td> <td>I(1)</td> <td>0.01</td> <td>0x1=0</td></tr>
<tr><td>1</td> <td>III(3)</td> <td>0.03</td> <td>1x3=3</td></tr>
<tr><td>2</td> <td>IIII I(5)</td> <td>0.05</td> <td>2x5=10</td></tr>
<tr><td>etc..</td><td></td><td></td><td></td></tr>
</table>
</li>

<li><p>Now construct a bar graph for the results, showing ''P(n)'' vs ''n'', where ''P(n)'' is the probability for finding n counts:</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn3.png|260px|center]]
</p>
</td></table>
<p>Then, using the Poisson distribution (Eq. 1) evaluate ''P(n)'' and graph the theoretical distribution over the same range of values. To do this, you require the value of n-bar; this should be the mean number of counts in your measurement:</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn4.png|110px|center]]
</p>
</td></table>
<p>Thus, your theoretical distribution and your experimental results will have the same mean.</p>
</li>
<li><p>Now calculate the standard deviation of your data:</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn5.png|180px|center]]
</p>
</td></table>
</li>

<li><p>Compare this with the expected standard deviation from the theoretical probability distribution, which is (for a Poisson distribution):</p>
<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-eqn6.png|140px|center]]
</p>
</td></table>
<p>Note that this simple relation between the '''mean''' and the standard deviation is not a property of all distributions.</p>
</li>

<li><p>To see if the numbers of counts obey Poisson statistics in a quantitative way, we use the Chi-squared (χ<sup>2</sup>) test (ch. 12 in ref. 5; an example is given on pg. 235). From the reduced χ<sup>2</sup> value one infers the agreement.</p>
</li>

</ol>

<h1>Experimental Procedure</h1>

<p>In this experiment a Geiger-Müller counter with a computer interface is used to detect the radiation coming from the natural background, as well as from some weak sources. The statistics of the decays is investigated to confirm the independence of the decay mechanism. The dependence of the count rate on the distance from the source is also investigated. Also, the Geiger-Müller method for detection of radioactivity will be investigated.</p>

<p>Familiarize yourself with the computer-interfaced GM counter and associated computer software.</p>

<h2>Required Components</h2>
<ol>
<li>[[Media:Radioactive-ACratemeter.JPG|AC Powered Table-Top GM Counter]]</li>
<li>[[Media:RDHandHeldGM.JPG|Hand-held GM Counter]]</li>
<li>[[Media:RDBeigeFiesta.JPG|Beige 'Fiesta' Ceramic Dish]]</li>
<li>[[Media:RDOrangeFiesta.JPG|Orange 'Fiesta' Ceramic Dish]]</li>
<li>[[Media:RDMantles.JPG|α,γ Source: <sub>90</sub>Th<sup>232</sup>, Lantern Mantles]]</li>
</ol>

<h2>Hardware instructions:</h2>
<p>The hand-held GM counter can be operated independent of the computer interface. You should use it in range I (up to 2000? counts per minute - cpm), and turn on the audio monitoring. The background rate should be in the range of up to a few counts per second. For sources we use a bag containing Coleman-type naphta lantern mantles and Fiesta plates. Original Coleman mantles used radioactive elements until 1990; the clones still use a <sub>90</sub>Th<sup>232</sup> α emitter to enhance fluorescence. Radioactive elements were also used in glazing for bathroom tiles and Fiesta plates (no longer on the market). Make sure that the sources are some distance away from the GM counter when measuring the background radiation.</p>

<h2>Computer Instruction</h2>

<p>Data will be collected using a program called "Particle Tracking.vi" located on the desktop.
This program uses the microphone input of the computer to monitor the counts from the "Radiation Alert- Monitor 4" detector. The operation of the program is is described below</p>

<table width=400 align=center>
<td>
<p align=justify>[[File:Rd-vi.png|800px|center]]
</p>
</td></table>

<p>''Note that the program displays a histogram of the results for you to see, but only the raw data of the counts is written to the output file.''</p>

<h2>Required Data</h2>
<ol>
<li>Test the statistics of nuclear background radiation. Note the direction in which the GM counter is pointing. Make sure that it is aiming at free space, and not at a potential radioactive source. Take at least two runs, one of which should be with a larger amount of data to observe an improvement in the fit to a Poissonian distribution. Comment on the χ<sup>2</sup> obtained, and quote the decay rate, with its standard error. Include histograms of the distributions. Repeat the longer run with the GM counter pointing in an orthogonal direction. Are the data consistent with the previous run? Should they be? What are some sources of background radiation? Save the data points for one of the long runs to a data file. Perform the Poisson statistics analysis explicitly as described in the example in the previous section. How do these results compare to the results from the computer program?</li>

<li>Perform measurements similar to (1) while bringing the bag with lantern mantles (<sub>90</sub>Th<sup>232</sup> α,γ source) close to the opening of the GM counter. Comment on the obtained distribution. Use a detailed table of isotopes (with decay schemes) to identify the radionuclide of the thorium family (ref. 6). </li>

<li>Place the orange 'Fiesta' ceramic dish plate on the table. Mount the GM counter centered above the plate using a retort stand. Measure average count rates as a function of distance, e.g., 0.5 cm, 5 cm, 10 cm, 15 cm, 20 cm, 25 cm. Has the count rate at 25 cm reached the background count rate within errors? Plot the count rates after subtraction of the background rate as a function of distance. What functional behaviour do you find? Can you explain why the Geiger counter is responding when exposed to the Fiesta plate? Show relevant decay chain diagrams.</li>

<li>Turn on the AC powered table-top GM counter. Set the knob to HV and dial up an operating voltage not exceeding 1200 Volts. Set the knob to display count rate X1 (in counts per minute) and note the background radiation. Place the beige Fiesta dish close to the exposed GM tube (the aluminium shield can be rotated such that an opening appears). You may need to reduce the sensitivity of the meter by setting the knob to the X10 range. Then measure the count rate as a function of the operating voltage.</li>
</ol>

<p>Incorporate in your report an outline on the three nuclear decay mechanisms. The function of the GM counter should also be explained briefly in the report.</p>

<h1>References</h1>

<ol>
<li>Knoll, G.F., ''Radiation Detection and Measurement'', 2nd ed.</li>
<li>Tsoulfanidis, N., ''Measurement and Detection of Radiation''.</li>
<li>Rohlf, J.W., ''Modern Physics from α to Z<sup>0</sup>'', Wiley 1994</li>
<li>Brehm J.J., Mullin, W.J. ''Modern Physics'', Wiley 1989</li>
<li>Taylor, J.R., ''An Introduction to Error Analysis'', University Science Books, 1997.</li>
<li>Cork, J.M., ''Radioactivity and Nuclear Physics'', D. van Nostrand 195</li>
</ol>

Main Page/BPHS 4090/In-Vivo Spectrocopy

2015-10-01T17:58:30Z

Mgeorge:

<h1> Required Components </h1>

<ol>
<li>[[Media:Spec_Spectrometer.JPG|USB Ocean Optics spectrometer]]</li>
<li>[[Media:Spec_Collection_Fiber.JPG|Collection fiber for spectrometer]]</li>
<li>PC with spectrometer software and MS Excel (or equivalent spreadsheet) for data processing</li>
<li>[[Media:Spec_White_Reference.JPG|White reflectance reference target]]</li>
<li>[[Media:Spec_Light_Source.JPG|White LED illumination source]]</li>
<li>[[Media:Spec_Pressure_Cuff.JPG|Blood pressure compression cuff]]</li>
<li>Excel calculation spreadsheets</li>
<li>Stopwatch timer (can use windows clock for this)</li>
<li>A usb stick or some way to take your data with you for analysis</li>
</ol>

<h1>Objective</h1>
<p>To measure the in-vivo oxygenation state of haemoglobin, and calculate the change in oxygenation before, during, and after reactive hyperaemia by analyzing the colour content of light diffusely reflected off of the skin.</p>

<h1>Introduction</h1>
<p>Optical methods of skin analysis are ideal because they can be performed non-invasively, and in real-time. It is quite intriguing that so much information can be discovered from something as simple as launching some photons at an object and analyzing what comes back. In this lab, you will be exploring the use of light as a non-invasive measurement tool to determine the in-vivo oxygenation status of haemoglobin in your blood. These measurements will be made in a non-invasive sense, so as much as you may enjoy slicing up your lab partner to get at their blood, it ain’t gonna happen here! You will, on the other hand, have the opportunity to cut off the blood flow to one of your lab partner(s) limbs, though sadly, this will only be temporary. In this lab you will get familiar with the concept of light propagation in turbid (scattering) media, as well as gain experience with optical spectroscopy methods. High resolution spectral information can be analyzed to allow semi-quantitative and fully quantitative analysis of biological materials, and is a very powerful technique, useful for a variety of biophysical applications.</p>
<table width=280 align=left ><td>
<p align=justify>[[File:Absorption_spectrum_of_melanin.JPG|240px|border|center]]
<b>Figure 1</b> - Absorption spectrum typical for melanin.
<br clear=right>
</p>
</td></table>
<p>Determination of physiologically relevant parameters in a quick, reliable and repeatable fashion is of paramount importance in healthcare and biological research. The optical properties of human skin have been the subject of numerous investigations over the years, and two of the most relevant parameters to measure are the haemoglobin (Hb) oxygenation state and melanin content. Hb and melanin are the two major cutaneous chromophores within human skin, which means that their concentrations are essentially responsible for the colour of your skin. Upon exposure to ultraviolet (UV) light, melatinocytes increase their production of melanin within the skin, we know this process by its more common name, a suntan. The absorption spectrum of melanin is shown in figure 1, and is almost linear over the visible spectrum. It is best measured in the spectral rang above 600 nm, as it is the main source of light absorption in the skin at this wavelength and beyond.</p>

<p> The main target we are after in this lab is the oxygenation state of Hb. Hb is the iron-containing protein attached to red blood cells, and aside from giving blood its red colour, it is responsible for transporting oxygen from the lungs to the rest of the body. The mechanism of oxygen binding in Hb is due to a single iron atom, contained within the protein structure of Hb, and just below a porphyrin ring. A 2D representation of the ring and iron is shown in Figure 2. This structure serves to trap an oxygen molecule and hold it for transport around the body. A typical Hb molecule consists of four of these binding sites surrounded by a protein matrix, and the overall structure of the Hb molecule changes when carrying oxygen. This structural change results in a change in the absorption spectrum of haemoglobin in the 400-600 nm spectral range (Figure 3). </p>
<br style="clear: both" />
<table width=280 align=left><td>
<p align=justify>[[File:Haeme_ring.jpg|240px|border|center]]
<b>Figure 2</b> - Schematic representation of the haeme porphyrin ring in Hb.
<br clear=right>
</p>
</td></table>
<table width=280 align=left><td>
<p align=justify>[[File:Absorption_spectrum_of_Hb.jpg|240px|border|center]]
<b>Figure 3</b> - Absorption spectra of oxygenated Hb (double peak) and de-oxygenated Hb (single peak).
<br clear=right>
</p>
</td></table>

<p>There is a significant shift of the absorption peak in the 400-450 nm spectral range. However, we will focus on measuring the changes between 500-600 nm since the measurements are easier to perform and more reliable in this range. The absorption spectrum of oxygenated Hb exhibits two peaks in the 500-600 nm spectral range, while the spectrum of de-oxygenated Hb exhibits only a single peak. It is the change between these two states that you will quantify, and to do this we will focus on measuring diffusely reflected light from your palm and the inside of your forearm. These diffuse reflectance measurements will allow us to calculate the absorption spectra of Hb, correct for the effects of melanin from different skin types, and monitor the oxygen saturation state of Hb as we simulate a state of reactive hyperaemia, which is a brief increase in blood flow following a period of ischemia, or arterial occlusion.</p>
<br style="clear: both" />
<table width=160 align=left ><td>
<p align=justify>[[File:Specular_reflection.jpg|140px|border|center]]
<b>Figure 4</b> - Specular reflection from a surface.
<br clear=right>
</p>
<p align=justify>[[File:Diffuse_reflection.jpg|140px|border|center]]
<b>Figure 5</b> - Diffuse reflection from a multi-layer structure.
<br clear=right>
</p>
</td></table>

<p>To understand how we can make measurements of absorption by analysing diffusely reflected light, we should first define what is meant by the term reflection. In general light reflection can be defined in two ways; specular reflection, and diffuse reflection. Specular reflection refers to light that has been directly reflected from an interface, and is directional. A highly polished metal surface, such as a mirror, is an example of a specular reflector. This type of reflector will follow the law of reflection first described by Descartes, namely that the angle of incidence equals the angle of reflection (Figure 4). Another property of a specular reflector is that it will retain image information, which is why you can see your reflection in a mirror.</p>
<p>In diffuse reflection, the light can be thought of as penetrating a small distance into the reflector and scattering multiple times before exiting (Figure 5). This type of reflectance is non-directional, and does not produce any image since all image information in the wavefront is lost due to multiple scatterings. An example of a diffuse reflector would be a piece of white marble. No matter how much you polish the marble, most of the light striking its surface is diffusely reflected, which is why marble makes for a very poor mirror. A perfect diffuse reflector will reflect light uniformly into the 2π steradian space above it, while a perfect specular reflector will reflect light at an angle defined by the angle of incidence. In general most objects will reflect light both specularly and diffusely.</p>
<br style="clear: both" />

<p>Human skin can also be thought of an object which is diffusely reflective, like the marble, only that it also contains absorbers, namely Hb and melanin. Skin is a heterogeneous, multi-layered structure consisting of three basic layers, each containing numerous sub-layers. The basic layers of skin are the epidermis, which is the outermost layer and provides protection, the dermis, which serves as the location for hair follicles, sweat glands, etc, and the hypodermis, which consists of connective tissue to secure the skin to bones and muscle, as well as blood vessels to deliver oxygen and nutrients to the skin (Figures 6 & 7). Note that it is not important for you to memorize the various layers that make up the skin, but it is important to note where the chromophores we will be measuring reside and originate from. </p>
<br style="clear: both" />
<table width=360 align=left><td>
<p align=justify>[[File:Human_skin.jpg|320px|border|center]]
<b>Figure 6</b> - Cross section of human skin showing the major layers and components.
<br clear=right>
</p>
</td></table>
<table width=360 align=left><td>
<p align=justify>[[File:Skin_cross_section.jpg|320px|border|center]]
<b>Figure 7</b> - 3D representation of the skins layers and components.
<br clear=right>
</p>
</td></table>
<br style="clear: both" />

<p>Most of the diffuse reflection you will measure originates from the epidermal layer, which contains no blood vessels or capillaries. The blood diffuses through the dermal layer and into the epidermis, essentially meaning that there is a homogeneous distribution of Hb in the epidermal layer. For the purposes of this lab, you can consider the epidermal layer to be a perfect diffuse reflector, with a uniform distribution of melanin and Hb ‘absorbers’ present in a given volume. Since the diffusely reflected light is interacting with melanin and Hb as it is scattered within the epidermal layer, there is information within this light regarding the absorption properties of Hb and melanin.</p>

<h1>Part A: In-Vivo Spectroscopy</h1>
<h2>Methods </h2>

<p>To measure the diffuse reflectance spectra, we will make use of a ‘white’ LED which will be used as an illumination source. The diffuse reflectance will be collected with a fiber optic cable coupled to a computer controlled spectrometer. To simulate reactive hyperaemia, a compression cuff from a blood pressure monitor will be used to temporarily restrict blood flow to the hand. The Hb oxygen concentration will slowly drop following vascular occlusion, and immediately following re-perfusion, you will measure a significant jump in Hb oxygenation, then a steady return to normal physiological levels.</p>
<p>Before getting to the measurements, you should first familiarize yourself with the concept of a spectrometer and how the software interface should be utilized to obtain spectra with a good signal-to-noise ratio. A general schematic for the spectrometer used in this lab is shown in Figure 8.
<table width=360 align=left><td>
<p align=justify>[[File:Spectrometer.jpg|320px|border|center]]
<b>Figure 8</b> - Schematic of the light path in the Ocean Optics spectrometer used for this lab.
<br clear=right>
</p>
</td></table>
A spectrometer essentially consists of some light collection optics coupled to an optical fiber (not shown), the light collected by the fiber is passed through a lens and slit assembly mounted inside the spectrometer (2 & 3) before striking a collimating mirror (4). This mirror produces a collimated beam of light, which is then reflected off of a diffraction grating (5) and is focused by a second mirror (6) and onto a linear CCD array (7). A CCD (Charge-Coupled Device) is a light-sensitive detector which produces a voltage proportional to the light striking the active area, or pixels. The diffraction grating will reflect light of different colour at slightly different angles, and thus red light is focused towards the side of the CCD indicated by (8) and blue light is focused towards (9). Reading out the voltage levels on the pixels across the CCD therefore allows us to measure the spectrum of light collected by the fiber. When light is spread across the CCD in this fashion, the wavelength range striking each pixel on the CCD is very small, typically less than 0.25 nm per pixel, which allows for the visualization of very fine spectral features.</p>
<p>Software operation of the spectrometer will be quite basic for our purposes, the software is pre-installed on the PC you will be using for data collection, and can be found under the windows start menu at: Start → Ocean Optics → Spectra Suite. After initialization, the software will be running and ready to collect data. Ensure that you have connected the fiber optic cable between the spectrometer and light delivery/collection housing. The main parameters we will have to change are the exposure, averaging and boxcar settings. Typically it is good to use 4x averaging and 2-4x boxcar averaging. The exposure setting will vary based on the individual, but should be in the range of 200-1000 ms. The ideal gain setting will have the most intense pixel values at ~60,000 levels of grey (see Figure 9).</p>
<table width=560 align=center><td>
<p align=justify>[[File:Software_interface.jpg|520px|border|center]]
<b>Figure 9</b> - Spectra Suite software interface.
<br clear=right>
</p>
</td></table>
<p> Before we are ready to collect data we must first acquire several calibration data sets using the spectrometer to account for the natural spectral shape of the light source and optical system being used (this is the spectrum shown in Figure 10). This will be accomplished by measuring the diffuse reflectance of a ‘white’ reference target, which should have been supplied to you at the start of the lab. This target will allow you to measure the natural spectrum of the LED being used, and this data will later be used to normalize the diffuse reflectance skin spectra and remove any artefacts from the light source and fiber collection system.</p>
<table width=380 align=left><td>
<p align=justify>[[File:Save_spectrum.jpg|320px|border|center]]
<b>Figure 10</b> - Save Spectrum setup.
<br clear=right>
</p>
</td></table>
<p>collection system.
Once you have the proper gain setting for the reference spectrum, open up the save spectrum window (File → Save → Save Spectrum, or hold down “ctrl + alt + s”). The dialogue box shown in Figure *** should appear, and you should fill in the following settings:
</p>
<ol>
<li>Under “Save Options” select to “Save every scan”</li>
<li>Check the “Stop after this many scans” box, and enter “1” in the box beside it.</li>
<li>Under “File Type” select “Tab Delimited”</li>
<li>Select your “Save To Directory”</li>
<li>Enter “Reference” for the “Base Filename”</li>
<li>Ensure “Padding Digits” is set to “5”</li>
<li>Hit “Accept”</li>
</ol>
<br style="clear: both" />
<p>You should now have a single text file in your save to directory with the reference spectrum data. Now, remove the white reference target and place it back in its container. We are ready to begin spectral measurements. For this you will need the blood pressure compression cuff. Pressure to the cuff is increased by pumping on the bladder, and a silver release valve in front of the bladder allows the pressure to be released. To start the measurements follow the steps below:</p>
<ol>
<li>Open the “Manage Spectrum Exports” dialogue by either going to File → Save → Pause/Resume Export or pressing “ctrl + s”.</li>
<li>Highlight any processes and select “Terminate All”</li>
<li>Close the “Pause/Resume Export” dialogue</li>
<li>Open the “Save Spectrum” window</li>
<li>Under “Save Options” set it to save after every 2 scans</li>
<li>Check the option to “Pause until started by user”</li>
<li>Check the “Stop after this many scans” box, and enter “50” in the box beside it.</li>
<li>Under “File Type” select “Tab Delimited”</li>
<li>Select your “Save To Directory”</li>
<li>Enter “Back of Hand” for the “Base Filename”</li>
<li>Ensure “Padding Digits” is set to “5”</li>

<p>The dialogue box should look like this:</p>
<br style="clear: both" />
<table width=380 align=left><td>
<p align=justify>[[File:Acquisition_parameters.png|320px|border|center]]
<b>Figure 11</b> - Acquisition parameters for time-series measurements.
<br clear=right>
</p>
</td></table>
<br style="clear: both" />
<li>Hit “Accept”</li>
<li>Place the compression cuff just above your elbow, covering you bicep. Ensure that the pressure is fully released by opening the release valve for a few seconds then close it shut.</li>
<li>Place the reflectance scan head on the inside of your forearm (you should hold it in place while your lab partner operates the spectrometer software)</li>
<li>Optimize the exposure time so that the signal is maximized and no data channels are saturated</li>
<li>Ensure that you are using 4x averaging and 4x boxcar</li>
<li>Open the spectrum export dialogue by pressing “ctrl + s”</li>

<table width=380 align=left><td>
<p align=justify>[[File:Manage_spectrum.jpg|320px|border|center]]
<b>Figure 12</b> - Manage spectrum exports dialogue.
<br clear=right>
</p>
</td></table>
<br style="clear: both" />

<li>Highlight the process you just set up, which should show its status as “paused”. When you are ready to being, press “Resume All”. Data will now be collecting, and you should begin timing.</li>
<li>After 20-30 seconds, begin inflating the pressure cuff to capacity. This will restrict blood flow. The pressure should be maintained to at least 200 mmHg on the pressure dial.</li>
<li>After maintaining at least 200 mmHg for 90 seconds of constriction, release the pressure valve to allow blood to re-circulate.</li>
<li>Continue monitoring the directory you are writing spectral files into. When you reach file 49 you are done.</li>
<li>Press “Terminate All” to remove the completed data capture. If you forget to do this, you will not be able to set up another time series for the next set of measurements. If you find that this occurs, re-open the “Manage Spectrum Exports” dialogue will allow you to terminate the process and use the spectrometer again.</li>
</ol>
<p>After completing the above steps, repeat them while taking measurements of your lab partner’s inside forearm. After those measurements are completed, record spectra from the inside of your palm, then your partner’s palm. In total, you should have 4 complete data sets, but it may be a good idea to take 2 measurements from each site (8 in total between you and your partner). This way if you find some error during data processing, you have another set to analyze and won’t have to go back to the lab and run the experiment again.</p>
<p>Before leaving the lab please ensure that you have copied all of your data to a usb stick, or emailed it to yourself. You will also need to take with you a copy of the excel macro spreadsheet (.xlm file), which will be used to import all the spectra and calculate everything you need to quantify the change between oxy- and deoxy-haemoglobin. Finally, please ensure that the light source and spectrometer are properly shut down and stored away before you leave the lab.</p>

<h2>Data Analysis</h2>

<h2> Using the Excel Analysis Spreadsheet</h2>
<p> There is an MS Excel worksheet on the Desktop of the computer called "In-Vivo Spectroscopy Analysis (copy first).xlsm. This was made in Office 2007, but any version of Office should open the file and run the macros. You should set your macro security settings in Excel to run all macros. Copy this file and perform your data analysis using the copy.</p>
<ol style="list-style-type:lower-latin">
<li> Copy the Excel Spreadsheet and paste the copy in the directory you created for yourself to save you spectral data collected during the experiment</li>
<li> Open this Excel spreadsheet, you will notice there are six sheets of calculations, and 2 charts, but since you haven't imported the data yet, they are blank or show errors.</li>
<li> From the "View" tab at the top the window, select the "Macros" icon at the top right. </li>
<li> From the list which pops up, select the "ImportSpectralData" macros and click "Edit". </li>
<li> You will need to make the following three changes:
<ol>
<li> Change the entry for Data_Str1 to match the location where you collected your data (ie "Back of Hand000" or "Inside of Forearm000"</li>
<li> Change the entry for Spreadsheet to match the name you gave your copied version.</li>
<li> Change the "DirPath" entry to match the directory where your data is stored.</li>
</ol>
<li> Save the macro by clicking the "Save" icon, and return to Excel sheet by clicking the "Excel" icon</li>
<li> While looking at the Main Sheet, select the macro "ImportSpectralData" as before, and click "Run".</li>
<li> Data will be imported. It will take a couple of minutes for this process to complete. </li>
</ol>

<h2> Calculation Theory </h2>
<p> There are a number of steps that we must perform to normalize the data and convert the reflectance measurements into absorption measurements. These calculations are automatically set up and run in the excel macro for you, but you should understand the steps used and why they are used for answering questions during your experiment write-up. Below we will briefly run through the calculation theory. There are three main calculation steps taken to get the final data once it has been imported into excel. </p>

<ol>
<li>First the recorded spectra are normalized by the reference spectrum from the white reflectance target. This allows us to remove the spectral shape contribution of the light source, which can bias results if not accounted for.</li>
<li>Next these spectra must be converted from reflectance spectra into absorption spectra. This is accomplished via the equation shown below, which essentially states that the absorption spectrum of an object is logarithmically related to the inverse of the reflectance spectrum.</li>

<table width=200 align=center><td>
<p align=justify>[[File:iv_eqn1.png|200px|center]]
<br clear=right>
</p>
</td></table>

<li>The absorbance spectra are corrected for the effects of melanin by calculating the slope of the absorption spectrum in the region from 650 – 700 nm. This can be done because the absorption spectrum of melanin is essentially linear across the visible spectrum, and the absorption of haemoglobin is essentially flat in this spectral region, therefore any slope in this region is primarily due melanin concentration within the tissue. For each spectrum is calculated in this region, and the result of the linear fit is subtracted from the spectral data. This step effectively removes the melanin absorption spectrum from the data set.</li>
<li>Changes between oxy- and deoxy- states of haemoglobin are related to the single and double-peak spectra of these states. The change between these states can be quantified in a few ways. Here we will employ a very simple method which is based on calculating the slope over two regions in the spectra. This will give us a metric which will be used to quantify the change between oxy- and deoxy- haemoglobin (see figure below).</li>
</ol>
<table width=560 align=center><td>
<p align=justify>[[File:iv_fig13.png|520px|border|center]]
<b>Figure 13</b> - Sample spectra of oxygenated and deoxygenated haemoglobin. Dashed lines indicate the slopes being calculated for quantification.
<br clear=right>
</p>
</td></table>
<p>The slope is calculated between 540-565 nm and 565-575 nm, and the difference between these two values gives a measure of the haemoglobin oxygen saturation. As can be seen in the figure above, when the blood is well oxygenated, the slope of the line segments are opposite, and at quite a large angle. In contrast, the slope of the two lines plotted on the de-oxy curve are almost the same value, and of the same sign. Therefore we would expect the value of H(t) to increase as the amount of oxygen is raised in the blood. The actual equation used is shown below, and as you can see it is quite simple mathematically, but it is important that you understand why it is valid to use such a simplified quantification model.</p>
<table width=200 align=center><td>
<p align=justify>[[File:iv_eqn2.png|250px|center]]
<br clear=right>
</p>
</td></table>

<p>This calculation is performed on each of the spectra you recorded, and the final step now is to generate a normalized haemoglobin oxygen concentration time series from this data. This is done by normalizing the ‘H(t)’ values in the above equation via:</p>

<table width=200 align=center><td>
<p align=justify>[[File:iv_eqn3.png|250px|center]]
<br clear=right>
</p>
</td></table>

<p>Plotting out H(t)norm as a function of time should then give a plot similar to the one shown below. From this plot you should be able to clearly see the steady decrease in oxygenation as the compression cuff was activated, and a dramatic spike in oxygenation following removal of the pressure and re-perfusion of the tissue with oxygenated blood.</p>

<table width=460 align=center><td>
<p align=justify>[[File:Haemoglobin_concentration.jpg‎|420px|border|center]]
<b>Figure 14</b> - - Haemoglobin concentration as a function of time during and after a period of vascular occlusion.
<br clear=right>
</p>
</td></table>

<h2>Questions/Write up</h2>

<p> The following questions should be answered in your notes.</p>

<ol>
<li>What is the main function of haemoglobin in the blood? Briefly describe the physical processes involved in haemoglobin’s biological functioning as well as what happens to the molecule in its various states of oxygenation.</li>
<li>How does the presence of melanin affect the data that you have collected and analyzed?</li>
<li>Briefly describe the difference between specular and diffuse reflection.</li>
<li>Why have we chosen to analyze absorption spectra by reflecting light off of a surface? What are the advantages of performing measurements such as these versus standard transmission spectroscopy?</li>
<li>Describe why the oxygen concentration increased so dramatically following the period of vascular occlusion. Is there anything you can say about how blood flows and oxygen is used up in the body on the basis of this data?</li>
<li>Was there any difference in your results between the palm of your hand and the inside of your forearm? Please give an explanation for this difference, if you detected any.</li>
</ol>

<p>The write-up for this lab does not have any specific formatting requirements. In general, you
should briefly describe the experiment and the experimental setup to give some background
information on what this lab intended to teach you (1-2 pages max). After this, you should
describe your data collection procedures as well as discuss your results in the context of the
questions asked of you below. The total report should not require more than 4-5 pages. If you
wish, you can simply answer the questions in the space provided below. Your write up should
answer or address the following questions and comments regarding the work you have done:</p>

<ol>
<li>Include the following plots with your final write up by taking a screenshot in excel and pasting them into your report. All of the values are calculated for you in the spreadsheet, but you must find the areas of max/min haemoglobin using the H(t)norm plot.
<ol style="list-style-type:lower-latin">
<li> H(t)<sub>norm</sub> vs time</li>
<li> I(t)<sub>max</sub>, I(t)<sub>min</sub>, I(t=10s), I(t=<sub>max</sub>)</li>
</ol>
</li>
<li>Briefly describe how a spectrometer works.</li>
<li>Can you suggest any improvements to this experimental setup that would make these measurements easier to perform in a clinical setting? What challenges would a clinical use of this technology face?</li>
<li>Why do we have to normalize our collected spectra with the spectrum reflected from the white reference target? What would happen to our measurements if we did not take this step?</li>
</ol>

<h1>Part B: Cytochrome C</h1>

<p>Two molecules: hemoglobin, cytochrome c, studied in the lab using the spectrophotometry technique, are shown below. They are members of a large family of metalloporphyrin molecules. The active component of these molecules is the heme group, consisting of the transition metal ion, surrounded by four nitrogen atoms. The heme is part of many proteins, whose functions are diverse and include oxygen transfer and storage (hemoglobin), electron transfer, for example, in cellular respiration (cytochrome) and energy conversion in the photosynthesis process (chlorophyll). </p>

<table width=800 align=center><td>
<p align=justify>[[File:iv_cyt_intro.png|800px|center]]
<br clear=right>
</p>
</td></table>

<p>The absorption of ultraviolet and visible light in metalloporphyrins is dominated by electrons located in the conjugated system of carbon bonds in the porphyrin ring and by electrons of the transition metal ion located on the 3d orbitals. The spectrum consists of a very strong transition between the ground electronic singlet (S<sub>0</sub>) and the second excited singlet (S<sub>2</sub>) at about 400 nm. This is so called the Soret or B band. The weak transition from S<sub>0</sub> to the first excited state S1 is at about 550 nm. This is so called Q band. Due to mixing of states, the probability of transitions from S<sub>0</sub> to S<sub>2</sub> and from S<sub>0</sub> to S<sub>1</sub> is very different. The former is strongly allowed while the latter is only weakly allowed, resulting in dramatically different extinction coefficient for the two wavelengths corresponding to these two transitions. The overlap of the π molecular orbitals of the porphyrin ring with the dπ metal orbitals plays a significant role in determining absorption spectrum of porphyrins. The electric field due to ligands removes the orbital degeneracy of the five 3d orbitals splitting them (typically) into lower lying triplet (hybridized into t<sub>2g</sub> orbitals) and higher energy doublet (hybridized into e<sub>g</sub> orbitals). Depending on the energy difference between the triplet and the doublet, the ion can be either in high or low spin configuration. When the splitting between the triplet and the doublet 3d orbitals is large (when oxygen is bound to the hemoglobin or when cytochrome c is oxidized) all six electrons of Fe<sup>2+</sup> occupy the lower triplet with the resultant spin equal to zero. When the splitting between the triplet and the doublet is small, electrons occupy all five 3d orbitals, resulting in high-spin configuration. The overlap between the π molecular orbitals of the porphyrin ring with the dπ metal orbitals is reflected in the slight shift of the Soret band and change of the Q band from a single line (oxyhemoglobin and oxidized cytochrome c) into a closely spaced doublet (deoxyhemoglobin and reduced cytochrome c).</p>

<p>Cytochrome is oxidized by potassium ferricyanide and reduced by sodium hydrosulfite.</p>
<p>We will be using the built-in Absorbance wizard of the SpectralSuite software to analyse the spectrum of cytochrome in the deoxygenated and oxygenated state.</p>
<p>The Absorbance wizard stores in its memory the spectrum of the sample under three different conditions. The first spectrum reading is of the phosphate buffered solution with the addition of either potassium ferricyanide or sodium hydrosulfite. This serves as the control sample. The second spectrum reading is of the sample without the illumination lighting—this therefore measures any ambient lighting that could interfere with the measurements. The final spectrum is of the buffered cytochrome solution with the addition of either potassium ferricyanide or sodium hydrosulfite. The Absorbance wizard stores in its memory the spectrum of the sample under these three different conditions. It then subtracts the first two sample readings from the third sample reading. In this way, the background spectrum is removed from the sample, leaving only the change in intensity of the different reflected wavelengths. A negative change in intensity indicates an absorption.</p>

<ol>
<li>Prepare the control sample, by pipetting 1 mL of phosphate buffered saline into a cuvette. It is important to always hold the cuvette by the top edge so that fingerprints do not distort the spectrometer reading of the sample.</li>
<li>Using the scoopula, add about 2 mg of potassium ferricyanide to the buffer within the cuvette. You can use the scale to measure the amount of potassium ferricyanide, however in practice it is only necessary to estimate the amount.</li>
<li>Mix the potassium ferricyanide into the buffer by slowly pipetting the solution in and out of the pipette a few times. Be careful to avoid producing air bubbles. </li>
<li>Place the cuvette containing the buffer and potassium ferricyanide solution into the cuvette holder of the spectrometer. Turn on the spectrometer illumination source.</li>
<li>Next, open the Ocean Optics SpectralSuite software.</li>
<li>Under “File” select “New” and then select “Absorbance Measurement”.</li>
<table width=460 align=center><td>
<p align=justify>[[File:iv_cyt_fig1.jpg‎|420px|border|center]]
<br clear=right>
</p>
</td></table>

<li>Select “Next” from the window that appears.</li>
<li>Adjust the “Integration Time” so that the entire spectrum appears within the Preview window.</li>
<table width=460 align=center><td>
<p align=justify>[[File:iv_cyt_fig2.jpg‎|420px|border|center]]
<br clear=right>
</p>
</td></table>
<li>Click “Next” and in the resulting window, click the light bulb. This stores the control spectrum in memory.</li>
<table width=460 align=center><td>
<p align=justify>[[File:iv_cyt_fig3.jpg‎|420px|border|center]]
<br clear=right>
</p>
</td></table>

<li><p>Click “Next”. Block the spectrometer illumination source from reaching the sample. It is important to NOT turn off the spectrometer illumination source, as turning it back on requires additional time to let it warm up. Click the light bulb in the window. This stores the background light in memory.</p>
<table width=460 align=center><td>
<p align=justify>[[File:iv_cyt_fig4.jpg‎|420px|border|center]]
<br clear=right>
</p>
</td></table>

<p>Now prepare the experimental sample. This consists of the cytochrome within buffer with the addition of either potassium ferricyanide or sodium hydrosulfite. This step is performed last because a spectrum measurement of the experimental sample is wanted immediately after mixing the reagents together. (Over time, the effect of the reagents on the cytochrome wears off)</p></li>

<li>To prepare the experimental sample, pipet 1 mL of phosphate buffered saline into a cuvette. Using a new scoopula, add about 1 mg of cytochrome into cuvette. (Typically, this amount is approximated as the smallest reasonable amount of cytochrome that can be transferred using the scoopula). Mix using the same procedure as before (It is crucial to avoid air bubbles!).</li>
<li>Next, add about 2 mg of potassium ferricyanide and mix as before.</li>
<li>Immediately place the cuvette into the holder of the spectrometer. Select “Finish” on the window. This takes the final spectrum of the experimental sample and automatically subtracts the two background spectrums from before.</li>
<li>Repeat this entire procedure but in “Step 12” add 2 mg of sodium hydrosulfite instead of potassium ferricyanide.</li>

<table width=460 align=center><td>
<p align=justify>[[File:iv_cyt_fig5.jpg‎|420px|border|center]]
A typical absorption spectrum of cytochrome mixed with sodium hydrosulfite.
<br clear=right>
</p>
</td></table>

Main Page/PHYS 3220

2015-09-08T17:21:27Z

Mgeorge:

<h1>PHYS 3220 3.0 Experiments in Modern Physics </h1>
<p>A selection of experiments in fluid mechanics,
electromagnetism, optics, and atomic, nuclear, and
particle physics. Analysis of the data and detailed
write-ups are required. One lecture hour which is
devoted to techniques of data analysis and three
laboratory hours per week.</p>

<p>Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<h1>Laboratory Manual</h1>
<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<ul>
<li>[[Main Page/PHYS 3220/Cavendish|Measurement of the Gravitation Constant G: The Cavendish Experiment]] </li>
<li>[[Main Page/PHYS 3220/Speed of Light|A Measurement of the Velocity of Light: The Foucault-Michelson Experiment]] </li>
<li> [[Main Page/PHYS 3220/Excitation Potentials|The Excitation Potentials of Mercury: The Franck-Hertz Experiment]] </li>
<li> [[Main Page/PHYS 3220/Radioactive Decays|Radioactive Decays]] </li>
<li>[[Main Page/PHYS 3220/Viscosity|Viscosity]] </li>
<li>[[Main Page/PHYS 3220/Millikan|Determination of the Electric Charge Unit ''e'' : The Millikan Oil Drop Experiment]] </li>
<li> [[Main Page/PHYS 3220/Thermionic|Thermionic Emission]]</li>
<li> [[Main Page/PHYS 3220/Particle Tracking|Particle Tracking Simulation]] </li>
<li> [[Main Page/PHYS 3220/Rutherford I|Rutherford Scattering I]] </li>
<li> [[Main Page/PHYS 3220/Digital Oscilloscope|Digital Storage Oscilloscope]] </li>
<li> [[Main Page/PHYS 3220/High-TC Superconductivity|High-TC Superconductivity]]</li>
<li> [[Main Page/PHYS 3220/Semiconductors I|Semiconductors I]] </li>
<li> [[Main Page/PHYS 3220/Holography| <s>Holography</s>]] </li>
</ul>

<h3>out of service</h3>
<ul>
<li>[[Main Page/PHYS 3220/Coupled Motion|Coupled Oscillatory and Rotational Motion]] </li>
<li> [[Main Page/PHYS 3220/Hydrogen Spectrum|The Visible Spectrum of Hydrogen]]</li>
<li> [[Main Page/PHYS 3220/Interferometer|The Michelson Interferometer ]] </li>
</ul>

<h3>Demonstration</h3>
[[Media:Solar_to_Mechanical_v2.pdf| Solar to Mechanical]]

Main Page/PHYS 3220

2015-09-08T17:20:46Z

Mgeorge:

<h1>PHYS 3220 3.0 Experiments in Modern Physics </h1>
<p>A selection of experiments in fluid mechanics,
electromagnetism, optics, and atomic, nuclear, and
particle physics. Analysis of the data and detailed
write-ups are required. One lecture hour which is
devoted to techniques of data analysis and three
laboratory hours per week.</p>

<p>Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<h1>Laboratory Manual</h1>
<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<ul>
<li>[[Main Page/PHYS 3220/Cavendish|Measurement of the Gravitation Constant G: The Cavendish Experiment]] </li>
<li>[[Main Page/PHYS 3220/Speed of Light|A Measurement of the Velocity of Light: The Foucault-Michelson Experiment]] </li>
<li> [[Main Page/PHYS 3220/Excitation Potentials|The Excitation Potentials of Mercury: The Franck-Hertz Experiment]] </li>
<li> [[Main Page/PHYS 3220/Radioactive Decays|Radioactive Decays]] </li>
<li>[[Main Page/PHYS 3220/Viscosity|Viscosity]] </li>
<li>[[Main Page/PHYS 3220/Millikan|Determination of the Electric Charge Unit ''e'' : The Millikan Oil Drop Experiment]] </li>
<li> [[Main Page/PHYS 3220/Thermionic|Thermionic Emission]]</li>
<li> [[Main Page/PHYS 3220/Particle Tracking|Particle Tracking Simulation]] </li>
<li> [[Main Page/PHYS 3220/Rutherford I|Rutherford Scattering I]] </li>
<li> [[Main Page/PHYS 3220/Digital Oscilloscope|Digital Storage Oscilloscope]] </li>
<li> [[Main Page/PHYS 3220/High-TC Superconductivity|High-TC Superconductivity]]</li>
<li> [[Main Page/PHYS 3220/Semiconductors I|Semiconductors I]] </li>
<li> [[Main Page/PHYS 3220/Holography| <st>Holography</st>]] </li>
</ul>

<h3>out of service</h3>
<ul>
<li>[[Main Page/PHYS 3220/Coupled Motion|Coupled Oscillatory and Rotational Motion]] </li>
<li> [[Main Page/PHYS 3220/Hydrogen Spectrum|The Visible Spectrum of Hydrogen]]</li>
<li> [[Main Page/PHYS 3220/Interferometer|The Michelson Interferometer ]] </li>
</ul>

<h3>Demonstration</h3>
[[Media:Solar_to_Mechanical_v2.pdf| Solar to Mechanical]]

PHYS 1010, 1410 & 1420

2015-09-08T15:37:50Z

Mgeorge:

<h2> General Information </h2>

<p><b> The most up-to-date information can be found on the Yorku Moodle site. (moodle.yorku.ca).</b></p>

<p> These labs serve as the practical teaching experience for PHYS 1010, PHYS 1410, and PHYS 1420. The labs are located in '''102C''' and '''102D''' Bethune College.Select your course below to view your lab schedule. The schedule also appears in the Lab Manual which you can pick up from the York Bookstore.</p>

<p><b>NOTE:</b> Be sure to pick up a copy of the lab manual from the bookstore, and preform the prelab exercise for Experiment 1 ''before'' coming to your first lab.</p>
<p> Check the schedule carefully to see which weeks you have experiments, and in which order you will be performing them.</p>

<h2>Lab Coordinator</h2>
<p> The lab coordinator is responsible for the administration of these labs. Should you have issues such as- you wish to change lab sections, you have missed your scheduled lab time, or other matters for which the TA cannot assist, please see the lab coordinator during the office hours listed below.</p>
<table>
<tr><td>'''Lab Coordinator'''</td><td>Matthew George</td></tr>
<tr><td>'''Office Hours'''</td><td> TW 3:00pm 4:00pm</td></tr>
<tr><td>'''Location'''</td><td> Petrie 113</td> </tr>
<tr><td>'''Email'''</td><td>mgeorge (at) yorku.ca</td></tr>
</table>

<h2>Teaching Assistants</h2>
<p> The Teaching Assistant is responsible for providing you the physics knowledge, and the practical know-how required in order to complete these experiments successfully in a timely manner. You should pay careful attention to what they have to say, and heed their advice. They will also be responsible for marking your lab report. They have the authority to deny entry or remove from the lab any student they feel is: acting in an unsafe manner, arriving more than 15 minutes late, grossly unprepared, causing major disruptions, or attempting to stay beyond the 3 hour limit.</p>

<h2> Help Sessions</h2>
<p>There will be help sessions in room 102C and/or 102D Bethune. Drop by and get expert help with your prelab exercises, get a sneak peak at the apparatus for your next experiment, and get prepared. The schedule of the Help Sessions will be determined shortly. </p>



<h2> Lab Rules </h2>
<ol>
<li> Lab safety is the number one priority. If you are unsure on how to operate the equipment, or believe you may be doing something which might cause harm to you or your classmates, stop and and ask the TA for clarification.</li>
<li> If you are purposely misusing the equipment in a manner which is obviously unsafe, you will be told to leave, and receive a mark of zero for this experiment.</li>
<li> Show up on time- the TA will give a short presentation at the beginning of each lab, where you will learn some very useful information. If you show up late, you will miss this. If you show up more than 15 mintues late, the TA can forbid you from performing the experiment, and you will receive a mark of zero.</li>
<li><b> You must leave the workstation as you have found it! All the equipment must be exactly in the manner in which you found it. All scraps of paper, eraser bits, and other garbage must be cleaned from the station before you leave. Failure to do so will result in a loss of up to 30% for that lab.</b></li>
<li> Each lab session is 3 hours, there are no provisions made for extra time. 15 minutes before the end of the lab, you should start cleaning up you workstation, and leave the room by the end of the lab session.</li>
<li> Report broken or damaged equipment to the TA immediately. You are not responsible for broken equipment, you will not be charged, and your mark will not suffer. We need to know of broken equipment so we can fix or replace it before the next lab session.</li>
<li> No more than two students working together as lab partners is allowed.</li>
<li> A valid medical note is the only acceptable reason for missing a lab. This must be presented to the lab coordinator in order to be considered for scheduling or an exemption.</li>
</ol>

<h2>Prelab Preparation</h2>
<p>You will know from the posted schedule which experiment you will be doing. Before coming to do the experiment, you are expected to read the appropriate section of the manual. Be sure you understand the theory involved, consult your textbook, and plan your practical work. Most of the experiments contain prelab exercises which must be completed on a separate sheet of paper before you come to the lab. This preparation is most important. It is unlikely that you will be able to finish the experiment satisfactorily or learn from them if you do not prepare beforehand. There may be short, unannounced quizzes on the experiment during some labs.</p>

<h2>Lab Reports</h2>
<p>A sample lab report is included in the lab manual (appendix F). </p>
<p>We do not require you to write an elaborate report for each experiment. The report should include name, name of partner, title and date. The experimental data, whenever possible, should be summarized in the form of a table, with title, column headings, units and experimental errors. Graphs should have titles, axes labelled and units included. Errors of all measured quantities should be indicated on graphs in the form of error bars. Calculations should be shown and organized in a logical way, with short comments and explanations. Just formulas with substituted data are not acceptable.
Calculations of errors is an important part of the lab report (next section in the manual provides more information regarding error calculations and rounding of final result and its error). </p>
<p>You are encouraged to record in your report for future reference any comments regarding the theory or method or apparatus which enhance your understanding. Your report should resemble a research scientist's day-to-day experimental log rather than a polished scientific paper. </p>
<p>It is preferred that you write laboratory reports in notebooks, which encourage better organization and neatness. Do not tear pages out of the books, if a mistake is made, simply cross out the mistake neatly. Two books will be required to be used alternately throughout the year. Light weight coil notebooks are suitable. Put your name and lab time clearly on the outside. </p>
<p>The three-hour session should be sufficient for the taking of measurements and for calculations and conclusions, etc. Be punctual - latecomers will find it difficult to complete the assignment. All lab reports, finished or unfinished, must be handed in to your demonstrator by the end of the three-hour lab session.
Your report will be marked by the demonstrator whose name appears on the top of the attendance list which you sign. It will be your responsibility to collect your report from this demonstrator during your next laboratory session. At this time you should discuss with your demonstrator any matters concerning the report(s).</p>

<h2> Lab Marks</h2>
<p> Depending in which course you are enrolled (1010,1410,1420) the amount your lab marks contribute to your final mark can vary from 10%-20%. The course requires 11 labs, and your lowest of the 11 will be dropped when calculating your final lab mark. Your lab reports will be marked by the TA, with some fraction for the prelab, error analysis, results, answers to questions, neatness and completeness.</p>

<h2> Lab Partners</h2>
<p>Some students claim that they learn more while working with a lab partner; others prefer to work alone. For certain experiments where basic techniques, etc. are explored, you will be required to work individually - this will be stated in the lab outline for those particular experiments. For the other experiments we will try to provide sufficient apparatus so that you may work with another student who has been assigned the same experiment or alone, as you prefer. For a few of the experiments the mechanical work is so difficult that one person cannot perform the experiment satisfactorily. If two students work together, <b>each should take a turn at reading all the instruments and although both will have the same data, each student must submit an independent report, with independent calculations.</b> </p>

<p><b>Lab partners are randomly assigned.</b> This facilitates meeting many friends, promotes social skills as well as reduces the probability of dishonesty when doing lab work. The details of how lab partners are assigned will be explained in the first lab.</p>

<h2>Lab Safety</h2>
<p>Scientists very commonly live to a grand old age in spite of their daily encounters with many hazards. The main reason for this is that a scientist doing an experiment is paying very close attention to everything that happens, is expecting the unknown and can react quickly to it. Your best protection against accidents in the lab is a constant thoughtful alertness which never permits your actions to become "mechanical" and "reflex". </p>
<p>Specific hazards which exist in particular experiments will be stressed in the respective lab outline. Please pay very careful attention to these warnings and act accordingly. </p>
<p> Notify the TA or lab coordinator of any accident or injury no matter how insignificant it may seem. </p>
<p>In the case of a fire, at the sound of the fire alarm in the building, the university stipulates that everyone must leave the building. In the case of a fire in the lab, the TA is responsible for taking the appropriate action to curb it, but the students must leave the building immediately. </p>

<b> A 24-hour Emergency Services Telephone Centre operates on York Campus and can be alerted by calling 33333 on all campus telephones or 736-2100 Ext. 33333 on public telephones.
Health services are located in York Lanes. </b>

<h2>Academic Honesty</h2>
<p>Students will certainly discuss and talk about their studies with their friends and this can be very useful; but any work that you hand in must have been done by yourself. This is the only way to test your own competence and to prepare yourself for positions of responsibility after graduation. If scientists are dishonest, they are useless.</p>
<p><b>THE UNIVERSITY CONSIDERS ALL FORMS OF COPYING AND CHEATING TO BE SERIOUS OFFENCES. </b>[[http://www.yorku.ca/secretariat/policies/index-policies.html YorkU Policy on Academic Honesty]].</p>

<ul>
<li>[[LAB INFORMATION|LAB INFORMATION]] </li>
<li>[[MEASUREMENTS AND ERRORS|MEASUREMENTS AND ERRORS]] </li>
<li>[[MEASURING LENGTH|MEASURING LENGTH]] </li>
<li>[[GRAPHS|GRAPHS]] </li>
</ul>

PHYS 1010, 1410 & 1420

2015-09-08T15:37:02Z

Mgeorge:

<h2> General Information </h2>

<p> The most up-to-date information can be found on the Moodle site. (moodle.yorku.ca).</p>

<p> These labs serve as the practical teaching experience for PHYS 1010, PHYS 1410, and PHYS 1420. The labs are located in '''102C''' and '''102D''' Bethune College.Select your course below to view your lab schedule. The schedule also appears in the Lab Manual which you can pick up from the York Bookstore.</p>

<p><b>NOTE:</b> Be sure to pick up a copy of the lab manual from the bookstore, and preform the prelab exercise for Experiment 1 ''before'' coming to your first lab.</p>
<p> Check the schedule carefully to see which weeks you have experiments, and in which order you will be performing them.</p>

<h2>Lab Coordinator</h2>
<p> The lab coordinator is responsible for the administration of these labs. Should you have issues such as- you wish to change lab sections, you have missed your scheduled lab time, or other matters for which the TA cannot assist, please see the lab coordinator during the office hours listed below.</p>
<table>
<tr><td>'''Lab Coordinator'''</td><td>Matthew George</td></tr>
<tr><td>'''Office Hours'''</td><td> TW 3:00pm 4:00pm</td></tr>
<tr><td>'''Location'''</td><td> Petrie 113</td> </tr>
<tr><td>'''Email'''</td><td>mgeorge (at) yorku.ca</td></tr>
</table>

<h2>Teaching Assistants</h2>
<p> The Teaching Assistant is responsible for providing you the physics knowledge, and the practical know-how required in order to complete these experiments successfully in a timely manner. You should pay careful attention to what they have to say, and heed their advice. They will also be responsible for marking your lab report. They have the authority to deny entry or remove from the lab any student they feel is: acting in an unsafe manner, arriving more than 15 minutes late, grossly unprepared, causing major disruptions, or attempting to stay beyond the 3 hour limit.</p>

<h2> Help Sessions</h2>
<p>There will be help sessions in room 102C and/or 102D Bethune. Drop by and get expert help with your prelab exercises, get a sneak peak at the apparatus for your next experiment, and get prepared. The schedule of the Help Sessions will be determined shortly. </p>



<h2> Lab Rules </h2>
<ol>
<li> Lab safety is the number one priority. If you are unsure on how to operate the equipment, or believe you may be doing something which might cause harm to you or your classmates, stop and and ask the TA for clarification.</li>
<li> If you are purposely misusing the equipment in a manner which is obviously unsafe, you will be told to leave, and receive a mark of zero for this experiment.</li>
<li> Show up on time- the TA will give a short presentation at the beginning of each lab, where you will learn some very useful information. If you show up late, you will miss this. If you show up more than 15 mintues late, the TA can forbid you from performing the experiment, and you will receive a mark of zero.</li>
<li><b> You must leave the workstation as you have found it! All the equipment must be exactly in the manner in which you found it. All scraps of paper, eraser bits, and other garbage must be cleaned from the station before you leave. Failure to do so will result in a loss of up to 30% for that lab.</b></li>
<li> Each lab session is 3 hours, there are no provisions made for extra time. 15 minutes before the end of the lab, you should start cleaning up you workstation, and leave the room by the end of the lab session.</li>
<li> Report broken or damaged equipment to the TA immediately. You are not responsible for broken equipment, you will not be charged, and your mark will not suffer. We need to know of broken equipment so we can fix or replace it before the next lab session.</li>
<li> No more than two students working together as lab partners is allowed.</li>
<li> A valid medical note is the only acceptable reason for missing a lab. This must be presented to the lab coordinator in order to be considered for scheduling or an exemption.</li>
</ol>

<h2>Prelab Preparation</h2>
<p>You will know from the posted schedule which experiment you will be doing. Before coming to do the experiment, you are expected to read the appropriate section of the manual. Be sure you understand the theory involved, consult your textbook, and plan your practical work. Most of the experiments contain prelab exercises which must be completed on a separate sheet of paper before you come to the lab. This preparation is most important. It is unlikely that you will be able to finish the experiment satisfactorily or learn from them if you do not prepare beforehand. There may be short, unannounced quizzes on the experiment during some labs.</p>

<h2>Lab Reports</h2>
<p>A sample lab report is included in the lab manual (appendix F). </p>
<p>We do not require you to write an elaborate report for each experiment. The report should include name, name of partner, title and date. The experimental data, whenever possible, should be summarized in the form of a table, with title, column headings, units and experimental errors. Graphs should have titles, axes labelled and units included. Errors of all measured quantities should be indicated on graphs in the form of error bars. Calculations should be shown and organized in a logical way, with short comments and explanations. Just formulas with substituted data are not acceptable.
Calculations of errors is an important part of the lab report (next section in the manual provides more information regarding error calculations and rounding of final result and its error). </p>
<p>You are encouraged to record in your report for future reference any comments regarding the theory or method or apparatus which enhance your understanding. Your report should resemble a research scientist's day-to-day experimental log rather than a polished scientific paper. </p>
<p>It is preferred that you write laboratory reports in notebooks, which encourage better organization and neatness. Do not tear pages out of the books, if a mistake is made, simply cross out the mistake neatly. Two books will be required to be used alternately throughout the year. Light weight coil notebooks are suitable. Put your name and lab time clearly on the outside. </p>
<p>The three-hour session should be sufficient for the taking of measurements and for calculations and conclusions, etc. Be punctual - latecomers will find it difficult to complete the assignment. All lab reports, finished or unfinished, must be handed in to your demonstrator by the end of the three-hour lab session.
Your report will be marked by the demonstrator whose name appears on the top of the attendance list which you sign. It will be your responsibility to collect your report from this demonstrator during your next laboratory session. At this time you should discuss with your demonstrator any matters concerning the report(s).</p>

<h2> Lab Marks</h2>
<p> Depending in which course you are enrolled (1010,1410,1420) the amount your lab marks contribute to your final mark can vary from 10%-20%. The course requires 11 labs, and your lowest of the 11 will be dropped when calculating your final lab mark. Your lab reports will be marked by the TA, with some fraction for the prelab, error analysis, results, answers to questions, neatness and completeness.</p>

<h2> Lab Partners</h2>
<p>Some students claim that they learn more while working with a lab partner; others prefer to work alone. For certain experiments where basic techniques, etc. are explored, you will be required to work individually - this will be stated in the lab outline for those particular experiments. For the other experiments we will try to provide sufficient apparatus so that you may work with another student who has been assigned the same experiment or alone, as you prefer. For a few of the experiments the mechanical work is so difficult that one person cannot perform the experiment satisfactorily. If two students work together, <b>each should take a turn at reading all the instruments and although both will have the same data, each student must submit an independent report, with independent calculations.</b> </p>

<p><b>Lab partners are randomly assigned.</b> This facilitates meeting many friends, promotes social skills as well as reduces the probability of dishonesty when doing lab work. The details of how lab partners are assigned will be explained in the first lab.</p>

<h2>Lab Safety</h2>
<p>Scientists very commonly live to a grand old age in spite of their daily encounters with many hazards. The main reason for this is that a scientist doing an experiment is paying very close attention to everything that happens, is expecting the unknown and can react quickly to it. Your best protection against accidents in the lab is a constant thoughtful alertness which never permits your actions to become "mechanical" and "reflex". </p>
<p>Specific hazards which exist in particular experiments will be stressed in the respective lab outline. Please pay very careful attention to these warnings and act accordingly. </p>
<p> Notify the TA or lab coordinator of any accident or injury no matter how insignificant it may seem. </p>
<p>In the case of a fire, at the sound of the fire alarm in the building, the university stipulates that everyone must leave the building. In the case of a fire in the lab, the TA is responsible for taking the appropriate action to curb it, but the students must leave the building immediately. </p>

<b> A 24-hour Emergency Services Telephone Centre operates on York Campus and can be alerted by calling 33333 on all campus telephones or 736-2100 Ext. 33333 on public telephones.
Health services are located in York Lanes. </b>

<h2>Academic Honesty</h2>
<p>Students will certainly discuss and talk about their studies with their friends and this can be very useful; but any work that you hand in must have been done by yourself. This is the only way to test your own competence and to prepare yourself for positions of responsibility after graduation. If scientists are dishonest, they are useless.</p>
<p><b>THE UNIVERSITY CONSIDERS ALL FORMS OF COPYING AND CHEATING TO BE SERIOUS OFFENCES. </b>[[http://www.yorku.ca/secretariat/policies/index-policies.html YorkU Policy on Academic Honesty]].</p>

<ul>
<li>[[LAB INFORMATION|LAB INFORMATION]] </li>
<li>[[MEASUREMENTS AND ERRORS|MEASUREMENTS AND ERRORS]] </li>
<li>[[MEASURING LENGTH|MEASURING LENGTH]] </li>
<li>[[GRAPHS|GRAPHS]] </li>
</ul>

Main Page/PHYS 3220/Viscosity

2015-07-23T17:57:52Z

Mgeorge:

<h1>Viscosity</h1>

<p>The purpose of this experiment is to determine the viscosity of a liquid and to find the variation of viscosity with temperature.</p>

<h1>Theory</h1>
<p>When a solid is subject to a shearing stress it deforms until the internal elastic forces of the solid exactly balance the external forces. Thus a finite force applied to a solid produces a finite deformation. If a similar force is applied to a liquid, however, the deformation increases indefinitely (the liquid flows). The flow can be imagined as the movement of adjacent layers over one another. The Newtonian friction caused by the relative motion between adjacent layers retards the flow and is called viscosity. This frictional force was assumed by Newton to be proportional to the velocity gradient perpendicular to the direction of the motion of the fluid, i.e., to dv/dr.</p>
<p>Consider an element of volume in a fluid as shown in the following diagram (ref. 1)</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig1v2.JPG|300px|border|center]]
<b>Figure 1 -</b> Element of volume of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>The shearing stress on this element of volume is F/A where F is the force on the upper surface and A is the cross section. <b>The shear is given by the ratio between the lateral displacement between the two surfaces to the separation between the surfaces.</b> Thus, if we assume that the upper surface is moving with a velocity, dv, greater than that of the lower surface, the amount of shear occurring in unit time is dv/dr. The coefficient of viscosity or simply <b>viscosity</b> is defined as follows (for streamline motion).</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn1.png|220px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>The c.g.s. unit of viscosity is called the <b>poise</b>; it represents the viscosity of a substance that acquires a unit velocity gradient under the influence of a shearing stress of 1 dyne/cm2.</p>
<p>One method of measuring viscosity is to determine the flow of a liquid through a capillary tube. Let us consider how to measure viscosity in this way.</p>

<p>When a liquid flows through a narrow tube so that each particle moves parallel to the axis of the tube with constant velocity, the motion is said to be regular or <b>streamlined</b>. In this case, liquid in contact with the walls is at rest while the velocity is a maximum at the centre of the tube.</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig2v2.JPG|300px|border|center]]
<b>Figure 2 -</b> Streamlined flow of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>We imagine the liquid as being divided up into a number of thin cylindrical shells, each shell sliding on the other. The viscous drag, f, per square cm. of one layer on the other is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn2.png|90px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>For a cylinder of radius, a, length l, through which a liquid is flowing under a pressure differential, p, the total viscous drag balances the force due to the pressure difference.</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn3.png|180px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Assuming that there is no radial flow the pressure is constant over any given cross-section.
At r = a, v = 0, while at r = r, v = u, thus</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn5.png|100px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>Thus, by measuring the quantity of liquid transferred through a capillary tube per unit time subject to a specific pressure difference, the viscosity of the liquid may be determined.</p>
<p>The viscosity may also be determined using the concentric cylinder viscosimeter. Consider a liquid between two concentric cylinders as illustrated in Figure 3. </p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig3v2.JPG|300px|border|center]]
<b>Figure 3 -</b> Liquid between concentric cylinders.
<br clear=right>
</p>
</td></table>

<p>The outer cylinder is moving with angular velocity wB. If the liquid adheres to the walls of the cylinder, a shearing takes place in which concentric cylindrical layers of the liquid slip over each other with the angular velocity w increasing progressively from zero at the stationary cylinder to wB at the rotating one. Now, the rate of shear is given as</p>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn6.png|250px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>Only the second term produces a viscosity effect, since a velocity gradient is needed to have relative slipping of layers and the associated friction. Thus, </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn7.png|130px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>

<p>If a torque L is applied to the rotating cylinder, (see Figure 3), the tangential force at the boundary SS' equals L/r and integration over r from A to B yields</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn8.png|140px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Note that this formula is also valid if the inner cylinder is rotated with angular velocity w<sub>B</sub> while the outer cylinder is held stationary.</p>
<p>For cylinders closed at either end, equation (8) is modified to take into account the friction between the two ends of the cylinders according to</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn9.png|160px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<h1>Method</h1>

<ol>
<li> <h2>Capillary tube.</h2>
<h3>Apparatus</h3>
<ul><li>Capillary Tube</li>
<li>2 Beakers (600ml and 400 ml)</li>
<li>Bunsen Burner Stand</li>
<li>Thermometer</li></ul>

<p>For the determination of viscosity by use of a capillary tube we need to know the pressure p, this is given by </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn10.png|80px|center]]
</p>
</td><td> <b>(10)</b></td></tr></table>
<p>where
<ul><li>h = height of water column</li>
<li>d = density of water</li>
<li>g = acceleration due to gravity = 981 cm/sec<sup>2</sup></li>
</ul></p>
<p>The capillary tube is positioned at the bottom of a beaker, allowing for the monitoring of the water level. Using regular tap water, fill the beaker until the water starts going through the capillary tube. (Notice that the height of the water column is changing as water flows out, it is up to you to figure out a solution, consult your T.A. for ideas). </p>
<p>Measure the flow rate through the tube for various p values and calculate the viscosity. How does the result compare with the accepted viscosity value for water? Would you expect the same result if the capillary tube was slightly wider? Much wider? Comment on the reason for any potential discrepancies.</p>
<p>Record the water temperature. Repeat the measurements for at least two other temperatures. Assuming that the dependence resembles the “Arrhenius” equation </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn11.png|110px|center]]
</p>
</td><td> <b>(11)</b></td></tr></table>
<p>where A can be viewed as a correction factor, E<sub>a</sub> plays a role similar to activation energy in chemical reactions and R is the gas constant. Plot a graph of the obtained values and fit to (11). Hint: it is possible to turn (11) into a linear graph. </p>
<p> Analyze the resulting fit with comments on the significance and the validity of the made assumption. </p>
</li>
<li><h2>Concentric cylinder viscosimeter</h2>
<h3>Apparatus</h3>
<ul><li>Vacuum Pump Oil</li>
<li>Viscosity Measuring Instrument</li>
<li>Vernier Caliper</li>
<li>Meter Stick</li>
<li>Photo Gate Interface</li>
<li>2 Photo Gate Sensors</li>
<li>Oscilloscope</li>
<li>Mass</li>
<li>1 Extension Cord</li>
<li>Heater</li></ul>

<p>This instrument is used to find the viscosity of vacuum pump oil and to determine its variation with temperature. The inner drum in the viscosimeter is mounted on two bearings and is free to rotate under a torque, L, supplied by a mass, m, falling through a given height. The torque is given by L = mgk where k is the radius of the pulley around which the string supporting the falling mass m, is wound. If the mass falls a distance s, in time t, the angular velocity w is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn12.png|60px|center]]
</p>
</td><td> <b>(12)</b></td></tr></table>

<p>Therefore, Equation (9) becomes</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn13.png|160px|center]]
</p>
</td><td> <b>(13)</b></td></tr></table>
<p>or</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn14.png|70px|center]]
</p>
</td><td> <b>(14)</b></td></tr></table>
<p>where c is a constant</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn15.png|160px|center]]
</p>
</td><td> <b>(15)</b></td></tr></table>
<p>To find the absolute value of η, remove the centre cylinder (being careful not to damage the supporting bearings) and measure all pertinent dimensions. Re-assemble the apparatus and fill the container with oil until the level is about 1.5 cm above the lower surface of the inner cylinder. Measure the length l using a vernier calliper (notice that l is not simply the height of the oil level). Place the apparatus on the edge of the wall mount so that the suspended mass has an unrestricted fall of several feet.</p>
<table width=300 align=center><td>
<p align=justify>[[File:Vis-fig4v2.JPG|400px|border|center]]
<b>Figure 4 -</b> Viscosimeter.
<br clear=right>
</p>
</td></table>
<p>Record the time required for a mass m suspended from the string (wound around the pulley) to descend through a given distance. You will find that the downward velocity is not constant over the total drop but changes rapidly over the first few centimetres. It is therefore necessary to neglect the first few centimetres of drop, i.e., the stopwatch must be started once the descending mass is moving with constant velocity. Make several measurements of the time required to fall through a distance, s, and obtain an average time. Make a series of five determinations keeping the mass constant and increasing the effective length of the cylinder by adding liquid. The last observation should be made with the apparatus filled to the top of the inner cylinder.</p>

<p> To collect the data, we can observe the transit of the masses through the two [[media:Visc_sensor.jpg|sensor gates]] on an [[media:Visc_scope.jpg|oscilloscope]]. With the oscilloscope set for a long timebase, and the sensor box outputs attached to one channel, you will notice the abrupt signal change when anything passes through either sensor gate. You will need to use the "Run/Stop" button on the top right of oscilloscope to stop the trace from scrolling off the screen after the data is collected so you can measure or save the data. The scope can be used as a precise measuring tool for the time require for the mass to fall a particular distance.</p>

<p>With the level of the liquid at the top of the inner cylinder, take a series of observations of time of descent vs. mass.</p>
<p>To analyze your data, plot two graphs: one of the length '''l''' vs. time '''t''', and the other of the time, '''t''', vs. reciprocal mass'''1 /m'''. The first graph will give the value of the length correction '''e'''. The second graph should be a straight line of slope '''mt'''. '''η''' can then be obtained from Equation (12).</p>
<p>To determine the variation of viscosity with temperature, repeat the above fixed mass measurement at several temperatures. Be sure to allow for expansion of the liquid when the temperature is increased. Compare the obtained results to the previous section.</p>
</ol>
<h1>Units</h1>
<p>Give your results in both CGS and MKS units. <b>The values of the viscosities are available from handbooks</b>, and are usually quoted in centipoises (compare your results).</p>

<h1>Questions and Discussion</h1>
<p>Why does the moment of inertia of the rotating cylinder not enter the analysis of the problem? Discuss the sign of the length correction. Explain what the important sources of imprecision are, and elaborate on the importance of the constants e and c.</p>

<h1>References</h1>
<p>Any intermediate-level classical mechanics text, e.g.,</p>
<ol>
<li>K. Symon, ''Mechanics'', 3rd ed., pp. 345 ff.</li>
<li>R. Feynman, Leighton, Sands,''Lectures on Physics'', vol. II, chapter 41.</li>
</ol>

Main Page/PHYS 3220/Viscosity

2015-07-23T17:56:52Z

Mgeorge:

<h1>Viscosity</h1>

<p>The purpose of this experiment is to determine the viscosity of a liquid and to find the variation of viscosity with temperature.</p>

<h1>Theory</h1>
<p>When a solid is subject to a shearing stress it deforms until the internal elastic forces of the solid exactly balance the external forces. Thus a finite force applied to a solid produces a finite deformation. If a similar force is applied to a liquid, however, the deformation increases indefinitely (the liquid flows). The flow can be imagined as the movement of adjacent layers over one another. The Newtonian friction caused by the relative motion between adjacent layers retards the flow and is called viscosity. This frictional force was assumed by Newton to be proportional to the velocity gradient perpendicular to the direction of the motion of the fluid, i.e., to dv/dr.</p>
<p>Consider an element of volume in a fluid as shown in the following diagram (ref. 1)</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig1v2.JPG|300px|border|center]]
<b>Figure 1 -</b> Element of volume of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>The shearing stress on this element of volume is F/A where F is the force on the upper surface and A is the cross section. <b>The shear is given by the ratio between the lateral displacement between the two surfaces to the separation between the surfaces.</b> Thus, if we assume that the upper surface is moving with a velocity, dv, greater than that of the lower surface, the amount of shear occurring in unit time is dv/dr. The coefficient of viscosity or simply <b>viscosity</b> is defined as follows (for streamline motion).</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn1.png|220px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>The c.g.s. unit of viscosity is called the <b>poise</b>; it represents the viscosity of a substance that acquires a unit velocity gradient under the influence of a shearing stress of 1 dyne/cm2.</p>
<p>One method of measuring viscosity is to determine the flow of a liquid through a capillary tube. Let us consider how to measure viscosity in this way.</p>

<p>When a liquid flows through a narrow tube so that each particle moves parallel to the axis of the tube with constant velocity, the motion is said to be regular or <b>streamlined</b>. In this case, liquid in contact with the walls is at rest while the velocity is a maximum at the centre of the tube.</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig2v2.JPG|300px|border|center]]
<b>Figure 2 -</b> Streamlined flow of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>We imagine the liquid as being divided up into a number of thin cylindrical shells, each shell sliding on the other. The viscous drag, f, per square cm. of one layer on the other is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn2.png|90px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>For a cylinder of radius, a, length l, through which a liquid is flowing under a pressure differential, p, the total viscous drag balances the force due to the pressure difference.</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn3.png|180px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Assuming that there is no radial flow the pressure is constant over any given cross-section.
At r = a, v = 0, while at r = r, v = u, thus</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn5.png|100px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>Thus, by measuring the quantity of liquid transferred through a capillary tube per unit time subject to a specific pressure difference, the viscosity of the liquid may be determined.</p>
<p>The viscosity may also be determined using the concentric cylinder viscosimeter. Consider a liquid between two concentric cylinders as illustrated in Figure 3. </p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig3v2.JPG|300px|border|center]]
<b>Figure 3 -</b> Liquid between concentric cylinders.
<br clear=right>
</p>
</td></table>

<p>The outer cylinder is moving with angular velocity wB. If the liquid adheres to the walls of the cylinder, a shearing takes place in which concentric cylindrical layers of the liquid slip over each other with the angular velocity w increasing progressively from zero at the stationary cylinder to wB at the rotating one. Now, the rate of shear is given as</p>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn6.png|250px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>Only the second term produces a viscosity effect, since a velocity gradient is needed to have relative slipping of layers and the associated friction. Thus, </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn7.png|130px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>

<p>If a torque L is applied to the rotating cylinder, (see Figure 3), the tangential force at the boundary SS' equals L/r and integration over r from A to B yields</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn8.png|140px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Note that this formula is also valid if the inner cylinder is rotated with angular velocity w<sub>B</sub> while the outer cylinder is held stationary.</p>
<p>For cylinders closed at either end, equation (8) is modified to take into account the friction between the two ends of the cylinders according to</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn9.png|160px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<h1>Method</h1>

<ol>
<li> <h2>Capillary tube.</h2>
<h3>Apparatus</h3>
<ul><li>Capillary Tube</li>
<li>2 Beakers (600ml and 400 ml)</li>
<li>Bunsen Burner Stand</li>
<li>Thermometer</li></ul>
<p> </p>
<p>For the determination of viscosity by use of a capillary tube we need to know the pressure p, this is given by </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn10.png|80px|center]]
</p>
</td><td> <b>(10)</b></td></tr></table>
<p>where
<ul><li>h = height of water column</li>
<li>d = density of water</li>
<li>g = acceleration due to gravity = 981 cm/sec<sup>2</sup></li>
</ul></p>
<p>The capillary tube is positioned at the bottom of a beaker, allowing for the monitoring of the water level. Using regular tap water, fill the beaker until the water starts going through the capillary tube. (Notice that the height of the water column is changing as water flows out, it is up to you to figure out a solution, consult your T.A. for ideas). </p>
<p>Measure the flow rate through the tube for various p values and calculate the viscosity. How does the result compare with the accepted viscosity value for water? Would you expect the same result if the capillary tube was slightly wider? Much wider? Comment on the reason for any potential discrepancies.</p>
<p>Record the water temperature. Repeat the measurements for at least two other temperatures. Assuming that the dependence resembles the “Arrhenius” equation </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn11.png|110px|center]]
</p>
</td><td> <b>(11)</b></td></tr></table>
<p>where A can be viewed as a correction factor, E<sub>a</sub> plays a role similar to activation energy in chemical reactions and R is the gas constant. Plot a graph of the obtained values and fit to (11). Hint: it is possible to turn (11) into a linear graph. </p>
<p> Analyze the resulting fit with comments on the significance and the validity of the made assumption. </p>
</li>
<li><h2>Concentric cylinder viscosimeter</h2>
<h2>Apparatus</h2>
<ul>
<li>Vacuum Pump Oil</li>
<li>Viscosity Measuring Instrument</li>
<li>Vernier Caliper</li>
<li>Meter Stick</li>
<li>Photo Gate Interface</li>
<li>2 Photo Gate Sensors</li>
<li>Oscilloscope</li>
<li>Mass</li>
<li>1 Extension Cord</li>
<li>Heater</li>
</ul>

<p>This instrument is used to find the viscosity of vacuum pump oil and to determine its variation with temperature. The inner drum in the viscosimeter is mounted on two bearings and is free to rotate under a torque, L, supplied by a mass, m, falling through a given height. The torque is given by L = mgk where k is the radius of the pulley around which the string supporting the falling mass m, is wound. If the mass falls a distance s, in time t, the angular velocity w is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn12.png|60px|center]]
</p>
</td><td> <b>(12)</b></td></tr></table>

<p>Therefore, Equation (9) becomes</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn13.png|160px|center]]
</p>
</td><td> <b>(13)</b></td></tr></table>
<p>or</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn14.png|70px|center]]
</p>
</td><td> <b>(14)</b></td></tr></table>
<p>where c is a constant</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn15.png|160px|center]]
</p>
</td><td> <b>(15)</b></td></tr></table>
<p>To find the absolute value of η, remove the centre cylinder (being careful not to damage the supporting bearings) and measure all pertinent dimensions. Re-assemble the apparatus and fill the container with oil until the level is about 1.5 cm above the lower surface of the inner cylinder. Measure the length l using a vernier calliper (notice that l is not simply the height of the oil level). Place the apparatus on the edge of the wall mount so that the suspended mass has an unrestricted fall of several feet.</p>
<table width=300 align=center><td>
<p align=justify>[[File:Vis-fig4v2.JPG|400px|border|center]]
<b>Figure 4 -</b> Viscosimeter.
<br clear=right>
</p>
</td></table>
<p>Record the time required for a mass m suspended from the string (wound around the pulley) to descend through a given distance. You will find that the downward velocity is not constant over the total drop but changes rapidly over the first few centimetres. It is therefore necessary to neglect the first few centimetres of drop, i.e., the stopwatch must be started once the descending mass is moving with constant velocity. Make several measurements of the time required to fall through a distance, s, and obtain an average time. Make a series of five determinations keeping the mass constant and increasing the effective length of the cylinder by adding liquid. The last observation should be made with the apparatus filled to the top of the inner cylinder.</p>

<p> To collect the data, we can observe the transit of the masses through the two [[media:Visc_sensor.jpg|sensor gates]] on an [[media:Visc_scope.jpg|oscilloscope]]. With the oscilloscope set for a long timebase, and the sensor box outputs attached to one channel, you will notice the abrupt signal change when anything passes through either sensor gate. You will need to use the "Run/Stop" button on the top right of oscilloscope to stop the trace from scrolling off the screen after the data is collected so you can measure or save the data. The scope can be used as a precise measuring tool for the time require for the mass to fall a particular distance.</p>

<p>With the level of the liquid at the top of the inner cylinder, take a series of observations of time of descent vs. mass.</p>
<p>To analyze your data, plot two graphs: one of the length '''l''' vs. time '''t''', and the other of the time, '''t''', vs. reciprocal mass'''1 /m'''. The first graph will give the value of the length correction '''e'''. The second graph should be a straight line of slope '''mt'''. '''η''' can then be obtained from Equation (12).</p>
<p>To determine the variation of viscosity with temperature, repeat the above fixed mass measurement at several temperatures. Be sure to allow for expansion of the liquid when the temperature is increased. Compare the obtained results to the previous section.</p>
</ol>
<h1>Units</h1>
<p>Give your results in both CGS and MKS units. <b>The values of the viscosities are available from handbooks</b>, and are usually quoted in centipoises (compare your results).</p>

<h1>Questions and Discussion</h1>
<p>Why does the moment of inertia of the rotating cylinder not enter the analysis of the problem? Discuss the sign of the length correction. Explain what the important sources of imprecision are, and elaborate on the importance of the constants e and c.</p>

<h1>References</h1>
<p>Any intermediate-level classical mechanics text, e.g.,</p>
<ol>
<li>K. Symon, ''Mechanics'', 3rd ed., pp. 345 ff.</li>
<li>R. Feynman, Leighton, Sands,''Lectures on Physics'', vol. II, chapter 41.</li>
</ol>

Main Page/PHYS 3220/Viscosity

2015-07-23T17:55:56Z

Mgeorge:

<h1>Viscosity</h1>

<p>The purpose of this experiment is to determine the viscosity of a liquid and to find the variation of viscosity with temperature.</p>

<h1>Theory</h1>
<p>When a solid is subject to a shearing stress it deforms until the internal elastic forces of the solid exactly balance the external forces. Thus a finite force applied to a solid produces a finite deformation. If a similar force is applied to a liquid, however, the deformation increases indefinitely (the liquid flows). The flow can be imagined as the movement of adjacent layers over one another. The Newtonian friction caused by the relative motion between adjacent layers retards the flow and is called viscosity. This frictional force was assumed by Newton to be proportional to the velocity gradient perpendicular to the direction of the motion of the fluid, i.e., to dv/dr.</p>
<p>Consider an element of volume in a fluid as shown in the following diagram (ref. 1)</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig1v2.JPG|300px|border|center]]
<b>Figure 1 -</b> Element of volume of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>The shearing stress on this element of volume is F/A where F is the force on the upper surface and A is the cross section. <b>The shear is given by the ratio between the lateral displacement between the two surfaces to the separation between the surfaces.</b> Thus, if we assume that the upper surface is moving with a velocity, dv, greater than that of the lower surface, the amount of shear occurring in unit time is dv/dr. The coefficient of viscosity or simply <b>viscosity</b> is defined as follows (for streamline motion).</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn1.png|220px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>The c.g.s. unit of viscosity is called the <b>poise</b>; it represents the viscosity of a substance that acquires a unit velocity gradient under the influence of a shearing stress of 1 dyne/cm2.</p>
<p>One method of measuring viscosity is to determine the flow of a liquid through a capillary tube. Let us consider how to measure viscosity in this way.</p>

<p>When a liquid flows through a narrow tube so that each particle moves parallel to the axis of the tube with constant velocity, the motion is said to be regular or <b>streamlined</b>. In this case, liquid in contact with the walls is at rest while the velocity is a maximum at the centre of the tube.</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig2v2.JPG|300px|border|center]]
<b>Figure 2 -</b> Streamlined flow of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>We imagine the liquid as being divided up into a number of thin cylindrical shells, each shell sliding on the other. The viscous drag, f, per square cm. of one layer on the other is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn2.png|90px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>For a cylinder of radius, a, length l, through which a liquid is flowing under a pressure differential, p, the total viscous drag balances the force due to the pressure difference.</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn3.png|180px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Assuming that there is no radial flow the pressure is constant over any given cross-section.
At r = a, v = 0, while at r = r, v = u, thus</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn5.png|100px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>Thus, by measuring the quantity of liquid transferred through a capillary tube per unit time subject to a specific pressure difference, the viscosity of the liquid may be determined.</p>
<p>The viscosity may also be determined using the concentric cylinder viscosimeter. Consider a liquid between two concentric cylinders as illustrated in Figure 3. </p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig3v2.JPG|300px|border|center]]
<b>Figure 3 -</b> Liquid between concentric cylinders.
<br clear=right>
</p>
</td></table>

<p>The outer cylinder is moving with angular velocity wB. If the liquid adheres to the walls of the cylinder, a shearing takes place in which concentric cylindrical layers of the liquid slip over each other with the angular velocity w increasing progressively from zero at the stationary cylinder to wB at the rotating one. Now, the rate of shear is given as</p>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn6.png|250px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>Only the second term produces a viscosity effect, since a velocity gradient is needed to have relative slipping of layers and the associated friction. Thus, </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn7.png|130px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>

<p>If a torque L is applied to the rotating cylinder, (see Figure 3), the tangential force at the boundary SS' equals L/r and integration over r from A to B yields</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn8.png|140px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Note that this formula is also valid if the inner cylinder is rotated with angular velocity w<sub>B</sub> while the outer cylinder is held stationary.</p>
<p>For cylinders closed at either end, equation (8) is modified to take into account the friction between the two ends of the cylinders according to</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn9.png|160px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<h1>Method</h1>

<ol>
<li> <h2>Capillary tube.</h2>
<h3>Apparatus</h3>
<ul>
<li>Capillary Tube</li>
<li>2 Beakers (600ml and 400 ml)</li>
<li>Bunsen Burner Stand</li>
<li>Thermometer</li>
</ul>

<p>For the determination of viscosity by use of a capillary tube we need to know the pressure p, this is given by </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn10.png|80px|center]]
</p>
</td><td> <b>(10)</b></td></tr></table>
<p>where
<ul><li>h = height of water column</li>
<li>d = density of water</li>
<li>g = acceleration due to gravity = 981 cm/sec<sup>2</sup></li>
</ul></p>
<p>The capillary tube is positioned at the bottom of a beaker, allowing for the monitoring of the water level. Using regular tap water, fill the beaker until the water starts going through the capillary tube. (Notice that the height of the water column is changing as water flows out, it is up to you to figure out a solution, consult your T.A. for ideas). </p>
<p>Measure the flow rate through the tube for various p values and calculate the viscosity. How does the result compare with the accepted viscosity value for water? Would you expect the same result if the capillary tube was slightly wider? Much wider? Comment on the reason for any potential discrepancies.</p>
<p>Record the water temperature. Repeat the measurements for at least two other temperatures. Assuming that the dependence resembles the “Arrhenius” equation </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn11.png|110px|center]]
</p>
</td><td> <b>(11)</b></td></tr></table>
<p>where A can be viewed as a correction factor, E<sub>a</sub> plays a role similar to activation energy in chemical reactions and R is the gas constant. Plot a graph of the obtained values and fit to (11). Hint: it is possible to turn (11) into a linear graph. </p>
<p> Analyze the resulting fit with comments on the significance and the validity of the made assumption. </p>
</li>
<li><h2>Concentric cylinder viscosimeter</h2>
<h2>Apparatus</h2>
<ul>
<li>Vacuum Pump Oil</li>
<li>Viscosity Measuring Instrument</li>
<li>Vernier Caliper</li>
<li>Meter Stick</li>
<li>Photo Gate Interface</li>
<li>2 Photo Gate Sensors</li>
<li>Oscilloscope</li>
<li>Mass</li>
<li>1 Extension Cord</li>
<li>Heater</li>
</ul>

<p>This instrument is used to find the viscosity of vacuum pump oil and to determine its variation with temperature. The inner drum in the viscosimeter is mounted on two bearings and is free to rotate under a torque, L, supplied by a mass, m, falling through a given height. The torque is given by L = mgk where k is the radius of the pulley around which the string supporting the falling mass m, is wound. If the mass falls a distance s, in time t, the angular velocity w is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn12.png|60px|center]]
</p>
</td><td> <b>(12)</b></td></tr></table>

<p>Therefore, Equation (9) becomes</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn13.png|160px|center]]
</p>
</td><td> <b>(13)</b></td></tr></table>
<p>or</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn14.png|70px|center]]
</p>
</td><td> <b>(14)</b></td></tr></table>
<p>where c is a constant</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn15.png|160px|center]]
</p>
</td><td> <b>(15)</b></td></tr></table>
<p>To find the absolute value of η, remove the centre cylinder (being careful not to damage the supporting bearings) and measure all pertinent dimensions. Re-assemble the apparatus and fill the container with oil until the level is about 1.5 cm above the lower surface of the inner cylinder. Measure the length l using a vernier calliper (notice that l is not simply the height of the oil level). Place the apparatus on the edge of the wall mount so that the suspended mass has an unrestricted fall of several feet.</p>
<table width=300 align=center><td>
<p align=justify>[[File:Vis-fig4v2.JPG|400px|border|center]]
<b>Figure 4 -</b> Viscosimeter.
<br clear=right>
</p>
</td></table>
<p>Record the time required for a mass m suspended from the string (wound around the pulley) to descend through a given distance. You will find that the downward velocity is not constant over the total drop but changes rapidly over the first few centimetres. It is therefore necessary to neglect the first few centimetres of drop, i.e., the stopwatch must be started once the descending mass is moving with constant velocity. Make several measurements of the time required to fall through a distance, s, and obtain an average time. Make a series of five determinations keeping the mass constant and increasing the effective length of the cylinder by adding liquid. The last observation should be made with the apparatus filled to the top of the inner cylinder.</p>

<p> To collect the data, we can observe the transit of the masses through the two [[media:Visc_sensor.jpg|sensor gates]] on an [[media:Visc_scope.jpg|oscilloscope]]. With the oscilloscope set for a long timebase, and the sensor box outputs attached to one channel, you will notice the abrupt signal change when anything passes through either sensor gate. You will need to use the "Run/Stop" button on the top right of oscilloscope to stop the trace from scrolling off the screen after the data is collected so you can measure or save the data. The scope can be used as a precise measuring tool for the time require for the mass to fall a particular distance.</p>

<p>With the level of the liquid at the top of the inner cylinder, take a series of observations of time of descent vs. mass.</p>
<p>To analyze your data, plot two graphs: one of the length '''l''' vs. time '''t''', and the other of the time, '''t''', vs. reciprocal mass'''1 /m'''. The first graph will give the value of the length correction '''e'''. The second graph should be a straight line of slope '''mt'''. '''η''' can then be obtained from Equation (12).</p>
<p>To determine the variation of viscosity with temperature, repeat the above fixed mass measurement at several temperatures. Be sure to allow for expansion of the liquid when the temperature is increased. Compare the obtained results to the previous section.</p>
</ol>
<h1>Units</h1>
<p>Give your results in both CGS and MKS units. <b>The values of the viscosities are available from handbooks</b>, and are usually quoted in centipoises (compare your results).</p>

<h1>Questions and Discussion</h1>
<p>Why does the moment of inertia of the rotating cylinder not enter the analysis of the problem? Discuss the sign of the length correction. Explain what the important sources of imprecision are, and elaborate on the importance of the constants e and c.</p>

<h1>References</h1>
<p>Any intermediate-level classical mechanics text, e.g.,</p>
<ol>
<li>K. Symon, ''Mechanics'', 3rd ed., pp. 345 ff.</li>
<li>R. Feynman, Leighton, Sands,''Lectures on Physics'', vol. II, chapter 41.</li>
</ol>

Main Page/PHYS 3220/Viscosity

2015-07-23T17:55:04Z

Mgeorge:

<h1>Viscosity</h1>

<p>The purpose of this experiment is to determine the viscosity of a liquid and to find the variation of viscosity with temperature.</p>

<h1>Theory</h1>
<p>When a solid is subject to a shearing stress it deforms until the internal elastic forces of the solid exactly balance the external forces. Thus a finite force applied to a solid produces a finite deformation. If a similar force is applied to a liquid, however, the deformation increases indefinitely (the liquid flows). The flow can be imagined as the movement of adjacent layers over one another. The Newtonian friction caused by the relative motion between adjacent layers retards the flow and is called viscosity. This frictional force was assumed by Newton to be proportional to the velocity gradient perpendicular to the direction of the motion of the fluid, i.e., to dv/dr.</p>
<p>Consider an element of volume in a fluid as shown in the following diagram (ref. 1)</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig1v2.JPG|300px|border|center]]
<b>Figure 1 -</b> Element of volume of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>The shearing stress on this element of volume is F/A where F is the force on the upper surface and A is the cross section. <b>The shear is given by the ratio between the lateral displacement between the two surfaces to the separation between the surfaces.</b> Thus, if we assume that the upper surface is moving with a velocity, dv, greater than that of the lower surface, the amount of shear occurring in unit time is dv/dr. The coefficient of viscosity or simply <b>viscosity</b> is defined as follows (for streamline motion).</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn1.png|220px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>The c.g.s. unit of viscosity is called the <b>poise</b>; it represents the viscosity of a substance that acquires a unit velocity gradient under the influence of a shearing stress of 1 dyne/cm2.</p>
<p>One method of measuring viscosity is to determine the flow of a liquid through a capillary tube. Let us consider how to measure viscosity in this way.</p>

<p>When a liquid flows through a narrow tube so that each particle moves parallel to the axis of the tube with constant velocity, the motion is said to be regular or <b>streamlined</b>. In this case, liquid in contact with the walls is at rest while the velocity is a maximum at the centre of the tube.</p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig2v2.JPG|300px|border|center]]
<b>Figure 2 -</b> Streamlined flow of a liquid in a tube.
<br clear=right>
</p>
</td></table>

<p>We imagine the liquid as being divided up into a number of thin cylindrical shells, each shell sliding on the other. The viscous drag, f, per square cm. of one layer on the other is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn2.png|90px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>

<p>For a cylinder of radius, a, length l, through which a liquid is flowing under a pressure differential, p, the total viscous drag balances the force due to the pressure difference.</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn3.png|180px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>

<p>Assuming that there is no radial flow the pressure is constant over any given cross-section.
At r = a, v = 0, while at r = r, v = u, thus</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn5.png|100px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>

<p>Thus, by measuring the quantity of liquid transferred through a capillary tube per unit time subject to a specific pressure difference, the viscosity of the liquid may be determined.</p>
<p>The viscosity may also be determined using the concentric cylinder viscosimeter. Consider a liquid between two concentric cylinders as illustrated in Figure 3. </p>

<table width=400 align=center><td>
<p align=justify>[[File:Vis-fig3v2.JPG|300px|border|center]]
<b>Figure 3 -</b> Liquid between concentric cylinders.
<br clear=right>
</p>
</td></table>

<p>The outer cylinder is moving with angular velocity wB. If the liquid adheres to the walls of the cylinder, a shearing takes place in which concentric cylindrical layers of the liquid slip over each other with the angular velocity w increasing progressively from zero at the stationary cylinder to wB at the rotating one. Now, the rate of shear is given as</p>

<p>The quantity of liquid, Q, flowing through the tube per second is given by Poiseuille's formula,</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn6.png|250px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p>Only the second term produces a viscosity effect, since a velocity gradient is needed to have relative slipping of layers and the associated friction. Thus, </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn7.png|130px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>

<p>If a torque L is applied to the rotating cylinder, (see Figure 3), the tangential force at the boundary SS' equals L/r and integration over r from A to B yields</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn8.png|140px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Note that this formula is also valid if the inner cylinder is rotated with angular velocity w<sub>B</sub> while the outer cylinder is held stationary.</p>
<p>For cylinders closed at either end, equation (8) is modified to take into account the friction between the two ends of the cylinders according to</p>

<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn9.png|160px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<h1>Method</h1>

<ol>
<li> <h2>Capillary tube.</h2>
<h2>Apparatus</h2>
<ul>
<li>Capillary Tube</li>
<li>2 Beakers (600ml and 400 ml)</li>
<li>Bunsen Burner Stand</li>
<li>Thermometer</li>
</ul>

<p>For the determination of viscosity by use of a capillary tube we need to know the pressure p, this is given by </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn10.png|80px|center]]
</p>
</td><td> <b>(10)</b></td></tr></table>
<p>where
<ul><li>h = height of water column</li>
<li>d = density of water</li>
<li>g = acceleration due to gravity = 981 cm/sec<sup>2</sup></li>
</ul></p>
<p>The capillary tube is positioned at the bottom of a beaker, allowing for the monitoring of the water level. Using regular tap water, fill the beaker until the water starts going through the capillary tube. (Notice that the height of the water column is changing as water flows out, it is up to you to figure out a solution, consult your T.A. for ideas). </p>
<p>Measure the flow rate through the tube for various p values and calculate the viscosity. How does the result compare with the accepted viscosity value for water? Would you expect the same result if the capillary tube was slightly wider? Much wider? Comment on the reason for any potential discrepancies.</p>
<p>Record the water temperature. Repeat the measurements for at least two other temperatures. Assuming that the dependence resembles the “Arrhenius” equation </p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn11.png|110px|center]]
</p>
</td><td> <b>(11)</b></td></tr></table>
<p>where A can be viewed as a correction factor, E<sub>a</sub> plays a role similar to activation energy in chemical reactions and R is the gas constant. Plot a graph of the obtained values and fit to (11). Hint: it is possible to turn (11) into a linear graph. </p>
<p> Analyze the resulting fit with comments on the significance and the validity of the made assumption. </p>
</li>
<li><h2>Concentric cylinder viscosimeter</h2>
<h2>Apparatus</h2>
<ul>
<li>Vacuum Pump Oil</li>
<li>Viscosity Measuring Instrument</li>
<li>Vernier Caliper</li>
<li>Meter Stick</li>
<li>Photo Gate Interface</li>
<li>2 Photo Gate Sensors</li>
<li>Oscilloscope</li>
<li>Mass</li>
<li>1 Extension Cord</li>
<li>Heater</li>
</ul>

<p>This instrument is used to find the viscosity of vacuum pump oil and to determine its variation with temperature. The inner drum in the viscosimeter is mounted on two bearings and is free to rotate under a torque, L, supplied by a mass, m, falling through a given height. The torque is given by L = mgk where k is the radius of the pulley around which the string supporting the falling mass m, is wound. If the mass falls a distance s, in time t, the angular velocity w is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn12.png|60px|center]]
</p>
</td><td> <b>(12)</b></td></tr></table>

<p>Therefore, Equation (9) becomes</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn13.png|160px|center]]
</p>
</td><td> <b>(13)</b></td></tr></table>
<p>or</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn14.png|70px|center]]
</p>
</td><td> <b>(14)</b></td></tr></table>
<p>where c is a constant</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Vis-eqn15.png|160px|center]]
</p>
</td><td> <b>(15)</b></td></tr></table>
<p>To find the absolute value of η, remove the centre cylinder (being careful not to damage the supporting bearings) and measure all pertinent dimensions. Re-assemble the apparatus and fill the container with oil until the level is about 1.5 cm above the lower surface of the inner cylinder. Measure the length l using a vernier calliper (notice that l is not simply the height of the oil level). Place the apparatus on the edge of the wall mount so that the suspended mass has an unrestricted fall of several feet.</p>
<table width=300 align=center><td>
<p align=justify>[[File:Vis-fig4v2.JPG|400px|border|center]]
<b>Figure 4 -</b> Viscosimeter.
<br clear=right>
</p>
</td></table>
<p>Record the time required for a mass m suspended from the string (wound around the pulley) to descend through a given distance. You will find that the downward velocity is not constant over the total drop but changes rapidly over the first few centimetres. It is therefore necessary to neglect the first few centimetres of drop, i.e., the stopwatch must be started once the descending mass is moving with constant velocity. Make several measurements of the time required to fall through a distance, s, and obtain an average time. Make a series of five determinations keeping the mass constant and increasing the effective length of the cylinder by adding liquid. The last observation should be made with the apparatus filled to the top of the inner cylinder.</p>

<p> To collect the data, we can observe the transit of the masses through the two [[media:Visc_sensor.jpg|sensor gates]] on an [[media:Visc_scope.jpg|oscilloscope]]. With the oscilloscope set for a long timebase, and the sensor box outputs attached to one channel, you will notice the abrupt signal change when anything passes through either sensor gate. You will need to use the "Run/Stop" button on the top right of oscilloscope to stop the trace from scrolling off the screen after the data is collected so you can measure or save the data. The scope can be used as a precise measuring tool for the time require for the mass to fall a particular distance.</p>

<p>With the level of the liquid at the top of the inner cylinder, take a series of observations of time of descent vs. mass.</p>
<p>To analyze your data, plot two graphs: one of the length '''l''' vs. time '''t''', and the other of the time, '''t''', vs. reciprocal mass'''1 /m'''. The first graph will give the value of the length correction '''e'''. The second graph should be a straight line of slope '''mt'''. '''η''' can then be obtained from Equation (12).</p>
<p>To determine the variation of viscosity with temperature, repeat the above fixed mass measurement at several temperatures. Be sure to allow for expansion of the liquid when the temperature is increased. Compare the obtained results to the previous section.</p>
</ol>
<h1>Units</h1>
<p>Give your results in both CGS and MKS units. <b>The values of the viscosities are available from handbooks</b>, and are usually quoted in centipoises (compare your results).</p>

<h1>Questions and Discussion</h1>
<p>Why does the moment of inertia of the rotating cylinder not enter the analysis of the problem? Discuss the sign of the length correction. Explain what the important sources of imprecision are, and elaborate on the importance of the constants e and c.</p>

<h1>References</h1>
<p>Any intermediate-level classical mechanics text, e.g.,</p>
<ol>
<li>K. Symon, ''Mechanics'', 3rd ed., pp. 345 ff.</li>
<li>R. Feynman, Leighton, Sands,''Lectures on Physics'', vol. II, chapter 41.</li>
</ol>

Main Page/PHYS 4210/Sonoluminescence

2015-06-02T17:44:52Z

Mgeorge:

<h1>Sonoluminescence and Blackbody Radiation</h1>

<p>Sonoluminescence is the process by which a gas bubble trapped at the antinode of an ultrasonic standing wave emits visible radiation. This strange phenomenon will be the platform on which 3-dimensional standing waves and black-body radiation will be investigated.</p>

<h1>Introduction</h1>

<p>Single bubble sonoluminescence, hereafter abbreviated SL, was discovered in the late 1980's and has since received a great deal of attention. This remarkable process involves, at its core, trapping a gas bubble at a sonic antinode location in a resonance mode of a cell. The exact geometry of the cell is not important but it is necessary that there exist a spatial pressure gradient in order for the bubble to be positionaly stabilized. In the presence of the alternating cycle of acoustic pressure the bubble expands and collapses. When the amplitude of the pressure becomes large enough the collapse of the bubble enters a new regime in which the radius collapses to its hard core limit heating up the gas contents inside and emitting a very brief but
copious amount of light. This light can be seen with the unaided eye.
Although the emission mechanism along with a number of other properties
of SL are still not fully understood, the basic hydrodynamic equations
governing the gross motion of the bubble have been around for quite
some time and do accurately describe over 99.9% of the bubble's motion.
The Rayleigh Plessett equation shown below has been used extensively to
describe the motion of the bubble in its many regimes.
Eq (1)</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT1.png|600px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>
<p>with the boundary condition at the fluid gas interface given by</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT2.png|220px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>
<p>and the use of a van der Waals hard core ''a'' in the ideal gas law to give a gas pressure ''P<sub>g</sub>''</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT3.png|170px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>
<p>where ''R'' is the bubble radius, ''c'' is the speed of sound in the fluid, ρ is the density, η is the viscosity, σ is the surface tension, ''P<sub>a</sub>'' is the acoustic pressure, and ''P<sub>o</sub>'' is the ambient pressure.</p>
<p>A graph of the bubble radius and driving amplitude as a function of
time is shown in Figure 1. This graph was generated by a numerical
integration of Eq. 1.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_fig1.png|500px|border|center]]
<b>Figure 1 </b>
<br clear=right>
</p>
</td></table>

<p>Among the first properties that were observed was the very brief nature of the light emission. Initial measurements using high speed photomultiplier tubes placed an upper limit of 50 ps on the emission
time. Recent measurements using time correlated photon counting
techniques have shown a diversity of emission times depending on the
gas contents, with some emission times as long as 350 ps. Another
observed property was the enhancement of the light emission by the
doping of the water with a small concentration of noble gases such as
Ne, Ar, and Xe. </p>

<p>The phenomenon of sonoluminescence is not the focus of your investigation. The details presented above were only presented in order to provide you with some context for what you will be observing. The exact mechanism of the light emission is not fully understood, for more details see M.P. Brenner 2002.<ref> M.P. Brenner,<i>"Single-bubble sonoluminescence"</i>, [http://rmp.aps.org/abstract/RMP/v74/i2/p425_1 Rev. Mod. Phys., '''74''', 425 (2002)]</ref> For the purpose of this experiment, we will assume that the light emitted from the sonoluminescence is due to blackbody radiation.</p>.

<h3> 3D Standing Waves</h3>
<p>Waves in three-dimensional space can be described by the wave equation.</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p> In a rectilinear coordinate system, the solution to the wave equation has the following form:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn2.png|220px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>
<p> Where X,Y, and Z have the familiar forms:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn3.png|130px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p> The ''cos'' is chosen when the boundary is a pressure release (i.e. not rigid) and the ''sin'' is chosen when the boundary is rigid and the velocity at the boundary must be zero. The eigen frequencies are given by:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT7.png|330px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>
<p> where ''v'' is the speed of sound in the medium, ''n<sub>x</sub>'',''n<sub>y</sub>'', and ''n<sub>z</sub>'' are the orders of the mode, and ''L<sub>x</sub>'', ''L<sub>y</sub>'', and ''L<sub>z</sub>'' are the physical dimensions of the cavity.</p>

<h3> The Ultrasonic Horn</h3>
<p>The ultrasonic horn is used to deliver acoustic power to the volume of water. Internally, the horn contains a series of annular shaped disc transducers which are bolted into its base. The basic structure and shape of the horn is designed to efficiently couple the pressure waves generated from the transducers to the narrow stem of the horn. All of the transducers are the same. They consist of a ceramic material which has been prepared in such a manner as to have a permanent polarization. In other words,there are specialized capacitors. As a charged is placed across this capacitor there is a force generated across the ends, and the capacitor wants to separate. Since the transducers are compressed, this repulsive force does not physically expand the disc but does produce dynamic pressure. As the charge across the transducer is reversed, there is now an attractive force which results in a negative pressure amplitude. The capacitance of the particular tranducers used is 11 nF. In order to efficiently couple electrical power into the transducers, it is advantageous to connect an inductor in series to achieve electrical resonance as given by the formula:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn0.png|100px|center]]
</p>
</td><td> </td></tr></table>
<p>The particular ultrasonic horn used has components which make it tuned for a frequency from 25kHz to 27kHz. Outside of those ranges, the acoustic energy available in the horn is strongly attenuated.</p>

<h3> The Cell</h3>
<p> The cell is a plastic container onto which is epoxied a small ceramic transducer that serves as a microphone. Since this transducer is not compressed small fluctuations in its diameter produce a measurable signal. By attaching this transducer to the bottom of the cell, one can easily detect when the pressure is the cell is in resonance by looking for large amplitude sine waves on an oscilloscope at the ultrasonic frequency. The cell is provided with a black shroud which has a circular opening on one side which allows light from the SL to enter the photomultiplier tube, but minimized stray light from entering the PMT.</p>

<h3> The Photomultiplier Tube</h3>
<p> A photomultiplier tube (PMT) is a device which coverts one incident photon into a large pulse of electrons which can then be read out on an oscilloscope. The photon passes through the glass enclosure of the PMT and liberates an electron from a coated surface, this electron is then accelerated by static electric fields into dynode 1, and this initial electron frees many more electrons from the surface. This bunch of electrons then accelerates into dynode 2 freeing a yet larger bunch of electrons. This process continues many times such that even one incident photon can produce a measurable number of electrons at the output. '''A PMT is a very sensitive optical detector.''' Due to the high sensitivity, having too many photons entering the PMT can damage the device, and this should be avoided. Even with the black shroud covering the cell, you should not apply power to the PMT without also shutting of the room lights.</p>
<p>The Fluke 412B power supply will provide the high voltage required to bias the dynodes of the PMT. Typically, the PMT should be run at around '''-1000''' V. The PMT will output a negative going pulse with a sharp rise time and a relatively slow fall time. The amplitude of this pulse is related to the number of photons hitting the PMT during a particular pulse. In this experiment, the effect of Sonoluminescence only occurs once during an acoustic wave period, hence, the SL bubbles is flashing at around 27 kHz. '''The PMT will output pulses synchronized with the acoustic frequency whose amplitude is related to the brightness of the sonoluminescence.'''</p>

<h2>BlackBody Radiation</h2>
<p> For a full treatment of blackbody radiation, refer to any Modern Physics textbook. All matter with a temperature greater than 0 Kelvin emits electromagnetic radiation. This common phenomenon is noticed in everyday life when you look inside your toaster, use a stove-top, or bask in the sunshine. The spectrum of emitted radiation depends on the properties of the particular material, and the temperature as described by Planck's Formula:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn_planck.png|280px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Related to Planck's formula is the Wien Displacment Law, which describes the wavelength at which the most energy is being emitted.</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn_wien.png|250px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<p> Using the above formula, one can determine that the Sun, which appears yellow (~500nm) has a surface temperature of around 5800 K.
In this experiment, you will be amazed to see the SL bubbles emitting blue/white radiation, suggesting a much higher temperature!</p>

<h1> Procedure</h1>

<h2> Required Components</h2>
<ol>
<li>Flask</li>
<li>De-ionized Water</li>
<li>Vacuum Pump</li>
<li>[[Media:HP33258.JPG|HP33258 Function Generator]]</li>
<li>[[Media:TDS2014B.JPG|TDS2014B Digital Oscilloscope]]</li>
<li>[[Media:SL100B.JPG|SL100B Sonoluminescence Control Box]]</li>
<li>[[Media:SL100B2.JPG|Ultrasonic Horn]]</li>
<li>[[Media:SLPMT1P28.JPG|1P28 PhotoMultiplier Tube]]</li>
<li>[[Media:SLOpticalLenses.JPG|Various Optical Filters]]</li>
<li>[[Media:SLPowerSupply.JPG|HV Power Supply]]</li>
</ol>

<h2> Degas the water</h2>
<p> In order for the water to support a sonoluminescence bubble it is necessary for the water to be partially degassed. To do this, start with approximately 600 mL of deionized water in a flask, place a rubber stopper in the top of the flask with a tube passing though it, then attach a roughing pump to end of the tube. The boiling point of water is reduced to below room temperature if the pressure in the flask can be reduced below ~25 torr. The vacuum pump you are using can easily achieve that. You will notice rapid bubbling of the water inside the flask after the pump is turned on. For the first 20 minutes, have the flask on the magnetic stirring platform, and set the Stirrer Control to > 80. After 20 minutes, place the flask into a bath of ice water (if available) and continue pumping for a further 10 minutes, as the sonoluminescence effect is greater when the liquid is at lower temperatures.<ref> G.E. Vazquez and S.J. Putterman, "<i>Temperature and Pressure Dependence of Sonoluminescence</i>", [http://prl.aps.org/abstract/PRL/v85/i14/p3037_1 Phys. Rev. Lett., '''85''', 3037 (1999)]</ref> </p>

<table width=400 align=center><td>
<p align=justify>[[File:SL_fig_degas.png|400px|border|center]]
<b>Figure 2 -</b> Degassing the water.
<br clear=right>
</p>
</td></table>

<p>Once the degassing procedure is complete, turn off the vacuum pump, and slowly open the pressure relief wave. Then, ''gently'' pour the water into the cell being careful not to introduce more bubbles. Fill the cell to the correct level to allow for standing waves whose frequency is near 25-27kHz for the [1,1,2] mode (Hint: solve Eqn. 7 for <i>L<sub>z</sub></i>.)</p>

<h2>Electrical Connections</h2>
<p> The basic setup for the experiment is shown in Figure 3. The acoustic frequency is provided by a 1 V<sub>pp</sub> sine wave from the HP3325A synthesizer/function generator. The appropriate resonance frequency, as determined by cell geometry is around 26kHz.
This sine wave is then amplifier by the SL100B control box, and fed into the ultrasonic horn. To electronically view the effects of sonoluminescence, the output of cell transducer is put to Channel A of the oscilloscope, Channel B of the scope should be the High Freq. Output of the transducer. This High Freq. Output filters the cell transducer signal with 150 kHz high-pass filter since the effect of a trapped bubble is to cause a high frequency response. There are two connections made from the Sonoluminescence SL100B to the cell box- a multi-pin power/control cable, and cell transducer input using coaxial connector.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_setupB.png|500px|border|center]]
<b>Figure 3 -</b> Electrical Connections.
<br clear=right>
</p>
</td></table>

<h2> Observe trapped bubbles and Sonoluminescence</h2>
<p> Once the water is added, place the black shroud around the cell. Lower the ultrasonic horn into the cell such that the tip of the horn is 5mm - 10mm below the surface of the water. Set the drive amplitude of the ultrasonic horn to 3/4 of maximum. The frequency of the function generator should be adjusted in steps of 10Hz to maximize the signal picked up by the cell transducer. Note that you will observe an electrical resonance centered at 25.9kHz, where the maximum signal picked up on the cell transducer will be about 4 as read off of the analog scale on the SL100 unit. This is not standing wave resonance. The standing wave resonance will have a much high amplitude signal (as high as 12) on the analog meter. Depending on the amount you have filled, you may observe modes other than the [1,1,2] mode as you tune the frequency of the function generator. When you are near the resonance you will see the amplitude rapidly increase as you adjust the frequency, and then begin to decrease as you continue increasing the frequency. ''Record and plot this relationship between applied frequency and cell transducer voltage.'' Typically, the quality factor of the resonance should be on the order of 100 to 200. </p>
<p> Set the frequency to the peak of acoustic resonance, the drive amplitude should be adjusted such that the analog meter reads around 4 and so that the output of the cell transducer is an undistorted sine wave. The conditions for SL to occur are very precise- it the drive amplitude is set to low, then no SL will be observed, if the drive amplitude is set too high (greater than 5) then the trapped bubbles jitter and and are lost from the trap.</p>
<p> Now that there is an acoustic standing wave inside of the cell, you can attempt to trap a bubble. To introduce a bubble into water, submerge the heater filament such that it is near (but not touching) the bottom of the cell. Briefly press the boiler button on the SL100B, this will boil a tiny amount of water near the filament creating small bubbles. With the room lights on, you should then be able to see a bubble held stationary in the cell at the location of an antinode. Now, turn off the room lights except for a small desk lamp. You may be able to see the bubble giving off a blueish-white light. If you cannot see the sonoluminescence, try increasing the drive amplitude- keeping an eye on the oscilloscope to ensure a bubble is still trapped. If you loose the bubble from the trap, you will need to load the trap again with another bubble.</p>

<table width=800 align=center><tr>
<td>
<p align=justify>[[File:SL_nobubble.png|350px|border|center]]
<b>Figure 4a -</b> No evidence of trapped bubble on oscilloscope.
<br clear=right>
</p>
</td>
<td width=100>
</td>
<td>
<p align=justify>[[File:SL_bubble.png|350px|border|center]]
<b>Figure 4b -</b> Clear evidence of trapped bubble on oscilloscope.
<br clear=right>
</p>
</td>
</tr></table>

<h3>Questions</h3>
<ol>
<li>Draw the a sketch illustrating the [1,1,3] mode inside of the cell, and indicate possible locations to trap bubbles.</li>
<li>What level would you have to fill to for the [1,1,1] mode?</li>
<li>Draw the a sketch illustrating the [1,1,2] mode inside of the cell, and indicate possible locations to trap bubbles.</li>
</ol>

<h2> Detect the Sonoluminescence using a PMT </h2>
<p>With the HV power supply still switched off, adjust the height of the PMT and bring it close to the opening in back of the black shroud. Once you have a trapped, sonoluminescence bubble, close the front viewing flap. Turn on a small desk lamp, and shut off the main room light. Turn on the HV power supply to about 1000V and look on the oscilloscope for pulses synchronous with the acoustic radiation. If the peak of the pulses exceeds 500mV amplitude, reduce the operating voltage of the PMT by 50V.</p>

<h3> Saving scope traces</h3>
<p>There is a Labview program called "TDS2014B read scope" on the desktop. You can use this to save all four scope traces to a tab delimited file (.txt) or a comma sperated file (.csv). The files will be saved in the directory "ScopeData" on the desktop.<b>Please email yourselves the resulting files. DO NOT USE YOUR USB KEY IN THE LAB COMPUTERS.</b> (We'd like to keep the lab computers as virus-free as possible.).</p>

<h3>Questions</h3>
<ol>
<li>Sketch or present the waveforms of for the cell transducer output and "High Freq. Output" when a bubble is trapped.</li>
<li> Determine the rise time and decay time of the PMT pulses.</li>
<li> What distribution of peak heights do you observe?</li>
</ol>

<h2>Determine the Temperature of the SL </h2>
<p> To determine the temperature of the SL bubble, we will use the assumption that the amplitude of the peak output from the PMT is proportional to the number of photons input to the PMT. There are some important factors which first need to be considered. </p>

<ul>
<li><p> The SL bubble is inside of the cell, and light has to travel half of the cell thickness through water. The absorption of water as a function of wavelength is:</p>
<table width=300 align=center><td>
<p align=justify>[[File:SL_abs_water.png|300px|border|center]]
<b>Figure 5 -</b> Absorption of Water <ref> R. C. Smith and K. S. Baker, "<i>Optical properties of the clearest natural waters (200-800nm)</i>", [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-20-2-177 Appl. Opt., '''20''', 177 (1981)].</ref><ref>R. M. Pope and E. S. Fry, "<i>Absorption spectrum (380-700nm) of pure
water. II. Integrating cavity measurements</i>", [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-33-8710 Appl. Opt., '''36''', 8710 (1997)]. </ref>
<br clear=right>
</p>
</td></table>
<p> A table of the above values is given here: [[Media:Water_Absorption.xls| Water_Absorption.xls]], [[Media:Water_Absorption.txt| Water_Absorption.txt]] </p></li>
<li> The photons from the SL must then pass through the plastic cell wall. For the purpose of our measurement, we will assume that all wavelengths pass through equally. Comment on the suitability of this assumption for light in the visible spectrum.</li>
<li><p> The PMT does not respond equally for all wavelengths. The efficiency as a function of wavelength is shown below.</p>
<table width=300 align=center><td>
<p align=justify>[[File:SL_eff_pmt.png|300px|border|center]]
<b>Figure 6 -</b> PMT Efficiency.<ref> Taken from [[Media:H1P28_datasheet.pdf|Hamamatsu 1P28 datasheet]].</ref>.
<br clear=right>
</p>
</td></table>
<p> A table of the above values is given here:[[Media:SL_PMT_efficiency.xls| SL_PMT_efficiency.xls]], [[Media:SL_PMT_efficiency2.txt| SL_PMT_efficiency.txt]] </p></li>
</ul>

<p> In addition to the above effects, you are provided with four optical filters which you will use to attenuate the SL in a controlled way. The transmission properties of each of the four filters is given in the figure below.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_filters.png|500px|border|center]]
<b>Figure 7 -</b> Filter transmission as function of wavelength.
<br clear=right>
</p>
</td></table>

<p> A table of the above values is given here:[[Media:SL_filters.xls| SL_filters.xls]], [[Media:SL_filters.txt| SL_filters.txt]] </p>

<p><b> It is your task to determine the temperature the sonoluminescence bubble based on the ratio of the average pulse heights of the PMT signals when the various filters are in place, taking into account the known absorptions and efficiencies of the system. Please carefully explain the algorithm for your analysis in your write-up. </b></p>

<h1> References</h1>
<references/>

Main Page/PHYS 4210/Sonoluminescence

2015-06-02T14:01:20Z

Mgeorge:

<h1>Sonoluminescence and Blackbody Radiation</h1>

<math> gfhgf</math>
<p>Sonoluminescence is the process by which a gas bubble trapped at the antinode of an ultrasonic standing wave emits visible radiation. This strange phenomenon will be the platform on which 3-dimensional standing waves and black-body radiation will be investigated.</p>

<h1>Introduction</h1>

<p>Single bubble sonoluminescence, hereafter abbreviated SL, was discovered in the late 1980's and has since received a great deal of attention. This remarkable process involves, at its core, trapping a gas bubble at a sonic antinode location in a resonance mode of a cell. The exact geometry of the cell is not important but it is necessary that there exist a spatial pressure gradient in order for the bubble to be positionaly stabilized. In the presence of the alternating cycle of acoustic pressure the bubble expands and collapses. When the amplitude of the pressure becomes large enough the collapse of the bubble enters a new regime in which the radius collapses to its hard core limit heating up the gas contents inside and emitting a very brief but
copious amount of light. This light can be seen with the unaided eye.
Although the emission mechanism along with a number of other properties
of SL are still not fully understood, the basic hydrodynamic equations
governing the gross motion of the bubble have been around for quite
some time and do accurately describe over 99.9% of the bubble's motion.
The Rayleigh Plessett equation shown below has been used extensively to
describe the motion of the bubble in its many regimes.
Eq (1)</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT1.png|600px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>
<p>with the boundary condition at the fluid gas interface given by</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT2.png|220px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>
<p>and the use of a van der Waals hard core ''a'' in the ideal gas law to give a gas pressure ''P<sub>g</sub>''</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT3.png|170px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>
<p>where ''R'' is the bubble radius, ''c'' is the speed of sound in the fluid, ρ is the density, η is the viscosity, σ is the surface tension, ''P<sub>a</sub>'' is the acoustic pressure, and ''P<sub>o</sub>'' is the ambient pressure.</p>
<p>A graph of the bubble radius and driving amplitude as a function of
time is shown in Figure 1. This graph was generated by a numerical
integration of Eq. 1.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_fig1.png|500px|border|center]]
<b>Figure 1 </b>
<br clear=right>
</p>
</td></table>

<p>Among the first properties that were observed was the very brief nature of the light emission. Initial measurements using high speed photomultiplier tubes placed an upper limit of 50 ps on the emission
time. Recent measurements using time correlated photon counting
techniques have shown a diversity of emission times depending on the
gas contents, with some emission times as long as 350 ps. Another
observed property was the enhancement of the light emission by the
doping of the water with a small concentration of noble gases such as
Ne, Ar, and Xe. </p>

<p>The phenomenon of sonoluminescence is not the focus of your investigation. The details presented above were only presented in order to provide you with some context for what you will be observing. The exact mechanism of the light emission is not fully understood, for more details see M.P. Brenner 2002.<ref> M.P. Brenner,<i>"Single-bubble sonoluminescence"</i>, [http://rmp.aps.org/abstract/RMP/v74/i2/p425_1 Rev. Mod. Phys., '''74''', 425 (2002)]</ref> For the purpose of this experiment, we will assume that the light emitted from the sonoluminescence is due to blackbody radiation.</p>.

<h3> 3D Standing Waves</h3>
<p>Waves in three-dimensional space can be described by the wave equation.</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p> In a rectilinear coordinate system, the solution to the wave equation has the following form:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn2.png|220px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>
<p> Where X,Y, and Z have the familiar forms:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn3.png|130px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p> The ''cos'' is chosen when the boundary is a pressure release (i.e. not rigid) and the ''sin'' is chosen when the boundary is rigid and the velocity at the boundary must be zero. The eigen frequencies are given by:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT7.png|330px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>
<p> where ''v'' is the speed of sound in the medium, ''n<sub>x</sub>'',''n<sub>y</sub>'', and ''n<sub>z</sub>'' are the orders of the mode, and ''L<sub>x</sub>'', ''L<sub>y</sub>'', and ''L<sub>z</sub>'' are the physical dimensions of the cavity.</p>

<h3> The Ultrasonic Horn</h3>
<p>The ultrasonic horn is used to deliver acoustic power to the volume of water. Internally, the horn contains a series of annular shaped disc transducers which are bolted into its base. The basic structure and shape of the horn is designed to efficiently couple the pressure waves generated from the transducers to the narrow stem of the horn. All of the transducers are the same. They consist of a ceramic material which has been prepared in such a manner as to have a permanent polarization. In other words,there are specialized capacitors. As a charged is placed across this capacitor there is a force generated across the ends, and the capacitor wants to separate. Since the transducers are compressed, this repulsive force does not physically expand the disc but does produce dynamic pressure. As the charge across the transducer is reversed, there is now an attractive force which results in a negative pressure amplitude. The capacitance of the particular tranducers used is 11 nF. In order to efficiently couple electrical power into the transducers, it is advantageous to connect an inductor in series to achieve electrical resonance as given by the formula:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn0.png|100px|center]]
</p>
</td><td> </td></tr></table>
<p>The particular ultrasonic horn used has components which make it tuned for a frequency from 25kHz to 27kHz. Outside of those ranges, the acoustic energy available in the horn is strongly attenuated.</p>

<h3> The Cell</h3>
<p> The cell is a plastic container onto which is epoxied a small ceramic transducer that serves as a microphone. Since this transducer is not compressed small fluctuations in its diameter produce a measurable signal. By attaching this transducer to the bottom of the cell, one can easily detect when the pressure is the cell is in resonance by looking for large amplitude sine waves on an oscilloscope at the ultrasonic frequency. The cell is provided with a black shroud which has a circular opening on one side which allows light from the SL to enter the photomultiplier tube, but minimized stray light from entering the PMT.</p>

<h3> The Photomultiplier Tube</h3>
<p> A photomultiplier tube (PMT) is a device which coverts one incident photon into a large pulse of electrons which can then be read out on an oscilloscope. The photon passes through the glass enclosure of the PMT and liberates an electron from a coated surface, this electron is then accelerated by static electric fields into dynode 1, and this initial electron frees many more electrons from the surface. This bunch of electrons then accelerates into dynode 2 freeing a yet larger bunch of electrons. This process continues many times such that even one incident photon can produce a measurable number of electrons at the output. '''A PMT is a very sensitive optical detector.''' Due to the high sensitivity, having too many photons entering the PMT can damage the device, and this should be avoided. Even with the black shroud covering the cell, you should not apply power to the PMT without also shutting of the room lights.</p>
<p>The Fluke 412B power supply will provide the high voltage required to bias the dynodes of the PMT. Typically, the PMT should be run at around '''-1000''' V. The PMT will output a negative going pulse with a sharp rise time and a relatively slow fall time. The amplitude of this pulse is related to the number of photons hitting the PMT during a particular pulse. In this experiment, the effect of Sonoluminescence only occurs once during an acoustic wave period, hence, the SL bubbles is flashing at around 27 kHz. '''The PMT will output pulses synchronized with the acoustic frequency whose amplitude is related to the brightness of the sonoluminescence.'''</p>

<h2>BlackBody Radiation</h2>
<p> For a full treatment of blackbody radiation, refer to any Modern Physics textbook. All matter with a temperature greater than 0 Kelvin emits electromagnetic radiation. This common phenomenon is noticed in everyday life when you look inside your toaster, use a stove-top, or bask in the sunshine. The spectrum of emitted radiation depends on the properties of the particular material, and the temperature as described by Planck's Formula:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn_planck.png|280px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Related to Planck's formula is the Wien Displacment Law, which describes the wavelength at which the most energy is being emitted.</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn_wien.png|250px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<p> Using the above formula, one can determine that the Sun, which appears yellow (~500nm) has a surface temperature of around 5800 K.
In this experiment, you will be amazed to see the SL bubbles emitting blue/white radiation, suggesting a much higher temperature!</p>

<h1> Procedure</h1>

<h2> Required Components</h2>
<ol>
<li>Flask</li>
<li>De-ionized Water</li>
<li>Vacuum Pump</li>
<li>[[Media:HP33258.JPG|HP33258 Function Generator]]</li>
<li>[[Media:TDS2014B.JPG|TDS2014B Digital Oscilloscope]]</li>
<li>[[Media:SL100B.JPG|SL100B Sonoluminescence Control Box]]</li>
<li>[[Media:SL100B2.JPG|Ultrasonic Horn]]</li>
<li>[[Media:SLPMT1P28.JPG|1P28 PhotoMultiplier Tube]]</li>
<li>[[Media:SLOpticalLenses.JPG|Various Optical Filters]]</li>
<li>[[Media:SLPowerSupply.JPG|HV Power Supply]]</li>
</ol>

<h2> Degas the water</h2>
<p> In order for the water to support a sonoluminescence bubble it is necessary for the water to be partially degassed. To do this, start with approximately 600 mL of deionized water in a flask, place a rubber stopper in the top of the flask with a tube passing though it, then attach a roughing pump to end of the tube. The boiling point of water is reduced to below room temperature if the pressure in the flask can be reduced below ~25 torr. The vacuum pump you are using can easily achieve that. You will notice rapid bubbling of the water inside the flask after the pump is turned on. For the first 20 minutes, have the flask on the magnetic stirring platform, and set the Stirrer Control to > 80. After 20 minutes, place the flask into a bath of ice water (if available) and continue pumping for a further 10 minutes, as the sonoluminescence effect is greater when the liquid is at lower temperatures.<ref> G.E. Vazquez and S.J. Putterman, "<i>Temperature and Pressure Dependence of Sonoluminescence</i>", [http://prl.aps.org/abstract/PRL/v85/i14/p3037_1 Phys. Rev. Lett., '''85''', 3037 (1999)]</ref> </p>

<table width=400 align=center><td>
<p align=justify>[[File:SL_fig_degas.png|400px|border|center]]
<b>Figure 2 -</b> Degassing the water.
<br clear=right>
</p>
</td></table>

<p>Once the degassing procedure is complete, turn off the vacuum pump, and slowly open the pressure relief wave. Then, ''gently'' pour the water into the cell being careful not to introduce more bubbles. Fill the cell to the correct level to allow for standing waves whose frequency is near 25-27kHz for the [1,1,2] mode (Hint: solve Eqn. 7 for <i>L<sub>z</sub></i>.)</p>

<h2>Electrical Connections</h2>
<p> The basic setup for the experiment is shown in Figure 3. The acoustic frequency is provided by a 1 V<sub>pp</sub> sine wave from the HP3325A synthesizer/function generator. The appropriate resonance frequency, as determined by cell geometry is around 26kHz.
This sine wave is then amplifier by the SL100B control box, and fed into the ultrasonic horn. To electronically view the effects of sonoluminescence, the output of cell transducer is put to Channel A of the oscilloscope, Channel B of the scope should be the High Freq. Output of the transducer. This High Freq. Output filters the cell transducer signal with 150 kHz high-pass filter since the effect of a trapped bubble is to cause a high frequency response. There are two connections made from the Sonoluminescence SL100B to the cell box- a multi-pin power/control cable, and cell transducer input using coaxial connector.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_setupB.png|500px|border|center]]
<b>Figure 3 -</b> Electrical Connections.
<br clear=right>
</p>
</td></table>

<h2> Observe trapped bubbles and Sonoluminescence</h2>
<p> Once the water is added, place the black shroud around the cell. Lower the ultrasonic horn into the cell such that the tip of the horn is 5mm - 10mm below the surface of the water. Set the drive amplitude of the ultrasonic horn to 3/4 of maximum. The frequency of the function generator should be adjusted in steps of 10Hz to maximize the signal picked up by the cell transducer. Note that you will observe an electrical resonance centered at 25.9kHz, where the maximum signal picked up on the cell transducer will be about 4 as read off of the analog scale on the SL100 unit. This is not standing wave resonance. The standing wave resonance will have a much high amplitude signal (as high as 12) on the analog meter. Depending on the amount you have filled, you may observe modes other than the [1,1,2] mode as you tune the frequency of the function generator. When you are near the resonance you will see the amplitude rapidly increase as you adjust the frequency, and then begin to decrease as you continue increasing the frequency. ''Record and plot this relationship between applied frequency and cell transducer voltage.'' Typically, the quality factor of the resonance should be on the order of 100 to 200. </p>
<p> Set the frequency to the peak of acoustic resonance, the drive amplitude should be adjusted such that the analog meter reads around 4 and so that the output of the cell transducer is an undistorted sine wave. The conditions for SL to occur are very precise- it the drive amplitude is set to low, then no SL will be observed, if the drive amplitude is set too high (greater than 5) then the trapped bubbles jitter and and are lost from the trap.</p>
<p> Now that there is an acoustic standing wave inside of the cell, you can attempt to trap a bubble. To introduce a bubble into water, submerge the heater filament such that it is near (but not touching) the bottom of the cell. Briefly press the boiler button on the SL100B, this will boil a tiny amount of water near the filament creating small bubbles. With the room lights on, you should then be able to see a bubble held stationary in the cell at the location of an antinode. Now, turn off the room lights except for a small desk lamp. You may be able to see the bubble giving off a blueish-white light. If you cannot see the sonoluminescence, try increasing the drive amplitude- keeping an eye on the oscilloscope to ensure a bubble is still trapped. If you loose the bubble from the trap, you will need to load the trap again with another bubble.</p>

<table width=800 align=center><tr>
<td>
<p align=justify>[[File:SL_nobubble.png|350px|border|center]]
<b>Figure 4a -</b> No evidence of trapped bubble on oscilloscope.
<br clear=right>
</p>
</td>
<td width=100>
</td>
<td>
<p align=justify>[[File:SL_bubble.png|350px|border|center]]
<b>Figure 4b -</b> Clear evidence of trapped bubble on oscilloscope.
<br clear=right>
</p>
</td>
</tr></table>

<h3>Questions</h3>
<ol>
<li>Draw the a sketch illustrating the [1,1,3] mode inside of the cell, and indicate possible locations to trap bubbles.</li>
<li>What level would you have to fill to for the [1,1,1] mode?</li>
<li>Draw the a sketch illustrating the [1,1,2] mode inside of the cell, and indicate possible locations to trap bubbles.</li>
</ol>

<h2> Detect the Sonoluminescence using a PMT </h2>
<p>With the HV power supply still switched off, adjust the height of the PMT and bring it close to the opening in back of the black shroud. Once you have a trapped, sonoluminescence bubble, close the front viewing flap. Turn on a small desk lamp, and shut off the main room light. Turn on the HV power supply to about 1000V and look on the oscilloscope for pulses synchronous with the acoustic radiation. If the peak of the pulses exceeds 500mV amplitude, reduce the operating voltage of the PMT by 50V.</p>

<h3> Saving scope traces</h3>
<p>There is a Labview program called "TDS2014B read scope" on the desktop. You can use this to save all four scope traces to a tab delimited file (.txt) or a comma sperated file (.csv). The files will be saved in the directory "ScopeData" on the desktop.<b>Please email yourselves the resulting files. DO NOT USE YOUR USB KEY IN THE LAB COMPUTERS.</b> (We'd like to keep the lab computers as virus-free as possible.).</p>

<h3>Questions</h3>
<ol>
<li>Sketch or present the waveforms of for the cell transducer output and "High Freq. Output" when a bubble is trapped.</li>
<li> Determine the rise time and decay time of the PMT pulses.</li>
<li> What distribution of peak heights do you observe?</li>
</ol>

<h2>Determine the Temperature of the SL </h2>
<p> To determine the temperature of the SL bubble, we will use the assumption that the amplitude of the peak output from the PMT is proportional to the number of photons input to the PMT. There are some important factors which first need to be considered. </p>

<ul>
<li><p> The SL bubble is inside of the cell, and light has to travel half of the cell thickness through water. The absorption of water as a function of wavelength is:</p>
<table width=300 align=center><td>
<p align=justify>[[File:SL_abs_water.png|300px|border|center]]
<b>Figure 5 -</b> Absorption of Water <ref> R. C. Smith and K. S. Baker, "<i>Optical properties of the clearest natural waters (200-800nm)</i>", [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-20-2-177 Appl. Opt., '''20''', 177 (1981)].</ref><ref>R. M. Pope and E. S. Fry, "<i>Absorption spectrum (380-700nm) of pure
water. II. Integrating cavity measurements</i>", [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-33-8710 Appl. Opt., '''36''', 8710 (1997)]. </ref>
<br clear=right>
</p>
</td></table>
<p> A table of the above values is given here: [[Media:Water_Absorption.xls| Water_Absorption.xls]], [[Media:Water_Absorption.txt| Water_Absorption.txt]] </p></li>
<li> The photons from the SL must then pass through the plastic cell wall. For the purpose of our measurement, we will assume that all wavelengths pass through equally. Comment on the suitability of this assumption for light in the visible spectrum.</li>
<li><p> The PMT does not respond equally for all wavelengths. The efficiency as a function of wavelength is shown below.</p>
<table width=300 align=center><td>
<p align=justify>[[File:SL_eff_pmt.png|300px|border|center]]
<b>Figure 6 -</b> PMT Efficiency.<ref> Taken from [[Media:H1P28_datasheet.pdf|Hamamatsu 1P28 datasheet]].</ref>.
<br clear=right>
</p>
</td></table>
<p> A table of the above values is given here:[[Media:SL_PMT_efficiency.xls| SL_PMT_efficiency.xls]], [[Media:SL_PMT_efficiency2.txt| SL_PMT_efficiency.txt]] </p></li>
</ul>

<p> In addition to the above effects, you are provided with four optical filters which you will use to attenuate the SL in a controlled way. The transmission properties of each of the four filters is given in the figure below.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_filters.png|500px|border|center]]
<b>Figure 7 -</b> Filter transmission as function of wavelength.
<br clear=right>
</p>
</td></table>

<p> A table of the above values is given here:[[Media:SL_filters.xls| SL_filters.xls]], [[Media:SL_filters.txt| SL_filters.txt]] </p>

<p><b> It is your task to determine the temperature the sonoluminescence bubble based on the ratio of the average pulse heights of the PMT signals when the various filters are in place, taking into account the known absorptions and efficiencies of the system. Please carefully explain the algorithm for your analysis in your write-up. </b></p>

<h1> References</h1>
<references/>

Main Page/PHYS 4210/Sonoluminescence

2015-06-02T13:49:48Z

Mgeorge:

Main Page/PHYS 4210/Sonoluminescence

2015-06-02T13:49:34Z

Mgeorge:

<h1>Sonoluminescence and Blackbody Radiation</h1>

<math>\pi^2 <\math>
<p>Sonoluminescence is the process by which a gas bubble trapped at the antinode of an ultrasonic standing wave emits visible radiation. This strange phenomenon will be the platform on which 3-dimensional standing waves and black-body radiation will be investigated.</p>

<h1>Introduction</h1>

<p>Single bubble sonoluminescence, hereafter abbreviated SL, was discovered in the late 1980's and has since received a great deal of attention. This remarkable process involves, at its core, trapping a gas bubble at a sonic antinode location in a resonance mode of a cell. The exact geometry of the cell is not important but it is necessary that there exist a spatial pressure gradient in order for the bubble to be positionaly stabilized. In the presence of the alternating cycle of acoustic pressure the bubble expands and collapses. When the amplitude of the pressure becomes large enough the collapse of the bubble enters a new regime in which the radius collapses to its hard core limit heating up the gas contents inside and emitting a very brief but
copious amount of light. This light can be seen with the unaided eye.
Although the emission mechanism along with a number of other properties
of SL are still not fully understood, the basic hydrodynamic equations
governing the gross motion of the bubble have been around for quite
some time and do accurately describe over 99.9% of the bubble's motion.
The Rayleigh Plessett equation shown below has been used extensively to
describe the motion of the bubble in its many regimes.
Eq (1)</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT1.png|600px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>
<p>with the boundary condition at the fluid gas interface given by</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT2.png|220px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>
<p>and the use of a van der Waals hard core ''a'' in the ideal gas law to give a gas pressure ''P<sub>g</sub>''</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT3.png|170px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>
<p>where ''R'' is the bubble radius, ''c'' is the speed of sound in the fluid, ρ is the density, η is the viscosity, σ is the surface tension, ''P<sub>a</sub>'' is the acoustic pressure, and ''P<sub>o</sub>'' is the ambient pressure.</p>
<p>A graph of the bubble radius and driving amplitude as a function of
time is shown in Figure 1. This graph was generated by a numerical
integration of Eq. 1.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_fig1.png|500px|border|center]]
<b>Figure 1 </b>
<br clear=right>
</p>
</td></table>

<p>Among the first properties that were observed was the very brief nature of the light emission. Initial measurements using high speed photomultiplier tubes placed an upper limit of 50 ps on the emission
time. Recent measurements using time correlated photon counting
techniques have shown a diversity of emission times depending on the
gas contents, with some emission times as long as 350 ps. Another
observed property was the enhancement of the light emission by the
doping of the water with a small concentration of noble gases such as
Ne, Ar, and Xe. </p>

<p>The phenomenon of sonoluminescence is not the focus of your investigation. The details presented above were only presented in order to provide you with some context for what you will be observing. The exact mechanism of the light emission is not fully understood, for more details see M.P. Brenner 2002.<ref> M.P. Brenner,<i>"Single-bubble sonoluminescence"</i>, [http://rmp.aps.org/abstract/RMP/v74/i2/p425_1 Rev. Mod. Phys., '''74''', 425 (2002)]</ref> For the purpose of this experiment, we will assume that the light emitted from the sonoluminescence is due to blackbody radiation.</p>.

<h3> 3D Standing Waves</h3>
<p>Waves in three-dimensional space can be described by the wave equation.</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT4.png|120px|center]]
</p>
</td><td> <b>(4)</b></td></tr></table>

<p> In a rectilinear coordinate system, the solution to the wave equation has the following form:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn2.png|220px|center]]
</p>
</td><td> <b>(5)</b></td></tr></table>
<p> Where X,Y, and Z have the familiar forms:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn3.png|130px|center]]
</p>
</td><td> <b>(6)</b></td></tr></table>

<p> The ''cos'' is chosen when the boundary is a pressure release (i.e. not rigid) and the ''sin'' is chosen when the boundary is rigid and the velocity at the boundary must be zero. The eigen frequencies are given by:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqnINT7.png|330px|center]]
</p>
</td><td> <b>(7)</b></td></tr></table>
<p> where ''v'' is the speed of sound in the medium, ''n<sub>x</sub>'',''n<sub>y</sub>'', and ''n<sub>z</sub>'' are the orders of the mode, and ''L<sub>x</sub>'', ''L<sub>y</sub>'', and ''L<sub>z</sub>'' are the physical dimensions of the cavity.</p>

<h3> The Ultrasonic Horn</h3>
<p>The ultrasonic horn is used to deliver acoustic power to the volume of water. Internally, the horn contains a series of annular shaped disc transducers which are bolted into its base. The basic structure and shape of the horn is designed to efficiently couple the pressure waves generated from the transducers to the narrow stem of the horn. All of the transducers are the same. They consist of a ceramic material which has been prepared in such a manner as to have a permanent polarization. In other words,there are specialized capacitors. As a charged is placed across this capacitor there is a force generated across the ends, and the capacitor wants to separate. Since the transducers are compressed, this repulsive force does not physically expand the disc but does produce dynamic pressure. As the charge across the transducer is reversed, there is now an attractive force which results in a negative pressure amplitude. The capacitance of the particular tranducers used is 11 nF. In order to efficiently couple electrical power into the transducers, it is advantageous to connect an inductor in series to achieve electrical resonance as given by the formula:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn0.png|100px|center]]
</p>
</td><td> </td></tr></table>
<p>The particular ultrasonic horn used has components which make it tuned for a frequency from 25kHz to 27kHz. Outside of those ranges, the acoustic energy available in the horn is strongly attenuated.</p>

<h3> The Cell</h3>
<p> The cell is a plastic container onto which is epoxied a small ceramic transducer that serves as a microphone. Since this transducer is not compressed small fluctuations in its diameter produce a measurable signal. By attaching this transducer to the bottom of the cell, one can easily detect when the pressure is the cell is in resonance by looking for large amplitude sine waves on an oscilloscope at the ultrasonic frequency. The cell is provided with a black shroud which has a circular opening on one side which allows light from the SL to enter the photomultiplier tube, but minimized stray light from entering the PMT.</p>

<h3> The Photomultiplier Tube</h3>
<p> A photomultiplier tube (PMT) is a device which coverts one incident photon into a large pulse of electrons which can then be read out on an oscilloscope. The photon passes through the glass enclosure of the PMT and liberates an electron from a coated surface, this electron is then accelerated by static electric fields into dynode 1, and this initial electron frees many more electrons from the surface. This bunch of electrons then accelerates into dynode 2 freeing a yet larger bunch of electrons. This process continues many times such that even one incident photon can produce a measurable number of electrons at the output. '''A PMT is a very sensitive optical detector.''' Due to the high sensitivity, having too many photons entering the PMT can damage the device, and this should be avoided. Even with the black shroud covering the cell, you should not apply power to the PMT without also shutting of the room lights.</p>
<p>The Fluke 412B power supply will provide the high voltage required to bias the dynodes of the PMT. Typically, the PMT should be run at around '''-1000''' V. The PMT will output a negative going pulse with a sharp rise time and a relatively slow fall time. The amplitude of this pulse is related to the number of photons hitting the PMT during a particular pulse. In this experiment, the effect of Sonoluminescence only occurs once during an acoustic wave period, hence, the SL bubbles is flashing at around 27 kHz. '''The PMT will output pulses synchronized with the acoustic frequency whose amplitude is related to the brightness of the sonoluminescence.'''</p>

<h2>BlackBody Radiation</h2>
<p> For a full treatment of blackbody radiation, refer to any Modern Physics textbook. All matter with a temperature greater than 0 Kelvin emits electromagnetic radiation. This common phenomenon is noticed in everyday life when you look inside your toaster, use a stove-top, or bask in the sunshine. The spectrum of emitted radiation depends on the properties of the particular material, and the temperature as described by Planck's Formula:</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn_planck.png|280px|center]]
</p>
</td><td> <b>(8)</b></td></tr></table>

<p>Related to Planck's formula is the Wien Displacment Law, which describes the wavelength at which the most energy is being emitted.</p>
<table width=200 align=center>
<tr><td>
<p align=justify>[[File:SL_eqn_wien.png|250px|center]]
</p>
</td><td> <b>(9)</b></td></tr></table>

<p> Using the above formula, one can determine that the Sun, which appears yellow (~500nm) has a surface temperature of around 5800 K.
In this experiment, you will be amazed to see the SL bubbles emitting blue/white radiation, suggesting a much higher temperature!</p>

<h1> Procedure</h1>

<h2> Required Components</h2>
<ol>
<li>Flask</li>
<li>De-ionized Water</li>
<li>Vacuum Pump</li>
<li>[[Media:HP33258.JPG|HP33258 Function Generator]]</li>
<li>[[Media:TDS2014B.JPG|TDS2014B Digital Oscilloscope]]</li>
<li>[[Media:SL100B.JPG|SL100B Sonoluminescence Control Box]]</li>
<li>[[Media:SL100B2.JPG|Ultrasonic Horn]]</li>
<li>[[Media:SLPMT1P28.JPG|1P28 PhotoMultiplier Tube]]</li>
<li>[[Media:SLOpticalLenses.JPG|Various Optical Filters]]</li>
<li>[[Media:SLPowerSupply.JPG|HV Power Supply]]</li>
</ol>

<h2> Degas the water</h2>
<p> In order for the water to support a sonoluminescence bubble it is necessary for the water to be partially degassed. To do this, start with approximately 600 mL of deionized water in a flask, place a rubber stopper in the top of the flask with a tube passing though it, then attach a roughing pump to end of the tube. The boiling point of water is reduced to below room temperature if the pressure in the flask can be reduced below ~25 torr. The vacuum pump you are using can easily achieve that. You will notice rapid bubbling of the water inside the flask after the pump is turned on. For the first 20 minutes, have the flask on the magnetic stirring platform, and set the Stirrer Control to > 80. After 20 minutes, place the flask into a bath of ice water (if available) and continue pumping for a further 10 minutes, as the sonoluminescence effect is greater when the liquid is at lower temperatures.<ref> G.E. Vazquez and S.J. Putterman, "<i>Temperature and Pressure Dependence of Sonoluminescence</i>", [http://prl.aps.org/abstract/PRL/v85/i14/p3037_1 Phys. Rev. Lett., '''85''', 3037 (1999)]</ref> </p>

<table width=400 align=center><td>
<p align=justify>[[File:SL_fig_degas.png|400px|border|center]]
<b>Figure 2 -</b> Degassing the water.
<br clear=right>
</p>
</td></table>

<p>Once the degassing procedure is complete, turn off the vacuum pump, and slowly open the pressure relief wave. Then, ''gently'' pour the water into the cell being careful not to introduce more bubbles. Fill the cell to the correct level to allow for standing waves whose frequency is near 25-27kHz for the [1,1,2] mode (Hint: solve Eqn. 7 for <i>L<sub>z</sub></i>.)</p>

<h2>Electrical Connections</h2>
<p> The basic setup for the experiment is shown in Figure 3. The acoustic frequency is provided by a 1 V<sub>pp</sub> sine wave from the HP3325A synthesizer/function generator. The appropriate resonance frequency, as determined by cell geometry is around 26kHz.
This sine wave is then amplifier by the SL100B control box, and fed into the ultrasonic horn. To electronically view the effects of sonoluminescence, the output of cell transducer is put to Channel A of the oscilloscope, Channel B of the scope should be the High Freq. Output of the transducer. This High Freq. Output filters the cell transducer signal with 150 kHz high-pass filter since the effect of a trapped bubble is to cause a high frequency response. There are two connections made from the Sonoluminescence SL100B to the cell box- a multi-pin power/control cable, and cell transducer input using coaxial connector.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_setupB.png|500px|border|center]]
<b>Figure 3 -</b> Electrical Connections.
<br clear=right>
</p>
</td></table>

<h2> Observe trapped bubbles and Sonoluminescence</h2>
<p> Once the water is added, place the black shroud around the cell. Lower the ultrasonic horn into the cell such that the tip of the horn is 5mm - 10mm below the surface of the water. Set the drive amplitude of the ultrasonic horn to 3/4 of maximum. The frequency of the function generator should be adjusted in steps of 10Hz to maximize the signal picked up by the cell transducer. Note that you will observe an electrical resonance centered at 25.9kHz, where the maximum signal picked up on the cell transducer will be about 4 as read off of the analog scale on the SL100 unit. This is not standing wave resonance. The standing wave resonance will have a much high amplitude signal (as high as 12) on the analog meter. Depending on the amount you have filled, you may observe modes other than the [1,1,2] mode as you tune the frequency of the function generator. When you are near the resonance you will see the amplitude rapidly increase as you adjust the frequency, and then begin to decrease as you continue increasing the frequency. ''Record and plot this relationship between applied frequency and cell transducer voltage.'' Typically, the quality factor of the resonance should be on the order of 100 to 200. </p>
<p> Set the frequency to the peak of acoustic resonance, the drive amplitude should be adjusted such that the analog meter reads around 4 and so that the output of the cell transducer is an undistorted sine wave. The conditions for SL to occur are very precise- it the drive amplitude is set to low, then no SL will be observed, if the drive amplitude is set too high (greater than 5) then the trapped bubbles jitter and and are lost from the trap.</p>
<p> Now that there is an acoustic standing wave inside of the cell, you can attempt to trap a bubble. To introduce a bubble into water, submerge the heater filament such that it is near (but not touching) the bottom of the cell. Briefly press the boiler button on the SL100B, this will boil a tiny amount of water near the filament creating small bubbles. With the room lights on, you should then be able to see a bubble held stationary in the cell at the location of an antinode. Now, turn off the room lights except for a small desk lamp. You may be able to see the bubble giving off a blueish-white light. If you cannot see the sonoluminescence, try increasing the drive amplitude- keeping an eye on the oscilloscope to ensure a bubble is still trapped. If you loose the bubble from the trap, you will need to load the trap again with another bubble.</p>

<table width=800 align=center><tr>
<td>
<p align=justify>[[File:SL_nobubble.png|350px|border|center]]
<b>Figure 4a -</b> No evidence of trapped bubble on oscilloscope.
<br clear=right>
</p>
</td>
<td width=100>
</td>
<td>
<p align=justify>[[File:SL_bubble.png|350px|border|center]]
<b>Figure 4b -</b> Clear evidence of trapped bubble on oscilloscope.
<br clear=right>
</p>
</td>
</tr></table>

<h3>Questions</h3>
<ol>
<li>Draw the a sketch illustrating the [1,1,3] mode inside of the cell, and indicate possible locations to trap bubbles.</li>
<li>What level would you have to fill to for the [1,1,1] mode?</li>
<li>Draw the a sketch illustrating the [1,1,2] mode inside of the cell, and indicate possible locations to trap bubbles.</li>
</ol>

<h2> Detect the Sonoluminescence using a PMT </h2>
<p>With the HV power supply still switched off, adjust the height of the PMT and bring it close to the opening in back of the black shroud. Once you have a trapped, sonoluminescence bubble, close the front viewing flap. Turn on a small desk lamp, and shut off the main room light. Turn on the HV power supply to about 1000V and look on the oscilloscope for pulses synchronous with the acoustic radiation. If the peak of the pulses exceeds 500mV amplitude, reduce the operating voltage of the PMT by 50V.</p>

<h3> Saving scope traces</h3>
<p>There is a Labview program called "TDS2014B read scope" on the desktop. You can use this to save all four scope traces to a tab delimited file (.txt) or a comma sperated file (.csv). The files will be saved in the directory "ScopeData" on the desktop.<b>Please email yourselves the resulting files. DO NOT USE YOUR USB KEY IN THE LAB COMPUTERS.</b> (We'd like to keep the lab computers as virus-free as possible.).</p>

<h3>Questions</h3>
<ol>
<li>Sketch or present the waveforms of for the cell transducer output and "High Freq. Output" when a bubble is trapped.</li>
<li> Determine the rise time and decay time of the PMT pulses.</li>
<li> What distribution of peak heights do you observe?</li>
</ol>

<h2>Determine the Temperature of the SL </h2>
<p> To determine the temperature of the SL bubble, we will use the assumption that the amplitude of the peak output from the PMT is proportional to the number of photons input to the PMT. There are some important factors which first need to be considered. </p>

<ul>
<li><p> The SL bubble is inside of the cell, and light has to travel half of the cell thickness through water. The absorption of water as a function of wavelength is:</p>
<table width=300 align=center><td>
<p align=justify>[[File:SL_abs_water.png|300px|border|center]]
<b>Figure 5 -</b> Absorption of Water <ref> R. C. Smith and K. S. Baker, "<i>Optical properties of the clearest natural waters (200-800nm)</i>", [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-20-2-177 Appl. Opt., '''20''', 177 (1981)].</ref><ref>R. M. Pope and E. S. Fry, "<i>Absorption spectrum (380-700nm) of pure
water. II. Integrating cavity measurements</i>", [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-36-33-8710 Appl. Opt., '''36''', 8710 (1997)]. </ref>
<br clear=right>
</p>
</td></table>
<p> A table of the above values is given here: [[Media:Water_Absorption.xls| Water_Absorption.xls]], [[Media:Water_Absorption.txt| Water_Absorption.txt]] </p></li>
<li> The photons from the SL must then pass through the plastic cell wall. For the purpose of our measurement, we will assume that all wavelengths pass through equally. Comment on the suitability of this assumption for light in the visible spectrum.</li>
<li><p> The PMT does not respond equally for all wavelengths. The efficiency as a function of wavelength is shown below.</p>
<table width=300 align=center><td>
<p align=justify>[[File:SL_eff_pmt.png|300px|border|center]]
<b>Figure 6 -</b> PMT Efficiency.<ref> Taken from [[Media:H1P28_datasheet.pdf|Hamamatsu 1P28 datasheet]].</ref>.
<br clear=right>
</p>
</td></table>
<p> A table of the above values is given here:[[Media:SL_PMT_efficiency.xls| SL_PMT_efficiency.xls]], [[Media:SL_PMT_efficiency2.txt| SL_PMT_efficiency.txt]] </p></li>
</ul>

<p> In addition to the above effects, you are provided with four optical filters which you will use to attenuate the SL in a controlled way. The transmission properties of each of the four filters is given in the figure below.</p>

<table width=500 align=center><td>
<p align=justify>[[File:SL_filters.png|500px|border|center]]
<b>Figure 7 -</b> Filter transmission as function of wavelength.
<br clear=right>
</p>
</td></table>

<p> A table of the above values is given here:[[Media:SL_filters.xls| SL_filters.xls]], [[Media:SL_filters.txt| SL_filters.txt]] </p>

<p><b> It is your task to determine the temperature the sonoluminescence bubble based on the ratio of the average pulse heights of the PMT signals when the various filters are in place, taking into account the known absorptions and efficiencies of the system. Please carefully explain the algorithm for your analysis in your write-up. </b></p>

<h1> References</h1>
<references/>

PHYS 1010, 1410 & 1420

2015-05-07T18:59:52Z

Mgeorge:

<h2> General Information </h2>

<p> These labs serve as the practical teaching experience for PHYS 1010, PHYS 1410, and PHYS 1420. The labs are located in '''102C''' and '''102D''' Bethune College.Select your course below to view your lab schedule. The schedule also appears in the Lab Manual which you can pick up from the York Bookstore.</p>

<p><b>NOTE:</b> Be sure to pick up a copy of the lab manual from the bookstore, and preform the prelab exercise for Experiment 1 ''before'' coming to your first lab.</p>
<p> Check the schedule carefully to see which weeks you have experiments, and in which order you will be performing them.</p>

<h2>Lab Coordinator</h2>
<p> The lab coordinator is responsible for the administration of these labs. Should you have issues such as- you wish to change lab sections, you have missed your scheduled lab time, or other matters for which the TA cannot assist, please see the lab coordinator during the office hours listed below.</p>
<table>
<tr><td>'''Lab Coordinator'''</td><td>Matthew George</td></tr>
<tr><td>'''Office Hours'''</td><td> MW 4:30pm 5:30pm</td></tr>
<tr><td>'''Location'''</td><td> Bethune 102 C</td> </tr>
<tr><td>'''Email'''</td><td>mgeorge (at) yorku.ca</td></tr>
</table>

<h2>Teaching Assistants</h2>
<p> The Teaching Assistant is responsible for providing you the physics knowledge, and the practical know-how required in order to complete these experiments successfully in a timely manner. You should pay careful attention to what they have to say, and heed their advice. They will also be responsible for marking your lab report. They have the authority to deny entry or remove from the lab any student they feel is: acting in an unsafe manner, arriving more than 15 minutes late, grossly unprepared, causing major disruptions, or attempting to stay beyond the 3 hour limit.</p>

<h2> Help Sessions</h2>
<p>There will be help sessions everyday from 1:00pm to 2:00pm in room 102C and/or 102D Bethune. Drop by and get expert help with your prelab exercises, get a sneak peak at the apparatus for your next experiment, and get prepared. The detailed schedule of TA coverage for the session is [[Media:15WinterHelpv3.pdf |here]]. </p>



<h2> Lab Rules </h2>
<ol>
<li> Lab safety is the number one priority. If you are unsure on how to operate the equipment, or believe you may be doing something which might cause harm to you or your classmates, stop and and ask the TA for clarification.</li>
<li> If you are purposely misusing the equipment in a manner which is obviously unsafe, you will be told to leave, and receive a mark of zero for this experiment.</li>
<li> Show up on time- the TA will give a short presentation at the beginning of each lab, where you will learn some very useful information. If you show up late, you will miss this. If you show up more than 15 mintues late, the TA can forbid you from performing the experiment, and you will receive a mark of zero.</li>
<li><b> You must leave the workstation as you have found it! All the equipment must be exactly in the manner in which you found it. All scraps of paper, eraser bits, and other garbage must be cleaned from the station before you leave. Failure to do so will result in a loss of up to 30% for that lab.</b></li>
<li> Each lab session is 3 hours, there are no provisions made for extra time. 15 minutes before the end of the lab, you should start cleaning up you workstation, and leave the room by the end of the lab session.</li>
<li> Report broken or damaged equipment to the TA immediately. You are not responsible for broken equipment, you will not be charged, and your mark will not suffer. We need to know of broken equipment so we can fix or replace it before the next lab session.</li>
<li> No more than two students working together as lab partners is allowed.</li>
<li> A valid medical note is the only acceptable reason for missing a lab. This must be presented to the lab coordinator in order to be considered for scheduling or an exemption.</li>
</ol>

<h2>Prelab Preparation</h2>
<p>You will know from the posted schedule which experiment you will be doing. Before coming to do the experiment, you are expected to read the appropriate section of the manual. Be sure you understand the theory involved, consult your textbook, and plan your practical work. Most of the experiments contain prelab exercises which must be completed on a separate sheet of paper before you come to the lab. This preparation is most important. It is unlikely that you will be able to finish the experiment satisfactorily or learn from them if you do not prepare beforehand. There may be short, unannounced quizzes on the experiment during some labs.</p>

<h2>Lab Reports</h2>
<p>A sample lab report is included in the lab manual (appendix F). </p>
<p>We do not require you to write an elaborate report for each experiment. The report should include name, name of partner, title and date. The experimental data, whenever possible, should be summarized in the form of a table, with title, column headings, units and experimental errors. Graphs should have titles, axes labelled and units included. Errors of all measured quantities should be indicated on graphs in the form of error bars. Calculations should be shown and organized in a logical way, with short comments and explanations. Just formulas with substituted data are not acceptable.
Calculations of errors is an important part of the lab report (next section in the manual provides more information regarding error calculations and rounding of final result and its error). </p>
<p>You are encouraged to record in your report for future reference any comments regarding the theory or method or apparatus which enhance your understanding. Your report should resemble a research scientist's day-to-day experimental log rather than a polished scientific paper. </p>
<p>It is preferred that you write laboratory reports in notebooks, which encourage better organization and neatness. Do not tear pages out of the books, if a mistake is made, simply cross out the mistake neatly. Two books will be required to be used alternately throughout the year. Light weight coil notebooks are suitable. Put your name and lab time clearly on the outside. </p>
<p>The three-hour session should be sufficient for the taking of measurements and for calculations and conclusions, etc. Be punctual - latecomers will find it difficult to complete the assignment. All lab reports, finished or unfinished, must be handed in to your demonstrator by the end of the three-hour lab session.
Your report will be marked by the demonstrator whose name appears on the top of the attendance list which you sign. It will be your responsibility to collect your report from this demonstrator during your next laboratory session. At this time you should discuss with your demonstrator any matters concerning the report(s).</p>

<h2> Lab Marks</h2>
<p> Depending in which course you are enrolled (1010,1410,1420) the amount your lab marks contribute to your final mark can vary from 10%-20%. The course requires 11 labs, and your lowest of the 11 will be dropped when calculating your final lab mark. Your lab reports will be marked by the TA, with some fraction for the prelab, error analysis, results, answers to questions, neatness and completeness.</p>

<h2> Lab Partners</h2>
<p>Some students claim that they learn more while working with a lab partner; others prefer to work alone. For certain experiments where basic techniques, etc. are explored, you will be required to work individually - this will be stated in the lab outline for those particular experiments. For the other experiments we will try to provide sufficient apparatus so that you may work with another student who has been assigned the same experiment or alone, as you prefer. For a few of the experiments the mechanical work is so difficult that one person cannot perform the experiment satisfactorily. If two students work together, <b>each should take a turn at reading all the instruments and although both will have the same data, each student must submit an independent report, with independent calculations.</b> </p>

<p><b>Lab partners are randomly assigned.</b> This facilitates meeting many friends, promotes social skills as well as reduces the probability of dishonesty when doing lab work. The details of how lab partners are assigned will be explained in the first lab.</p>

<h2>Lab Safety</h2>
<p>Scientists very commonly live to a grand old age in spite of their daily encounters with many hazards. The main reason for this is that a scientist doing an experiment is paying very close attention to everything that happens, is expecting the unknown and can react quickly to it. Your best protection against accidents in the lab is a constant thoughtful alertness which never permits your actions to become "mechanical" and "reflex". </p>
<p>Specific hazards which exist in particular experiments will be stressed in the respective lab outline. Please pay very careful attention to these warnings and act accordingly. </p>
<p> Notify the TA or lab coordinator of any accident or injury no matter how insignificant it may seem. </p>
<p>In the case of a fire, at the sound of the fire alarm in the building, the university stipulates that everyone must leave the building. In the case of a fire in the lab, the TA is responsible for taking the appropriate action to curb it, but the students must leave the building immediately. </p>

<b> A 24-hour Emergency Services Telephone Centre operates on York Campus and can be alerted by calling 33333 on all campus telephones or 736-2100 Ext. 33333 on public telephones.
Health services are located in York Lanes. </b>

<h2>Academic Honesty</h2>
<p>Students will certainly discuss and talk about their studies with their friends and this can be very useful; but any work that you hand in must have been done by yourself. This is the only way to test your own competence and to prepare yourself for positions of responsibility after graduation. If scientists are dishonest, they are useless.</p>
<p><b>THE UNIVERSITY CONSIDERS ALL FORMS OF COPYING AND CHEATING TO BE SERIOUS OFFENCES. </b>[[http://www.yorku.ca/secretariat/policies/index-policies.html YorkU Policy on Academic Honesty]].</p>

<ul>
<li>[[LAB INFORMATION|LAB INFORMATION]] </li>
<li>[[MEASUREMENTS AND ERRORS|MEASUREMENTS AND ERRORS]] </li>
<li>[[MEASURING LENGTH|MEASURING LENGTH]] </li>
<li>[[GRAPHS|GRAPHS]] </li>
</ul>

Main Page/PHYS 4210/Bell's Inequalities

2015-05-01T13:52:30Z

Mgeorge:

<h1>Bell's Inequalities and Quantum Entanglement</h1>

<p> Deep at the root of the underlying principles of quantum mechanics lies shadowy principles based on probability which never sit well with some people. This experiment is meant to shine some (laser)light on these principles, and see if we can't come to some deeper understanding of the underlying framework of Quantum Dynamics.</p>
<p>No better introduction can be given than the following set of famous papers, commonly referred to today by their author lists.</p>
<ul>
<li>Einstein, Podolsky, Rosen<ref>A. Einstein, B. Podolsky & N. Rosen, <i>"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"</i> [http://prola.aps.org/abstract/PR/v47/i10/p777_1 Phys. Rev., '''47''', 777-780 (1935)]</ref></li>
<li>Bell<ref><i>J.S. Bell, "On the Einstein Podolsky Rosen Paradox"</i> [[Media:Bell1964.pdf| Physics, '''1''', 195 (1964)]]</ref> </li>
<li>CHSH (Clauser, Horne, Shimony, & Holt)<ref>J.F. Clauser, M.A. Horne, A. Shimony, & R.A. Holt, <i>"Proposed Experiment to Test Local Hidden-Variable Theories"</i> [http://prl.aps.org/abstract/PRL/v23/i15/p880_1 Phys. Rev. Lett., '''23''', 880 (1969)]</ref></li>
</ul>
<p>Another useful resource, more directly relevant to our experiment and summarizing the information in the above papers is from Dehlinger and Mitchell <ref name="Dehlinger">D. Dehlinger & M.W. Mitchell. <i>"Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory."</i> [http://scitation.aip.org/content/aapt/journal/ajp/70/9/10.1119/1.1498860 Am. J. Phys. '''70''', 903 (2002)]</ref>.</p>
<p>It is imperative that you read and understand these papers ''before'' you attempt to perform this experiment.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Entanglement</li>
<li>Parametric down conversion</li>
<li>Nonlocality</li>
<li>Coincidence</li>
<li>Correlation</li>

</ul>
</td>
<td width=250>
<ul>
<li>Logic Analyzer</li>
<li>Avalanche Photodiode</li>
<li></li>
<li></li>
</ul>
</td>
</table>

<h2> Method </h2>
<p> All optical components have to be precisely aligned in order for your data to yield the expected results. Please take time to understand fully what is described below, and to diligently follow the directions.</p>
<b> Laser Safety goggles are provided, and are mandatory to be worn when the laser is on. THERE ARE NO EXCEPTIONS. If you are noticed not wearing the goggles, you will be forbidden from continuing.</b>
<p><b>Question: </b> What is the relative sensitivity of the human eye to 405nm? Does this make it more or less dangerous than green light?</p>

<table width=400 align=center>
<tr>
<td>
<p align=justify>[[File:BE-LaserRegion.png|400px|border|center]]
<b>Figure 1 -</b> Laser Region.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-MainRegionv2.png|600px|border|center]]
<b>Figure 1 -</b> Experiment setup.
<br clear=right>
</p>
</td>
</tr></table>

<h3>Step 1: Align the laser and BBO crystal</h3>
<ol>
<li>Remove the mounts containing the half-wave plate, quarter-wave plate and BBO crystal.</li>
<li>Put on your safety goggles, and turn on the 405nm laser by plugging in the power supply. Using the two mirrors, adjust the path of the beam to follow at a constant height and consistently directly above one line of holes in the optics table. </li>
<li>Insert the BBO crystal into position above the vertex of the rails. Adjust the mounting so the laser is passing through the crystal without clipping. Fine adjust the angle of the crystal so the retro-reflected beam off of the face of the crystal is directly back onto the incoming beam.</li>
<li>Shut off the laser.</li>
</ol>
<h3>Step 2: Align the 810nm-photon collection optics</h3>
<ol>
<li>For Detector Assembly A, remove the linear polarizer and unscrew the 810nm filter from the front of the photon collection optics.</li>
<table width=400 align=center>
<tr>
<td>
<p align=justify>[[File:BE-RemovePolarizer1.png|260px|border|center]]
<b>Figure 2a -</b> Remove Linear Polarizer.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-RemovePolarizer2.png|230px|border|center]]
<b>Figure 2b -</b> Remove Linear Polarizer.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-Remove810Filter1.png|245px|border|center]]
<b>Figure 2c -</b>Unscrew 810nm Filter.
<br clear=right>
</p>
</td>
<td>
<p align=justify>[[File:BE-Remove810Filter2.png|250px|border|center]]
<b>Figure 2d -</b>Filter and Polarizer Removed.
<br clear=right>
</p>
</td>
</tr></table>
<li>Adjust (if necessary) the height of the detector assembly to be the same height as the 405nm laser beam.</li>
<li>Adjust the angle of rail containing the detector assembly to 3º.</li>
<li>Remove the optical fiber attached to the single photon detector corresponding to that detector assembly. Attach the Fiber Checker to this free end of the optical fiber. This will send a beam of red light backwards through the system.</li>
<li>Adjust the mount of the detector assembly so the red beam is aligned onto the back of the BBO crystal at the point where the 405nm passes through.</li>
<li>The reflection of the red beam off of the back of the BBO crystal should reflect back into the other detector system. If not, your detectors are not symmetric about the 405nm beam path, or the BBO crystal pair is not perpendicular to the incoming 405nm beam.</li>
<li>Replace the 810nm filter, linear polarizer, and fiber connection to the single photon detector.</li>
<li>Repeat above for Detector Assembly B.</li>
</ol>
<h3>Step 3: Power up the Electronics</h3>
<p>The single photon detectors are extremely sensitive pieces of equipment. Special care must be taken to minimize stray photons from entering and overloading the internal electronics.<b>The overhead room lights must be turned off before the power supply for the single photon detectors are turned on.</b> The acceptable ambient light sources are the desk lamp shining on the electronics rack, and a handheld red led keychain (particularly useful since your laser safety goggles transmit red light well.).</p>
<table width=400 align=center><td>
<p align=justify>[[File:BE-Electronicsv2.png|500px|border|center]]
<b>Figure 3 -</b> Electronics Rack.
<br clear=right>
</p>
</td></table>
<ol>
<li>Turn on the desk lamp so it shines onto the electronics rack.</li>
<li>Turn the room lights off.</li>
<li>Turn on the power to the electronics rack</li>
<li>Turn on the power supply for the single photon counting modules. The voltage on this supply must be set greater than 5 volts. This is subsequently limited to precisely 5 volts by use of a voltage regulator downstream.</li>
<li>Connect the outputs of each of the single photon counting modules to an Integral Discriminator. This device will look for an input signal greater than a user-set threshhold value and output a 1-microsecond-long TTL pulse. The discriminator value should be set to the lowest setting.</li>
<li>Connect the outputs of the Discriminators each to a ratemeter. The user manual for the ratemeter in the binder in the lab contains information on how to understand the integration time it used for various settings. This needs to be understood to properly compute the uncertainties. Observe and record the number of counts on each detectors (will be around 10,000 per second).</li>
</ol>
<h3>Step 4: Insert and align the half-wave and quarter-wave plates</h3>
<ol>
<li>Insert the quarter-wave plate mount. Ensure the fast axis of the quarter-wave plate is vertical. The fine adjustment of the rotation will be done later.</li>
<li>Disconnect the output of the Discriminators from the Ratemeters and attach them to the inputs of the Coincidence unit. Have the output of the Coincidence unit go to one of the Ratemeters. Note how you can ''enable'' and ''disable'' the various inputs of the Coincidence unit. Does it give the expected output when only one channel is enabled?</li>
<li>Insert the half-wave plate rotational mount. Ensure the 405nm beam is not clipping. The correct rotational setting of the half-wave plate is when the coincidence rates are equal when having the detector assembly linear polarizers both at 0º and both at 90º. </li>
<li> Set both linear polarizers to 0º. Fine adjust the detectors assembly mounts to maximize this rate of the output from the Coincidence unit.</li>
<li>Set the linear polarizers to 45º. Rotate the post of the quarter-wave plate so that the coincidence rate is a maximum.</li>
</ol>
<h3>Step 5: Fine Adjust</h3>
<ol>
<li>Patiently cycle through adjusting the mounts of the detector assemblies, and the rail angle to maximize coincidence.</li>
</ol>
<h3>Step 6: Take Data!</h3>
<ol>
<li>Following the scheme described in Dehlinger and Mitchell <ref name="Dehlinger"/>, collect the data required to test a Bell's Inequality.</li>
<li>''Note:'' If your coincidence count rate for the first set of angles in Table I of <ref name="Dehlinger"/> is not at least 300 cps (though ideally 600+), then you have not set up the experiment properly.</li>
<li>''Note:'' You must subtract off the background coincidence counts from each of your readings. (see <ref name="Dehlinger"/>).</li>

</ol>

<h2> Core Experiment </h2>
<p>To setup the experiment as described in the Method section and to take one complete set of data required to test a Bell's Inequality as described in <ref name="Dehlinger"/> using the readings from the ratemeter. A full analysis of the data with proper treatment of uncertainties is required.</p>

<p><b>You are required to complete the core experiment along with your choice of one of the modules listed below. </b></p>

<h2> Module 1: Purity of Correlation</h2>
<p>In this module, you will try to improve on the purity of the correlation by reducing the acceptance angle of the single-photon detectors by placing adjustable collimating slits into each path before the single photon detectors. You have to determine(research) how purity of correlation can be measured in this experiment.</p>

<h2> Module 2: Computer Analysis </h2>
<p> In this module, you will use a Logic Analyzer to collect the raw outputs from the individual single photon detectors, then create an analysis program to calculate coincidence. Once this is accomplished, you can take data for longer periods of time, reduce the statistical uncertainty of the Bell's Inequality, and really put nail in the coffin of Hidden Variable Theories. Be sure to motivate your choice of coincidence window.</p>

<h2> Module 3: Pump Laser Power </h2>
<p>In this module, you will vary the power of the 405nm pump laser beam using neutral density filters in order to study the rate of coincident photon as a function of pump laser power. Does this trend follow expectations?</p>

<h1>References</h1>
<references/>

Main Page/PHYS 3220

2015-04-24T15:17:54Z

Mgeorge:

<h1>PHYS 3220 3.0 Experiments in Modern Physics </h1>
<p>A selection of experiments in fluid mechanics,
electromagnetism, optics, and atomic, nuclear, and
particle physics. Analysis of the data and detailed
write-ups are required. One lecture hour which is
devoted to techniques of data analysis and three
laboratory hours per week.</p>

<p>Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<h1>Laboratory Manual</h1>
<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<ul>
<li>[[Main Page/PHYS 3220/Cavendish|Measurement of the Gravitation Constant G: The Cavendish Experiment]] </li>
<li>[[Main Page/PHYS 3220/Speed of Light|A Measurement of the Velocity of Light: The Foucault-Michelson Experiment]] </li>
<li> [[Main Page/PHYS 3220/Excitation Potentials|The Excitation Potentials of Mercury: The Franck-Hertz Experiment]] </li>
<li> [[Main Page/PHYS 3220/Radioactive Decays|Radioactive Decays]] </li>
<li>[[Main Page/PHYS 3220/Viscosity|Viscosity]] </li>
<li>[[Main Page/PHYS 3220/Millikan|Determination of the Electric Charge Unit ''e'' : The Millikan Oil Drop Experiment]] </li>
<li> [[Main Page/PHYS 3220/Thermionic|Thermionic Emission]]</li>
<li> [[Main Page/PHYS 3220/Particle Tracking|Particle Tracking Simulation]] </li>
<li> [[Main Page/PHYS 3220/Rutherford I|Rutherford Scattering I]] </li>
<li> [[Main Page/PHYS 3220/Digital Oscilloscope|Digital Storage Oscilloscope]] </li>
<li> [[Main Page/PHYS 3220/High-TC Superconductivity|High-TC Superconductivity]]</li>
<li> [[Main Page/PHYS 3220/Semiconductors I|Semiconductors I]] </li>
<li> [[Main Page/PHYS 3220/Holography| Holography]] </li>
</ul>

<h3>out of service</h3>
<ul>
<li>[[Main Page/PHYS 3220/Coupled Motion|Coupled Oscillatory and Rotational Motion]] </li>
<li> [[Main Page/PHYS 3220/Hydrogen Spectrum|The Visible Spectrum of Hydrogen]]</li>
<li> [[Main Page/PHYS 3220/Interferometer|The Michelson Interferometer ]] </li>
</ul>

<h3>Demonstration</h3>
[[Media:Solar_to_Mechanical_v2.pdf| Solar to Mechanical]]

File:Solar to Mechanical v2.pdf

2015-04-24T15:17:40Z

Mgeorge:

Main Page/PHYS 3220

2015-04-24T15:17:19Z

Mgeorge:

<h1>PHYS 3220 3.0 Experiments in Modern Physics </h1>
<p>A selection of experiments in fluid mechanics,
electromagnetism, optics, and atomic, nuclear, and
particle physics. Analysis of the data and detailed
write-ups are required. One lecture hour which is
devoted to techniques of data analysis and three
laboratory hours per week.</p>

<p>Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<h1>Laboratory Manual</h1>
<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<ul>
<li>[[Main Page/PHYS 3220/Cavendish|Measurement of the Gravitation Constant G: The Cavendish Experiment]] </li>
<li>[[Main Page/PHYS 3220/Speed of Light|A Measurement of the Velocity of Light: The Foucault-Michelson Experiment]] </li>
<li> [[Main Page/PHYS 3220/Excitation Potentials|The Excitation Potentials of Mercury: The Franck-Hertz Experiment]] </li>
<li> [[Main Page/PHYS 3220/Radioactive Decays|Radioactive Decays]] </li>
<li>[[Main Page/PHYS 3220/Viscosity|Viscosity]] </li>
<li>[[Main Page/PHYS 3220/Millikan|Determination of the Electric Charge Unit ''e'' : The Millikan Oil Drop Experiment]] </li>
<li> [[Main Page/PHYS 3220/Thermionic|Thermionic Emission]]</li>
<li> [[Main Page/PHYS 3220/Particle Tracking|Particle Tracking Simulation]] </li>
<li> [[Main Page/PHYS 3220/Rutherford I|Rutherford Scattering I]] </li>
<li> [[Main Page/PHYS 3220/Digital Oscilloscope|Digital Storage Oscilloscope]] </li>
<li> [[Main Page/PHYS 3220/High-TC Superconductivity|High-TC Superconductivity]]</li>
<li> [[Main Page/PHYS 3220/Semiconductors I|Semiconductors I]] </li>
<li> [[Main Page/PHYS 3220/Holography| Holography]] </li>
</ul>

<h3>out of service</h3>
<ul>
<li>[[Main Page/PHYS 3220/Coupled Motion|Coupled Oscillatory and Rotational Motion]] </li>
<li> [[Main Page/PHYS 3220/Hydrogen Spectrum|The Visible Spectrum of Hydrogen]]</li>
<li> [[Main Page/PHYS 3220/Interferometer|The Michelson Interferometer ]] </li>
</ul>

<h3>Demonstration</h3>
[[Media:GrotrianH.pdf| Solar to Mechanical]]

Main Page/PHYS 3220

2015-04-24T15:16:27Z

Mgeorge:

<h1>PHYS 3220 3.0 Experiments in Modern Physics </h1>
<p>A selection of experiments in fluid mechanics,
electromagnetism, optics, and atomic, nuclear, and
particle physics. Analysis of the data and detailed
write-ups are required. One lecture hour which is
devoted to techniques of data analysis and three
laboratory hours per week.</p>

<p>Your username is your student number, and the password is studentnumberLastname (note the capitalization of the first letter of your last name).</p>

<h1>Laboratory Manual</h1>
<p> To sign up for an experiment : [http://www.phas.yorku.ca/labs/ Experiment Sign-up] </p>
<ul>
<li>[[Main Page/PHYS 3220/Cavendish|Measurement of the Gravitation Constant G: The Cavendish Experiment]] </li>
<li>[[Main Page/PHYS 3220/Speed of Light|A Measurement of the Velocity of Light: The Foucault-Michelson Experiment]] </li>
<li> [[Main Page/PHYS 3220/Excitation Potentials|The Excitation Potentials of Mercury: The Franck-Hertz Experiment]] </li>
<li> [[Main Page/PHYS 3220/Radioactive Decays|Radioactive Decays]] </li>
<li>[[Main Page/PHYS 3220/Viscosity|Viscosity]] </li>
<li>[[Main Page/PHYS 3220/Millikan|Determination of the Electric Charge Unit ''e'' : The Millikan Oil Drop Experiment]] </li>
<li> [[Main Page/PHYS 3220/Thermionic|Thermionic Emission]]</li>
<li> [[Main Page/PHYS 3220/Particle Tracking|Particle Tracking Simulation]] </li>
<li> [[Main Page/PHYS 3220/Rutherford I|Rutherford Scattering I]] </li>
<li> [[Main Page/PHYS 3220/Digital Oscilloscope|Digital Storage Oscilloscope]] </li>
<li> [[Main Page/PHYS 3220/High-TC Superconductivity|High-TC Superconductivity]]</li>
<li> [[Main Page/PHYS 3220/Semiconductors I|Semiconductors I]] </li>
<li> [[Main Page/PHYS 3220/Holography| Holography]] </li>
</ul>

<h3>out of service</h3>
<ul>
<li>[[Main Page/PHYS 3220/Coupled Motion|Coupled Oscillatory and Rotational Motion]] </li>
<li> [[Main Page/PHYS 3220/Hydrogen Spectrum|The Visible Spectrum of Hydrogen]]</li>
<li> [[Main Page/PHYS 3220/Interferometer|The Michelson Interferometer ]] </li>
</ul>

<h3>Demonstration</h3>

Main Page/PHYS 4210/Zeeman Effect

2015-04-14T18:20:48Z

Mgeorge:

<h1>Zeeman Effect</h1>
<p>In this classic experiment that predates the development of quantum mechanics one investigates the light emitted by atoms in the presence of a homogeneous magnetic field. Of particular interest is the observation that this light is polarized in the presence of a magnetic field. The high-resolution spectroscopy required to resolve the line splittings is performed with a multiple-beam interferometer called a Lummer-Gehrcke plate which is similar to a Fabry-Perot interferometer.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Magnetic Sublevels</li>
<li>Total Angular Momentum</li>
<li>TEM wave</li>
<li>Quantization Axis</li>
<li>Orbital Angular Momentum</li>
<li>Spin Angular Momentum</li>
</ul>
</td>

<td width=250>
<ul>
<li>Normal Zeeman Effect</li>
<li>Anomalous Zeeman Effect</li>
<li>Lummer-Gehrcke Plate</li>
<li>Multi-beam Interferometer</li>
<li>Quarter-wave Plate</li>
</ul>
</td>
</table>

<h2> Required Components</h2>

<ol>
<li>[[Media:ZEMagnetPower.JPG|Magnet Power Supply]]</li>
<li>[[Media:ZEElectromagnet.JPG|Electromagnet]]</li>
<li>[[Media:ZEDischargePower.JPG|Discharge Power Supply]]</li>
<li>[[Media:ZECCDCamera.JPG|CCD Camera]]</li>
<li>[[Media:ZELummer.JPG|Lummer-Gehrcke Plate]]</li>
<li>[[Media:ZEPolarizers.JPG|Polarizers and Waveplate]]</li>
</ol>

<h1>Introduction</h1>
<p>The Zeeman effect is a powerful demonstration of the splittings of magnetic sublevels in an angular momentum multiplet. Many aspects of the emission of light by excited atoms, particularly when exposed to strong magnetic fields ('''B''') were understood by Lorentz in a classical model <ref name="Jenkins">Jenkins F.A., White H.E., [https://www.library.yorku.ca/find/Record/48797 ''Fundamentals of Optics''], McGraw-Hill</ref><ref name="Mullin">Brehm J.J., Mullin W.J., [https://www.library.yorku.ca/find/Record/1126595 ''Introduction to the Structure of Matter''], Wiley </ref> before the advent of quantum mechanics. It is possible to understand the changes to classical electron orbits due to the Lorentz force in a 3D harmonic oscillator model. When one complements this with the idea that electromagnetic waves are transverse (the associated electric and magnetic fields of the EM wave oscillate in a plane perpendicular to the propagation direction of the wave), one can understand why circularly polarized light emerges as the atoms are observed in a direction longitudinal with the external '''B''' field, and why they appear as plane-polarized as viewed from the transverse direction. The understanding in the classical framework helps to build an intuition about the problem.</p>
<p>In the modern quantum mechanical description <ref name="Mullin"/><ref>Merzbacher E., [https://www.library.yorku.ca/find/Record/47405 ''Quantum Mechanics''], Wiley</ref><ref name="Bethe">Bethe H.A., Salpeter E.E., [https://www.library.yorku.ca/find/Record/2227072 ''Quantum Mechanics of One- and Two-Electron Systems''], Springer</ref> one has to take into account that the presence of the '''B''' field singles out an axis. The additional interaction term between the magnetic moment of the electronic state (proportional to the ''z'' component of the total angular momentum) and '''B''' serves to split the magnetic sublevels of states with non-zero angular momentum. The additional interaction forces the use of this axis as a quantization axis. Without an external field one usually picks a ''z'' axis, but should arrive at results that are independent of this choice. To obtain the observed result that the light emanating from spontaneous transitions without an external field is unpolarized, one has to average over random orientations of the quantization axis. The observation that a definite orientation is singled out as quantization axis in the Zeeman effect is sometimes referred to as ‘space quantization’.</p>
<p>The problem can be illustrated by using pure orbital angular momentum states, i.e.,ignoring spin, and considering an np - ms transition. This transition is an allowed electric dipole transition, since a single unit of orbital angular momentum is changed, and this difference of one unit is carried away in the form of the spin for the spontaneously radiated photon. The important quantity to watch is the change in the projection of the orbital angular momentum, which can be +1, 0, -1 depending on the choice of the magnetic sublevel.</p>
<p>A transition 2p<sub>0</sub> - 1s is associated with the emission of linearly polarized light with the oscillating electric field vector aligned with the z axis, with the wave propagation vector being orthogonal to this axis. This can be understood from the fact that the only non-vanishing matrix element for the dipole operator is <1s|''z''|2p<sub>0</sub>>. Similar calculations show that the transitions originating in the ''m'' = 1 and ''m'' = -1 sublevels result in circularly polarized light being emitted, which can propagate in the z direction only. One of the fascinating aspects of the Zeeman experiment is the following. For field-free atoms no axis is singled out, and thus, one has to include all possible orientations of the ''z'' axis, which results in the prediction that the light emitted from free atoms is unpolarized. However, once a homogeneous magnetic field is applied, an axis is singled out in space, which becomes the natural quantization axis. By probing the polarization of the spontaneously emitted light of atoms in the presence of a magnetic field one can verify that indeed the turn-on of the field causes a repopulation of the magnetic sublevels in a way that corresponds to the classical predictions of the Lorentz model. Thus, it is necessary to observe the light emitted longitudinally and transverse to the magnetic field.</p>
<p>The general theory of the Zeeman effect is complicated by the fact that the total angular momentum, i.e., added orbital and spin angular momentum of the active electron has to be considered. Based on orbital angular momentum alone the magnetic moment of an electron in a non-zero m sublevel is an integer multiple of the projection ''l<sub>z</sub>''. Once one couples ''l'' and ''s'' to form ''j'' = ''l'' + ''s'', the magnetic moment can be, but need not to be an integer multiple of ''j<sub>z</sub>'', and the proportionality is given by the Lande factor ''g''. The Lande factor can take on half-integer numbers for the initial and/or final states involved in the transition. One distinguishes between the normal and anomalous Zeeman effects depending on whether this complication arises or not <ref name="Melissinos">Melissinos A.C., [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press</ref>. The anomalous effect is rather common in atomic transitions, but in this experiment a transition with the normal Zeeman effect has been selected. The red line in cadmium (643.8 nm), which is the equivalent of the yellow line in mercury, cf.. the Grotrian diagram shown in the appendix, and the level diagram in Fig. 1 (which is Fig. 7.3 from <ref name="Melissinos"/>).
</p>
<table width=500 align=center><td>
<p align=justify>[[File:Zee-fig1.png|500px|border|center]]
<b>Figure 1 -</b> Level diagram for the Cd 643.8 nm transition with and without B field.
<br clear=right>
</p>
</td></table>
<p>From an experimental point of view a high demand is placed on the optical resolution of the interferometer. The idea is to inspect the interference pattern for a given line and to observe the quantitative changes in the pattern as the B field is applied to determine the wavelengths of the various components. The high resolution required can be obtained from multiple-beam interferometers, such as the Fabry-Perot (FP) interferometer <ref name="Jenkins"/><ref name="Melissinos"/>. Melissinos <ref name="Melissinos"/> discusses the analysis of the circular fringe pattern as produced by the FP. An easier alternative is provided by a special instrument that perfects the same method, called a Lummer-Gehrcke (LG) plate <ref name="Jenkins"/>. Since its interference pattern is more complicated to derive, you should concentrate on understanding the principles of multiple-beam interferometry using the FP and be aware of the analogies. Note that the FP has a wide range of applications in optics.</p>
<table width=500 align=center><td>
<p align=justify>[[File:Zee-fig2a.png|500px|border|center]]
<b>Figure 2a -</b> Multiple reflection between the surfaces of a Lummer-Gehrcke plate.
<br clear=right>
</p>
</td></table>
<table width=500 align=center><td>
<p align=justify>[[File:Zee-fig2b.png|500px|border|center]]
<b>Figure 2b -</b> Apparatus for the Zeeman experiment with a Lummer-Gehrcke plate.
<br clear=right>
</p>
</td></table>

<table width=700 align=center><td>
<p align=justify>[[File:800px-Zee_fig2c.png‎|700px|border|center]]
<b>Figure 2c -</b> Apparatus for the Zeeman experiment.
<br clear=right>
</p>
</td></table>

<p>The LG plate shown as part of the apparatus in Fig. 2 consists of a precisely polished quartz glass plate of given thickness d with a prism attached at one end so that light entering from the slit has an angle of incidence on the plate that is near the critical angle. This results in some refractive transmission and mostly reflection at the glass/air surface. The reflected light inside the glass plate undergoes multiple ‘bounces’ of this type (interior reflection and partial refractive transmission). Two different interference patterns emerge when looking at a grazing angle at the top or bottom of the LG plate. The pattern formed at the top shows sharp bright lines on a dark background. In contrast to a Michelson interferometer a multiple-beam interferometer such as the FP and LG can produce an uneven interference pattern <ref name="Jenkins"/><ref name="Melissinos"/>.</p>
<p>The separation between the fringes that appear without the magnetic field depends on the angle of observation. This spacing ''ΔA'' has to be determined for the particular fringe chosen for observation. As a magnetic field is applied each bright fringe splits either into two or into three depending on the orientation with respect to the magnetic field. To obtain a quantitative measure of the Zeeman effect, one needs to determine the '''B''' dependent splitting ''ΔS'' relative to ''ΔA''. Making use of the ratio eliminates the need to know the optical magnification, observation angle and distance from the plate. The frequency splitting depends also on the LG plate thickness d (as in the FP case), and additionally on the index of refraction η of the quartz glass. In the FP case this would be equal to 1, but there are versions of the experiment where the evacuation of a sealed FP interferometer is used to produce a scanning effect in the fringe pattern <ref name="Preston">Preston D.W. Dietz E.R., [https://www.library.yorku.ca/find/Record/1038893 ''The Art of Experimental Physics''],Wiley</ref>. The frequency splitting can be written as</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Zee-eqn1.png|160px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>
<p>The corresponding energy difference should equal</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Zee-eqn2v2.PNG|280px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>
<p>One common method of determining the electron charge-to-mass ratio is through eq (2). Our interest is, however, to determine the energy splitting as a function of the magnetic field strength ''B''.</p>
<p>In our version of the Zeeman experiment the intense red Cd line at 643.8 nm is used. For optical transitions Cd acts as an effective two-electron system, i.e., it has a He-like configuration, as has Hg. Compare the Grotrian diagram shown in Fig. 1 to the one for mercury provided in the appendix (cf.. the Franck-Hertz experiment). In order to understand the selection rules for allowed electric dipole transitions follow the arguments given in <ref name="Preston"/> in the context of the HeNe laser experiment. The two active electrons have combined orbital angular momentum ''L'' = l<sub>1</sub>+l<sub>2</sub>, spin S = s<sub>1</sub>+s<sub>2</sub>, and total angular momentum J = j<sub>1</sub>+j<sub>2</sub>. Allowed transitions require a change of one unit in ''L'' and ''J'' to make up for the spin of the photon, considering that spin flip is unlikely. Using <sup>(2''S''+1)</sup>''L<sub>J</sub>'' notation (with ''L'' = 0 denoted as S, ''L'' = 1 as P, ''L'' = 2 as D, etc) we have for the relevant line a <sup>1</sup>D<sub>2</sub> - <sup>1</sup>P<sub>1</sub> transition. This means that the spins are paired up (spin singlet) and that in nonrelativistic notation a 5s5d to 5s5p transition takes place. In Hg the equivalent line at the n = 6 level is the yellow line at 579 nm. The shift of the same line towards yellow is the result of having an additional electron shell in the core. What wavelength is associated with this transition in He?</p>
<p>For the advanced student: note that the initial level splits into 5 sublevels ''M<sub>J</sub>'' = -2,-1,0,1,2 , while the final state has ''M<sub>J</sub>'' = -1,0,1. They split equidistantly and one can group the nine possible transitions according to the allowed ''ΔM'' = -1,0,1 (cf.. Ref. <ref name="Melissinos"/> Fig. 7.3). To understand the polarization of the emitted light in the presence of the external B field note that for an electromagnetic wave its electric, magnetic fields and the wave propagation vector '''k''' form a right-handed coordinate system. Understand the validity of the dipole approximation (the wavelength λ is much longer than atomic dimensions) and how the electric field of the EM wave can be replaced by a constant vector times a temporary oscillatory factor (ref. <ref name="Melissinos"/><ref name="Bethe"/>). Convince yourself why no linearly polarized light can be observed in the longitudinal direction as the magnetic field is turned on. Correspondingly understand why circularly polarized light as observed in the longitudinal direction must appear as linearly polarized when observed in a direction transverse to the ''B'' field. Why can all three components associated with the ''ΔM'' = -1,0,1 selection rule be observed in the transverse direction?</p>
<p>To verify these predictions about the polarization states of the light when the B field is turned on you need to recall some optical properties of polarizers and of quarter-wave plates (cf.. Ref.1). By placing these in the correct order you can verify the following:</p>
<p>In the transverse direction, use a linear polarizer to identify the polarization states of the three components with '''B''' turned on; what happens for ''B'' = 0?</p>
<p><b>NOTE: To perform these tests, place the polarizers (and/or waveplates) before the the LG plate, <u>not</u> in between the LG plate and CCD.</b></p>
<p>In the longitudinal direction, use a quarter-wave plate convert the circularly polarized (CP) light to two perpendicular
linearly polarized components corresponding to left- and right CP light respectively. Use a polarizer to extinguish each of these components separately; what happens for ''B'' = 0?</p>
<p>Collect sufficient data for both observation directions to demonstrate the linearity of the line
splitting with the magnetic field. You will need to perform a calibration of the magnetic field as a function of the current and should comment on possible saturation effects, i.e., a linear behaviour of the splitting with ''B'', but non-linear with the magnet current ''I'' at strong fields, where part of the electric energy may be converted to heat. Determine the gyromagnetic ratio (''g'') from your observations. </p>
<p>'''Warning:''' The Cd lamp emits ultraviolet light in addition to other lines such as the red Cd line. The apparatus contains a narrow-band red filter so that your eyes are protected when observing through the telescope. Avoid looking into the lamp itself (even though it is rated to be safe), i.e., cover the apparatus with a sheet of paper to reduce unnecessary eye contact with the lamp. The lamp takes several minutes to reach a proper operating temperature for the red line to be visible.</p>
<p><b>Obtain assistance when changing the observation direction from transverse to longitudinal or vice versa!</b></p>

<h3> Using the CCD Camera</h3>
<p>A CCD camera (AmScope MU300) is provided to allow for easy viewing of the lines. To operate the CCD, run the program "ToupView", then select ''Acquire''-> ''Live Capture''-> ''UCMOS03100KPA'' from the menu. A window will appear which is the live image being collected by the CCD. The brightness of the image can be changed using the ''Setup'' -> ''View Souce Properties'' -> ''Expose'' tab. A reasonable choice of values is an ''Exposure'' of 700ms with an ''Analog Gain'' of 3. Correct adjustment of the support system will allow you to clearly view the lines. Sliding of the CCD camera in and out will allow for focus. You can Save the image using ''Capture'' -> ''Capture a Frame'' command.</p>
<table width=500 align=center><td>
<p align=justify>[[File:ToupView.png|500px|border|center]]
<b>Figure 3-</b> ToupView CCD Camera Interface.
<br clear=right>
</p>
</td></table>
<p>Once you are able to see nice clear lines as shown in Figure 3, use the ''Region of Interest'' tool to focus in on a few lines in center. You can now use the ''Zoom'' to expand the image. One the left margin of the video image, there is a scale showing the pixel number. You can use this as a fixed reference point- as you increase the applied magnetic field, the line will split into sublevels, check the dial gauge, and then use the adjusting screw to place the shifted line back to the pixel number of the original line, then check the new reading of the dial gauge and record the measurement.</p>

<h1>Appendix</h1>
<ul>
<li><b>Data for the Lummer-Gehrcke plate</b> [from Leybold’s manual]: ''d'' = 4.04 mm η = 1.4567 </li>
<li>Grotrian diagrams for Cd, Hg, and He taken from <ref>Radzig A.A., Smirnov B.M.,[https://www.library.yorku.ca/find/Record/243579 ''Reference Data on Atoms Molecules and Ions''], Springer 1985.</ref>. A copy of these are in the binder in the laboratory.
<ul>
<li>[[Media:GrotrianH.pdf| Hydrogen]]</li>
<li>[[Media:GrotrianHe.pdf| Helium]]</li>
<li>[[Media:GrotrianHg.pdf| Mercury]]</li>
<li>[[Media:GrotrianHgCd.pdf| Cadmium and Mercury]]</li>
</ul>
</li>
</ul>

<h1>References</h1>
<references/>

Main Page/PHYS 4210/Zeeman Effect

2015-04-14T18:20:25Z

Mgeorge:

<h1>Zeeman Effect</h1>
<p>In this classic experiment that predates the development of quantum mechanics one investigates the light emitted by atoms in the presence of a homogeneous magnetic field. Of particular interest is the observation that this light is polarized in the presence of a magnetic field. The high-resolution spectroscopy required to resolve the line splittings is performed with a multiple-beam interferometer called a Lummer-Gehrcke plate which is similar to a Fabry-Perot interferometer.</p>

<h2>Key Concepts</h2>
<table width=500>
<td width=250>
<ul>
<li>Magnetic Sublevels</li>
<li>Total Angular Momentum</li>
<li>TEM wave</li>
<li>Quantization Axis</li>
<li>Orbital Angular Momentum</li>
<li>Spin Angular Momentum</li>
</ul>
</td>

<td width=250>
<ul>
<li>Normal Zeeman Effect</li>
<li>Anomalous Zeeman Effect</li>
<li>Lummer-Gehrcke Plate</li>
<li>Multi-beam Interferometer</li>
<li>Quarter-wave Plate</li>
</ul>
</td>
</table>

<h2> Required Components</h2>

<ol>
<li>[[Media:ZEMagnetPower.JPG|Magnet Power Supply]]</li>
<li>[[Media:ZEElectromagnet.JPG|Electromagnet]]</li>
<li>[[Media:ZEDischargePower.JPG|Discharge Power Supply]]</li>
<li>[[Media:ZECCDCamera.JPG|CCD Camera]]</li>
<li>[[Media:ZELummer.JPG|Lummer-Gehrcke Plate]]</li>
<li>[[Media:ZEPolarizers.JPG|Polarizers and Waveplate]]</li>
</ol>

<h1>Introduction</h1>
<p>The Zeeman effect is a powerful demonstration of the splittings of magnetic sublevels in an angular momentum multiplet. Many aspects of the emission of light by excited atoms, particularly when exposed to strong magnetic fields ('''B''') were understood by Lorentz in a classical model <ref name="Jenkins">Jenkins F.A., White H.E., [https://www.library.yorku.ca/find/Record/48797 ''Fundamentals of Optics''], McGraw-Hill</ref><ref name="Mullin">Brehm J.J., Mullin W.J., [https://www.library.yorku.ca/find/Record/1126595 ''Introduction to the Structure of Matter''], Wiley </ref> before the advent of quantum mechanics. It is possible to understand the changes to classical electron orbits due to the Lorentz force in a 3D harmonic oscillator model. When one complements this with the idea that electromagnetic waves are transverse (the associated electric and magnetic fields of the EM wave oscillate in a plane perpendicular to the propagation direction of the wave), one can understand why circularly polarized light emerges as the atoms are observed in a direction longitudinal with the external '''B''' field, and why they appear as plane-polarized as viewed from the transverse direction. The understanding in the classical framework helps to build an intuition about the problem.</p>
<p>In the modern quantum mechanical description <ref name="Mullin"/><ref>Merzbacher E., [https://www.library.yorku.ca/find/Record/47405 ''Quantum Mechanics''], Wiley</ref><ref name="Bethe">Bethe H.A., Salpeter E.E., [https://www.library.yorku.ca/find/Record/2227072 ''Quantum Mechanics of One- and Two-Electron Systems''], Springer</ref> one has to take into account that the presence of the '''B''' field singles out an axis. The additional interaction term between the magnetic moment of the electronic state (proportional to the ''z'' component of the total angular momentum) and '''B''' serves to split the magnetic sublevels of states with non-zero angular momentum. The additional interaction forces the use of this axis as a quantization axis. Without an external field one usually picks a ''z'' axis, but should arrive at results that are independent of this choice. To obtain the observed result that the light emanating from spontaneous transitions without an external field is unpolarized, one has to average over random orientations of the quantization axis. The observation that a definite orientation is singled out as quantization axis in the Zeeman effect is sometimes referred to as ‘space quantization’.</p>
<p>The problem can be illustrated by using pure orbital angular momentum states, i.e.,ignoring spin, and considering an np - ms transition. This transition is an allowed electric dipole transition, since a single unit of orbital angular momentum is changed, and this difference of one unit is carried away in the form of the spin for the spontaneously radiated photon. The important quantity to watch is the change in the projection of the orbital angular momentum, which can be +1, 0, -1 depending on the choice of the magnetic sublevel.</p>
<p>A transition 2p<sub>0</sub> - 1s is associated with the emission of linearly polarized light with the oscillating electric field vector aligned with the z axis, with the wave propagation vector being orthogonal to this axis. This can be understood from the fact that the only non-vanishing matrix element for the dipole operator is <1s|''z''|2p<sub>0</sub>>. Similar calculations show that the transitions originating in the ''m'' = 1 and ''m'' = -1 sublevels result in circularly polarized light being emitted, which can propagate in the z direction only. One of the fascinating aspects of the Zeeman experiment is the following. For field-free atoms no axis is singled out, and thus, one has to include all possible orientations of the ''z'' axis, which results in the prediction that the light emitted from free atoms is unpolarized. However, once a homogeneous magnetic field is applied, an axis is singled out in space, which becomes the natural quantization axis. By probing the polarization of the spontaneously emitted light of atoms in the presence of a magnetic field one can verify that indeed the turn-on of the field causes a repopulation of the magnetic sublevels in a way that corresponds to the classical predictions of the Lorentz model. Thus, it is necessary to observe the light emitted longitudinally and transverse to the magnetic field.</p>
<p>The general theory of the Zeeman effect is complicated by the fact that the total angular momentum, i.e., added orbital and spin angular momentum of the active electron has to be considered. Based on orbital angular momentum alone the magnetic moment of an electron in a non-zero m sublevel is an integer multiple of the projection ''l<sub>z</sub>''. Once one couples ''l'' and ''s'' to form ''j'' = ''l'' + ''s'', the magnetic moment can be, but need not to be an integer multiple of ''j<sub>z</sub>'', and the proportionality is given by the Lande factor ''g''. The Lande factor can take on half-integer numbers for the initial and/or final states involved in the transition. One distinguishes between the normal and anomalous Zeeman effects depending on whether this complication arises or not <ref name="Melissinos">Melissinos A.C., [https://www.library.yorku.ca/find/Record/1641963 ''Experiments in Modern Physics''], Academic Press</ref>. The anomalous effect is rather common in atomic transitions, but in this experiment a transition with the normal Zeeman effect has been selected. The red line in cadmium (643.8 nm), which is the equivalent of the yellow line in mercury, cf.. the Grotrian diagram shown in the appendix, and the level diagram in Fig. 1 (which is Fig. 7.3 from <ref name="Melissinos"/>).
</p>
<table width=500 align=center><td>
<p align=justify>[[File:Zee-fig1.png|500px|border|center]]
<b>Figure 1 -</b> Level diagram for the Cd 643.8 nm transition with and without B field.
<br clear=right>
</p>
</td></table>
<p>From an experimental point of view a high demand is placed on the optical resolution of the interferometer. The idea is to inspect the interference pattern for a given line and to observe the quantitative changes in the pattern as the B field is applied to determine the wavelengths of the various components. The high resolution required can be obtained from multiple-beam interferometers, such as the Fabry-Perot (FP) interferometer <ref name="Jenkins"/><ref name="Melissinos"/>. Melissinos <ref name="Melissinos"/> discusses the analysis of the circular fringe pattern as produced by the FP. An easier alternative is provided by a special instrument that perfects the same method, called a Lummer-Gehrcke (LG) plate <ref name="Jenkins"/>. Since its interference pattern is more complicated to derive, you should concentrate on understanding the principles of multiple-beam interferometry using the FP and be aware of the analogies. Note that the FP has a wide range of applications in optics.</p>
<table width=500 align=center><td>
<p align=justify>[[File:Zee-fig2a.png|500px|border|center]]
<b>Figure 2a -</b> Multiple reflection between the surfaces of a Lummer-Gehrcke plate.
<br clear=right>
</p>
</td></table>
<table width=500 align=center><td>
<p align=justify>[[File:Zee-fig2b.png|500px|border|center]]
<b>Figure 2b -</b> Apparatus for the Zeeman experiment with a Lummer-Gehrcke plate.
<br clear=right>
</p>
</td></table>

<table width=700 align=center><td>
<p align=justify>[[File:800px-Zee_fig2c.png‎|700px|border|center]]
<b>Figure 2c -</b> Apparatus for the Zeeman experiment.
<br clear=right>
</p>
</td></table>

<p>The LG plate shown as part of the apparatus in Fig. 2 consists of a precisely polished quartz glass plate of given thickness d with a prism attached at one end so that light entering from the slit has an angle of incidence on the plate that is near the critical angle. This results in some refractive transmission and mostly reflection at the glass/air surface. The reflected light inside the glass plate undergoes multiple ‘bounces’ of this type (interior reflection and partial refractive transmission). Two different interference patterns emerge when looking at a grazing angle at the top or bottom of the LG plate. The pattern formed at the top shows sharp bright lines on a dark background. In contrast to a Michelson interferometer a multiple-beam interferometer such as the FP and LG can produce an uneven interference pattern <ref name="Jenkins"/><ref name="Melissinos"/>.</p>
<p>The separation between the fringes that appear without the magnetic field depends on the angle of observation. This spacing ''ΔA'' has to be determined for the particular fringe chosen for observation. As a magnetic field is applied each bright fringe splits either into two or into three depending on the orientation with respect to the magnetic field. To obtain a quantitative measure of the Zeeman effect, one needs to determine the '''B''' dependent splitting ''ΔS'' relative to ''ΔA''. Making use of the ratio eliminates the need to know the optical magnification, observation angle and distance from the plate. The frequency splitting depends also on the LG plate thickness d (as in the FP case), and additionally on the index of refraction η of the quartz glass. In the FP case this would be equal to 1, but there are versions of the experiment where the evacuation of a sealed FP interferometer is used to produce a scanning effect in the fringe pattern <ref name="Preston">Preston D.W. Dietz E.R., [https://www.library.yorku.ca/find/Record/1038893 ''The Art of Experimental Physics''],Wiley</ref>. The frequency splitting can be written as</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Zee-eqn1.png|160px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>
<p>The corresponding energy difference should equal</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Zee-eqn2v2.PNG|220px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>
<p>One common method of determining the electron charge-to-mass ratio is through eq (2). Our interest is, however, to determine the energy splitting as a function of the magnetic field strength ''B''.</p>
<p>In our version of the Zeeman experiment the intense red Cd line at 643.8 nm is used. For optical transitions Cd acts as an effective two-electron system, i.e., it has a He-like configuration, as has Hg. Compare the Grotrian diagram shown in Fig. 1 to the one for mercury provided in the appendix (cf.. the Franck-Hertz experiment). In order to understand the selection rules for allowed electric dipole transitions follow the arguments given in <ref name="Preston"/> in the context of the HeNe laser experiment. The two active electrons have combined orbital angular momentum ''L'' = l<sub>1</sub>+l<sub>2</sub>, spin S = s<sub>1</sub>+s<sub>2</sub>, and total angular momentum J = j<sub>1</sub>+j<sub>2</sub>. Allowed transitions require a change of one unit in ''L'' and ''J'' to make up for the spin of the photon, considering that spin flip is unlikely. Using <sup>(2''S''+1)</sup>''L<sub>J</sub>'' notation (with ''L'' = 0 denoted as S, ''L'' = 1 as P, ''L'' = 2 as D, etc) we have for the relevant line a <sup>1</sup>D<sub>2</sub> - <sup>1</sup>P<sub>1</sub> transition. This means that the spins are paired up (spin singlet) and that in nonrelativistic notation a 5s5d to 5s5p transition takes place. In Hg the equivalent line at the n = 6 level is the yellow line at 579 nm. The shift of the same line towards yellow is the result of having an additional electron shell in the core. What wavelength is associated with this transition in He?</p>
<p>For the advanced student: note that the initial level splits into 5 sublevels ''M<sub>J</sub>'' = -2,-1,0,1,2 , while the final state has ''M<sub>J</sub>'' = -1,0,1. They split equidistantly and one can group the nine possible transitions according to the allowed ''ΔM'' = -1,0,1 (cf.. Ref. <ref name="Melissinos"/> Fig. 7.3). To understand the polarization of the emitted light in the presence of the external B field note that for an electromagnetic wave its electric, magnetic fields and the wave propagation vector '''k''' form a right-handed coordinate system. Understand the validity of the dipole approximation (the wavelength λ is much longer than atomic dimensions) and how the electric field of the EM wave can be replaced by a constant vector times a temporary oscillatory factor (ref. <ref name="Melissinos"/><ref name="Bethe"/>). Convince yourself why no linearly polarized light can be observed in the longitudinal direction as the magnetic field is turned on. Correspondingly understand why circularly polarized light as observed in the longitudinal direction must appear as linearly polarized when observed in a direction transverse to the ''B'' field. Why can all three components associated with the ''ΔM'' = -1,0,1 selection rule be observed in the transverse direction?</p>
<p>To verify these predictions about the polarization states of the light when the B field is turned on you need to recall some optical properties of polarizers and of quarter-wave plates (cf.. Ref.1). By placing these in the correct order you can verify the following:</p>
<p>In the transverse direction, use a linear polarizer to identify the polarization states of the three components with '''B''' turned on; what happens for ''B'' = 0?</p>
<p><b>NOTE: To perform these tests, place the polarizers (and/or waveplates) before the the LG plate, <u>not</u> in between the LG plate and CCD.</b></p>
<p>In the longitudinal direction, use a quarter-wave plate convert the circularly polarized (CP) light to two perpendicular
linearly polarized components corresponding to left- and right CP light respectively. Use a polarizer to extinguish each of these components separately; what happens for ''B'' = 0?</p>
<p>Collect sufficient data for both observation directions to demonstrate the linearity of the line
splitting with the magnetic field. You will need to perform a calibration of the magnetic field as a function of the current and should comment on possible saturation effects, i.e., a linear behaviour of the splitting with ''B'', but non-linear with the magnet current ''I'' at strong fields, where part of the electric energy may be converted to heat. Determine the gyromagnetic ratio (''g'') from your observations. </p>
<p>'''Warning:''' The Cd lamp emits ultraviolet light in addition to other lines such as the red Cd line. The apparatus contains a narrow-band red filter so that your eyes are protected when observing through the telescope. Avoid looking into the lamp itself (even though it is rated to be safe), i.e., cover the apparatus with a sheet of paper to reduce unnecessary eye contact with the lamp. The lamp takes several minutes to reach a proper operating temperature for the red line to be visible.</p>
<p><b>Obtain assistance when changing the observation direction from transverse to longitudinal or vice versa!</b></p>

<h3> Using the CCD Camera</h3>
<p>A CCD camera (AmScope MU300) is provided to allow for easy viewing of the lines. To operate the CCD, run the program "ToupView", then select ''Acquire''-> ''Live Capture''-> ''UCMOS03100KPA'' from the menu. A window will appear which is the live image being collected by the CCD. The brightness of the image can be changed using the ''Setup'' -> ''View Souce Properties'' -> ''Expose'' tab. A reasonable choice of values is an ''Exposure'' of 700ms with an ''Analog Gain'' of 3. Correct adjustment of the support system will allow you to clearly view the lines. Sliding of the CCD camera in and out will allow for focus. You can Save the image using ''Capture'' -> ''Capture a Frame'' command.</p>
<table width=500 align=center><td>
<p align=justify>[[File:ToupView.png|500px|border|center]]
<b>Figure 3-</b> ToupView CCD Camera Interface.
<br clear=right>
</p>
</td></table>
<p>Once you are able to see nice clear lines as shown in Figure 3, use the ''Region of Interest'' tool to focus in on a few lines in center. You can now use the ''Zoom'' to expand the image. One the left margin of the video image, there is a scale showing the pixel number. You can use this as a fixed reference point- as you increase the applied magnetic field, the line will split into sublevels, check the dial gauge, and then use the adjusting screw to place the shifted line back to the pixel number of the original line, then check the new reading of the dial gauge and record the measurement.</p>

<h1>Appendix</h1>
<ul>
<li><b>Data for the Lummer-Gehrcke plate</b> [from Leybold’s manual]: ''d'' = 4.04 mm η = 1.4567 </li>
<li>Grotrian diagrams for Cd, Hg, and He taken from <ref>Radzig A.A., Smirnov B.M.,[https://www.library.yorku.ca/find/Record/243579 ''Reference Data on Atoms Molecules and Ions''], Springer 1985.</ref>. A copy of these are in the binder in the laboratory.
<ul>
<li>[[Media:GrotrianH.pdf| Hydrogen]]</li>
<li>[[Media:GrotrianHe.pdf| Helium]]</li>
<li>[[Media:GrotrianHg.pdf| Mercury]]</li>
<li>[[Media:GrotrianHgCd.pdf| Cadmium and Mercury]]</li>
</ul>
</li>
</ul>

<h1>References</h1>
<references/>

File:Zee-eqn2v2.PNG

2015-04-14T18:19:55Z

Mgeorge:

Main Page/PHYS 4210/Mass Spectrometer

2015-04-10T19:49:11Z

Mgeorge:

<h1>Mass Spectrometer</h1>
<p>The mass spectrometer is a device that separates and identifies ions according to their mass-to-charge ratio using the linear acceleration and deflection of ions, in electric and magnetic fields respectively.</p>
<table width=500 align=center><td>
<p align=justify>[[File:Mspec-fig1.png|500px|border|center]]
<b>Figure 1 -</b> Schematic diagram of the magnetic selector mass spectrometer.
<br clear=right>
</p>
</td></table>

<h1>Key Concepts</h1>
<ul>
<li>Charge-to-mass ratio</li>
<li>A/D Converter</li>
<li>Mean free path</li>
<li>Faraday Cup</li>
<li>Diffusion pump </li>
<li>magnetic selector</li>
<li>Roughing pump</li>
<li>Ion gauge </li>
<li>Thermocouple gauge</li>
</ul>

<h1>Pre-Lab Requirement</h1>
<p><b>This experiment has a prelab component. You must complete this exercise before you meet the TA for a demonstration.</b></p>
<p>Prepare a table of showing at which accelerating voltage you would expect to see a signal for the isotopes listed in Table I below. Provide these for various values of magnetic field between 0.1T and 0.3T.</p>
<p>For example:</p>

<table border='1'>
<tr><td width=100> </td><td width=100><b>0.10 T</b></td><td width=100><b>0.12 T</b> </td><td width=100><b>0.14 T</b> </td><td width=100><b>...</b> </td><td width=100><b>0.30 T</b> </td> </tr>
<tr><td><b><sup>1</sup>H</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>4</sup>He</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>6</sup>Li</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>7</sup>Li</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>7</sup>LiH</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>9</sup>Be</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>12</sup>C</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>14</sup>N</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>16</sup>O</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>23</sup>Na</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>24</sup>Mg</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>28</sup>Si</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>32</sup>S</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>39</sup>K</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>40</sup>Ca</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
<tr><td><b><sup>41</sup>K</b></td><td> </td><td> </td><td> </td><td> </td><td> </td></tr>
</table>

<h1>Theory</h1>
<p>A filament coated with a salt (e.g. sodium sulfate) when heated, produces neutral atoms and ions (e.g., Na<sup>+</sup>). This process of surface ionization works if the ionization potential of the atom is not too large compared to the work function of the metal <ref>Duckworth, H.E., [https://www.library.yorku.ca/find/Record/49255 ''Mass Spectroscopy''], (Cambridge University Press 1958) (pp. 35-36 on Surface Ionization)</ref>. </p>
<p>In turn these ions are accelerated towards collimating slit by a potential difference V, and acquire a (small) kinetic energy of</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Mspec-eqn1.png|110px|center]]
</p>
</td><td> <b>(1)</b></td></tr></table>

<p>where q, m, and v are the charge, mass and velocity of the ions respectively. </p>
<p>Some ions pass through the collimating slit and into the homogeneous magnetic field of strength B, this field will deflect them into circular paths of radius R such that the centrifugal and magnetic forces balance. For this condition we have:</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Mspec-eqn2.png|110px|center]]
</p>
</td><td> <b>(2)</b></td></tr></table>
<p>Thence from eqs. 1 and 2 the mass-to-charge ratio is given by</p>
<table width=400 align=center>
<tr><td>
<p align=justify>[[File:Mspec-eqn3.png|90px|center]]
</p>
</td><td> <b>(3)</b></td></tr></table>
<p>The value of R is fixed by the geometry of the spectrometer. In practice there is a problem with determining its accurate value, since the magnetic field has fringes both where the ions enter and exit. Therefore, it is not simply determined by the size of the magnet, but an effective radius has to be determined. By varying B or V, ions with different mass-charge ratios can be collected.</p>
<p>Assuming singly charged ions (q = 1e) and a radius that is fixed by the size of the magnet, we see that knowledge of V and B allows us to identify the mass of a given isotope.</p>
<ul>
<li> e = 1.60 x 10<sup>-19</sup> Coulombs</li>
<li> R = 4.8 x 10<sup>-2</sup> meters (you may have to calibrate for a known mass number)</li>
<li> m = atomic weight in a.m.u., and 1 a.m.u. = 1.66 x 10<sup>-27</sup> kg.</li>
</ul>
<p>Note that the magnetic field strength B is measured in Tesla (in SI units). (The Earth's magnetic field has a strength on the order of 1 Gauss = 10<sup>-4</sup> T). By reading the voltage at the peaks for a particular magnetic field, and substituting into equation (3), it is possible to identify the isotope(s) [use Maple or Mathematica].</p>

<p>A typical I-V plot for fixed B looks as follows (identity of peaks removed):</p>
<table width=500 align=center><td>
<p align=justify>[[File:Mspec-fig2.png|500px|border|center]]
<b>Figure 2 -</b> A typical mass spectrum.
<br clear=right>
</p>
</td></table>
<p>You will find it useful to consult a [[Media:Atomic_mass_abund.pdf| list of atomic weights]] to determine which ions correspond to the masses appearing in your spectrum.</p>

<p>A problem arises in making the experiment work properly. If the ions were allowed to travel through air, they would collide with air molecules and the simple theory would be inapplicable. Hence the mass spectrometer has to be evacuated via vacuum pumps to increase the mean free path of the ions to be at least as large as the entire distance of travel from the filament to the detector (a simple Faraday cup).</p>
<p>Using kinetic theory it can be estimated from the relationship between the mean free path λ [in mm] and the pressure p [in pascals, 1 Pa = 1 Nm-2 10 μ bar; 1 Torr = 1 mmHg = 133.32 Pa] (ref. <ref name="Delchar">Delchar, T.A., [https://www.library.yorku.ca/find/Record/1178993 ''Vacuum Physics and Techniques''], (Chapman & Hall, London 1993)</ref>, eq. 1.16:λ = 6.6/p) that a vacuum better than 10<sup>-4</sup> Torr is required to allow the ions to pass 10-15 cm with an insignificant probability of collision.</p>
<p>Two practical problems arise in the context of vacuum technology: (1) how does one generate a high vacuum? and (2) how does one measure a high vacuum? Ref. <ref name="Delchar"/> provides an excellent in-depth overview for both of these problems. We can only summarize here briefly the two-stage approach used for this apparatus:</p>
<p>A rotary forepump is used to provide a rough vacuum (hence the term 'roughing pump') in the range of 50-100 milliTorr, and this vacuum can be measured with a thermocouple gauge (useful down to 1 mTorr). A rotary pump is a more efficient version of a piston pump and is filled with oil to lubricate and seal. The pump chamber drags air molecules from the vacuum chamber to an exhaust outlet.</p>
<p>To achieve a 'high' vacuum (ref. <ref name="Delchar"/>, p. 110) an oil diffusion pump is used. An oil chosen for its low boiling temperature is heated and air molecules are dragged along with the vaporized oil. Such a pump has to be backed by a roughing pump. Since one operates the two pumps in series (cf.. Fig. 3), care has to be taken not to create a vacuum in a part of the system that would suck out the oil from one of the two pumps. Thus, careful procedures have to be followed! Also the diffusion pump has to be 'backed' (i.e., the roughing pump must be on) after shutdown until it has properly cooled. If air is allowed to reach the oil of the diffusion pump while it is still hot, the diffusion pump oil will burn and contaminate the high-vacuum system, making extensive clean-up procedures necessary.</p>
<p>A high vacuum can be measured using an ion gauge. A tube with a filament, and separate cathode and anode driven by a controller, is attached to the vacuum system. It detects the presence of a residual gas by measuring the current that is carried between the cold cathode and anode by ions produced from the residual gas striking the hot filament. This gauge is extremely sensitive and varies the filament current to set its range. It cannot be used above 0.1 mTorr (the controller shuts off the filament current). Thus, the ion gauge should not be turned on until the oil diffusion pump has had enough time (at least 20 min.) to warm up and evacuate the chamber to at least this level. Otherwise the lifetime of the $200 tube will be reduced significantly. A vacuum of below 10<sup>-5</sup> Torr should be reached after the diffusion pump has typically been in operation for about an hour, provided that the vacuum system was sealed properly.</p>
<p>Very clear step-by-step procedures for the start-up and shut-down procedures for the operation of the vacuum pumps are provided. Follow them carefully. From start-up to measurement and from last measurement to complete shutdown takes about 45 min. respectively. </p>
<p>Familiarize yourself with the vacuum system, the electrical apparatus to drive the mass spectrometer, the magnet assembly and its supplies, the electrometer/XY recorder set-up (that measures currents in the 10<sup>-11</sup> A range!). During shut-down you can analyze the spectra.</p>

<h1>Procedure</h1>
<p>To prepare a filament the holder has to be unscrewed (this should only be done in the presence of a supervisor). Before removing the banana plugs that supply the filament current, accelerating voltage and focusing plate voltages make sure that the power supplies are turned off! Handle the screws carefully! Undo the top screw last and hold the assembly so that it does not bang into the vacuum chamber. Observe how an O-ring is used to ensure a proper vacuum and do not scratch the brass plate or damage the O-ring.</p>
<p>Connect a piece of tungsten wire wound in the form of a coil between the two posts. This is the filament. Paint a weak aqueous solution of Na<sub>2</sub>SO<sub>4</sub> onto the filament (not touching the electrodes or focusing plates). Dry using a blow dryer and reassemble the vacuum system. Make sure the O-ring is seated properly and carefully insert the assembly such that the filament is parallel to the slit. The screws that hold the plate have to be screwed in carefully by hand for the first several turns to avoid damage. Gentle repeated tightening cross-wise ensures a parallel attachment without a torque which is crucial to obtain a good vacuum.</p>
<p><b>Before you begin the pump down procedure, measure the resistance across the filament from the electrical feedthrough ports to ensure the filament is not broken and is attached correctly.</b></p>

<table width=500 align=center><td>
<p align=justify>[[File:MS_VacuumSystem.png|400px|border|center]]
<b>Figure 3 -</b> The Vacuum Pump System.
<br clear=right>
</p>
</td></table>
<p>Use the diagram to understand how air molecules flow for the different phases of the start-up and shut-down procedures. Draw arrows that indicate the flow. The procedures are given below.</p>

<h2>Start-up Procedure (if diffusion pump cold, and system is at atmospheric pressure)</h2>
<ol>
<li>Turn on FAN (by connecting the diffusion pump plug to the power bar)</li>
<li>Turn on WATER (a cooling mechanism above the diffusion pump to trap oil vapour)</li>
<li>Close VALVES A and B, open VALVE C.</li>
<li>Close AIR INLET valve</li>
<li>Turn on ROTARY pump (wall plug) and wait until pressure on TC gauge < 150 mTorr</li>
<li>Open B-valve to rough out the vacuum chamber; Close B-valve when TC gauge reaches < 150 mTorr again</li>
<li>Open A-valve to rough the diffusion pump and vacuum chamber (and to back the diffusion pump later)</li>
<li>Close B-Valve to shut off the bypass path.</li>
<li>When pressure on TC < 150 mTorr, turn on DIFFUSION pump (switch on metal box with indicator light) </li>
<li>Wait for 30 minutes</li>
<li>Turn on ION GAUGE controller: a) Power on; b) Filament on</li>
<li>Turn on filament current, accelerating voltage, (magnetic field supply) when the pressure is below 2x10<sup>-5</sup> Torr.</li>
</ol>

<h2>Shut Down Procedure</h2>
<ol>
<li>Turn OFF the ION GAUGE: a) Filament off; b) Power off</li>
<li>Turn of filament current and accelerating voltage.</li>
<li>Turn off DIFFUSION pump (switch on the metal box), but leave the FAN on</li>
<li>Wait ONE HOUR for diffusion pump to cool (this can be accelerated by air cooling)</li>
<li>Close valve A</li>
<li>Turn ROTARY pump OFF (pull the plug)</li>
<li>Open AIR INLET valve</li>
<li>Turn WATER off</li>
<li>Turn FAN off.</li>
</ol>

<h2>Filament Change/Re-coat Procedure (if diffusion pump is hot, and system is under vacuum)</h2>
<p> Preform this procedure if the experiment has been working, and now the filament is either broken or needs to be re-coated with more salt solution. The current state should be diffusion pump and roughing pump ON, VALVE A and VALVE C open, VALVE B closed.</p>
<ol>
<li>Turn OFF the ION GAUGE: a) Filament off; b) Power off</li>
<li>Turn of filament current and accelerating voltage.</li>
<li>Close VAVLE C. Now the experiment chamber is isolated from the pumping system.</li>
<li> To bring the experiment chamber to atmospheric pressure, loosen the screw nut at the base of the glass ion gauge. Gently lift the ion gauge- you should be able to hear air rushing into the experiment chamber. Allow the pressures to equalize. </li>
<li> Remove the flange with the filament (watch out when removing the last screw to hold the flange!), and repair/re-coat as necessary.</li>
<li> It is a good idea at this point to thoroughly rinse the filament to remove any previous coatings so your mass spectra can be more easily interpreted </li>
<li> When coating the filament, dab some of the provided solution onto the filament (being careful not to contaminate the deflector plates) and dry using the hair dryer. Repeat this until you can see salt residue on the filament, usually this requires 5 or more coats.</li>
<li> Replace the flange with the filament after ensuring the o-ring and sealing surfaces are clean. Tighten all screws.</li>
<li> Before we can use the diffusion pump on the experiment chamber, we first have to reach a pressure below 150 mtorr. So, our technique will be to stop "backing" the diffusion pump while we "rough out" the experiment chamber.</li>
<li> Close VALVE A.</li>
<li> Open VALVE B fully to quickly rough out the experiment chamber. </li>
<li> One the thermocouple gauge reads below 150 mtorr (hopefully no more than a couple of minutes), close VALVE B and open VALVE A. If you do not reach below 150 mtorr in 5 minutes, close VALVE A and open VALVE B and seek out help.</li>
<li> Open VALVE C to start pumping on the experiment chamber with the diffusion pump. </li>
<li>Wait for 30 minutes</li>
<li>Turn on ION GAUGE controller: a) Power on; b) Filament on</li>
<li>Turn on filament current, accelerating voltage, (magnetic field supply) when the pressure is below 2x10<sup>-5</sup> Torr.</li>
</ol>

<p>'''If you are unclear about any of the above steps, please consult the TA or the Lab Technologist or the Course Director. Any incorrect ordering of opening and closing valves can damage the pumps.'''</p>

<h2>Experimental Procedure</h2>

<table width=800 align=center><tr><td>
<p align=justify>[[File:MS_ElectronicsLayout.png|350px|border|center]]
<b>Figure 4a -</b> Electronic System block diagram.
</p>
<br clear=right>
</td>
<td>
<p align=justify>[[File:MS_VoltageDividerBox.png|350px|border|center]]
<b>Figure 4b -</b> Voltage Divider Box.
<br clear=right>
</p>
</td></tr></table>

<table width=500 align=center><td>
<p align=justify>[[File:Mspec-fig5.png|500px|border|center]]
<b>Figure 5 -</b> Electromagnetic, supply and measurement probe assembly.
<br clear=right>
</p>
</td></table>

<h3>Part A</h3>
<ol>
<li>Familiarize yourself with the electric circuit shown in Figs. 4 and 5.</li>
<li>Turn on the magnet power and the gaussmeter. The appropriate range of magnetic field strengths is from 100 to 350 mT. The solenoid current can be tuned by coarse and fine voltage control knobs. Be careful to change the voltages slowly, to not harm the power supply.</li>
<li>On the accelerating voltage power supply, lower the voltage control knob fully CCW, and current control knob fully CW. Turn on the electrometer. The full-scale reading of the electrometer should be in the range of 10 x 10<sup>-11</sup> amps. Watch that the needle does not exceed the scale!</li>
<li>When the vessel has been evacuated to 2x10<sup>-5</sup> Torr or less (ion gauge) and not before, turn the filament supply on (otherwise the filament would burn). Slowly turn the filament setting up to about 2 Amps. If the ammeter does not give a reading, the filament is broken, and must be replaced.</li>
<li><p>Ions striking the detector cause a current to pass through the picoammeter. This is amplified, and input to the data collection computer using an LabJack™ Analog-to-Digital (A/D) converter. The accelerating voltage monitored and recorded using another channel of the A/D converter. The accelerating voltage should range from 0 to 400 volts.</p>
<p><b>Note on the Keithly 610C Electrometer</b> The electrometer being used to measure the ion currents has the unfortunate feature that when the input becomes too large (off scale) the analog output drops to zero. Be aware of this, and monitor the front panel of the electrometer to ensure that the needle is comfortably in the range when on a peak.</p> </li>

<li>Data will be collected and displayed using a LabView™ program called “Mass Spectrometer with USBHV.vi”. The operation of the vi is described below.</li>
<table width=500 align=center><td>
<p align=justify>[[File:Mspec-fig6.png|700px|border|center]]
<b>Figure 6 -</b> LabView™ control program operation.
<br clear=right>
</p>
</td></table>
<li> Notes on the program:
<ul>
<li>The USBHV power supply performance is poor below 15V, so never set a value below that. </li>
<li> Data is recorded from the time the program runs, until you press "STOP", so in your processing of the data, you need to trim off the unwanted bits.</li>
<li>A reasonable V/sec setting would be 1 second, but you may decide on other values.</li>
<li>Data will be recorded from the moment the program start running until the program ends. Before clicking “STOP” ensure the filename is entered correctly and that the “Save?” button is activated. </li>
</ul>
</li>
<li>If may be necessary optimize the output by using the 'focusing' dials and the 'filament supply' dial while 'sitting' on a peak. Do not exceed a filament current of I<sub>f</sub> = 2A. Data will be collected using a LabJack A/D converter interfaced to a LabView™ control program. </li>
<li>Attain a mass spectrum for 6 values of applied magnetic field in the range of 0.1T to 0.3T.</li>

</ol>

<h3>Part B</h3>

<p> Now that you have learned how the mass spectrometer works, and have used the expected Na peaks to calibrate the mass spectrometer, you can now use the mass spectrometer to determine the identity of an "unknown" ion.</p>
<p> Follow the [[#Filament_Change/Re-coat_Procedure_(if_diffusion_pump_is_hot,_and_system_is_under_vacuum)|Filament Change/Re-coat Procedure]], coating the filament the unknown salt solution provided in the vial labeled with a "?". Take scans with an applied B field of 0.16T, 0.2T, and 0.24T. Use your results to determine the unknown salt. Assume an ion charge of +1.</p>
<p> When finished, follow the [[#Shut_Down_Procedure| shut down procedure]].</p>

<h2>Required for the Report</h2>
<ol>
<li>Part A Experimental results. Six graphs (or more) should be recorded for various values of B ranging from 0.1T - 0.3T. Record the current reading on the electrometer for at least one peak on every spectrum.</li>
<li>Attempt to identify all obtained peaks by calculating q/m values. Draw a graph of V against B<sup>2</sup> for the Na<sup>+</sup> ions. What can you conclude from this?</li>
<li>Comment on the variation of the peak current values for the same ionic species for the graphs produced at different B-values. Does the transmissivity of the system vary with V (and B)? Comment on the mass resolution reached at different B-values.</li>
<li>Part B Experimental results. Three graphs (or more) as detailed above. Identify all peaks. What is the unknown salt? Comment on the expected features of that ions peak.(hint: are there multiple mass isotopes?)</li>
<li>Provide a drawing of the vacuum chamber and magnet geometry (just where the ions travel) with dimensions (measure roughly with a ruler and estimate slit positions!) and indicate how 90 degree focusing works <ref>Marcley R.G., ''Apparatus Drawings Project. Report Number 7. Versatile Mass Spectrometer'' [http://ajp.aapt.org/resource/1/ajpias/v28/i5/p418_s1 Am. J. Phys. '''28''', 418 (1960)]</ref><ref>Dewdney, J.W., ''Undergraduate Mass Spectrometer'' [http://ajp.aapt.org/resource/1/ajpias/v28/i5/p452_s1 Am. J. Phys. '''28''', 452 (1960)]</ref>.</li>
</ol>

<h1>References</h1>
<references/>

PHYS 1010, 1410 & 1420

2015-04-07T15:03:53Z

Mgeorge:

<h1> Special Note </h1>
<p><b> The strike is over, please carefully follow the revised schedule below. Thank you to our fantastic TAs who continued to offer their services during the strike ensuring student's learning was only minimally interrupted. For students who missed labs during the strike, opportunities to perform Exp 10 and Exp 11 will be offered during the week of April 14 to April 17- see below.</b></p>

<h1> Remediation Option </h1>
<p> The following sessions are offered as remediation to any student in any course who missed Experiment 10 or Experiment 11. Please note, you are obliged to complete Experiment 10 and Experiment 11. Please simply show up to any of the sessions listed below to complete your experiments.</p>
<ul>
<li>Tuesday April 14th, 9:30am - 12:30pm </li>
<li>Tuesday April 14th, 2:30pm - 5:30pm </li>
<li>Wednesday April 15th, 2:30pm - 5:30pm </li>
<li>Thursday April 16th, 2:30pm - 5:30pm </li>
<li>Friday April 17th, 2:30pm - 5:30pm </li>
</ul>

<h1> REVISED LAB SCHEDULE </h1>
<ul>
<li> [[PHYS1010 Schedule|SECTION X PHYS1010 Schedule (and PHYS1420 Lab sections 9,12,16)]] </li>
<li> [[PHYS1410 Schedule|SECTION Y PHYS1410 Schedule]] </li>
<li> [[PHYS1420 Schedule|SECTION Z PHYS1420 Schedule (all sections except 9,12,16)]] </li>
</ul>

<h2> General Information </h2>

<p> These labs serve as the practical teaching experience for PHYS 1010, PHYS 1410, and PHYS 1420. The labs are located in '''102C''' and '''102D''' Bethune College.Select your course below to view your lab schedule. The schedule also appears in the Lab Manual which you can pick up from the York Bookstore.</p>

<p><b>NOTE:</b> Be sure to pick up a copy of the lab manual from the bookstore, and preform the prelab exercise for Experiment 1 ''before'' coming to your first lab.</p>
<p> Check the schedule carefully to see which weeks you have experiments, and in which order you will be performing them.</p>

<h2>Lab Coordinator</h2>
<p> The lab coordinator is responsible for the administration of these labs. Should you have issues such as- you wish to change lab sections, you have missed your scheduled lab time, or other matters for which the TA cannot assist, please see the lab coordinator during the office hours listed below.</p>
<table>
<tr><td>'''Lab Coordinator'''</td><td>Matthew George</td></tr>
<tr><td>'''Office Hours'''</td><td> MW 4:30pm 5:30pm</td></tr>
<tr><td>'''Location'''</td><td> Bethune 102 C</td> </tr>
<tr><td>'''Email'''</td><td>mgeorge (at) yorku.ca</td></tr>
</table>

<h2>Teaching Assistants</h2>
<p> The Teaching Assistant is responsible for providing you the physics knowledge, and the practical know-how required in order to complete these experiments successfully in a timely manner. You should pay careful attention to what they have to say, and heed their advice. They will also be responsible for marking your lab report. They have the authority to deny entry or remove from the lab any student they feel is: acting in an unsafe manner, arriving more than 15 minutes late, grossly unprepared, causing major disruptions, or attempting to stay beyond the 3 hour limit.</p>

<h2> Help Sessions</h2>
<p>There will be help sessions everyday from 1:00pm to 2:00pm in room 102C and/or 102D Bethune. Drop by and get expert help with your prelab exercises, get a sneak peak at the apparatus for your next experiment, and get prepared. The detailed schedule of TA coverage for the session is [[Media:15WinterHelpv3.pdf |here]]. </p>



<h2> Lab Rules </h2>
<ol>
<li> Lab safety is the number one priority. If you are unsure on how to operate the equipment, or believe you may be doing something which might cause harm to you or your classmates, stop and and ask the TA for clarification.</li>
<li> If you are purposely misusing the equipment in a manner which is obviously unsafe, you will be told to leave, and receive a mark of zero for this experiment.</li>
<li> Show up on time- the TA will give a short presentation at the beginning of each lab, where you will learn some very useful information. If you show up late, you will miss this. If you show up more than 15 mintues late, the TA can forbid you from performing the experiment, and you will receive a mark of zero.</li>
<li><b> You must leave the workstation as you have found it! All the equipment must be exactly in the manner in which you found it. All scraps of paper, eraser bits, and other garbage must be cleaned from the station before you leave. Failure to do so will result in a loss of up to 30% for that lab.</b></li>
<li> Each lab session is 3 hours, there are no provisions made for extra time. 15 minutes before the end of the lab, you should start cleaning up you workstation, and leave the room by the end of the lab session.</li>
<li> Report broken or damaged equipment to the TA immediately. You are not responsible for broken equipment, you will not be charged, and your mark will not suffer. We need to know of broken equipment so we can fix or replace it before the next lab session.</li>
<li> No more than two students working together as lab partners is allowed.</li>
<li> A valid medical note is the only acceptable reason for missing a lab. This must be presented to the lab coordinator in order to be considered for scheduling or an exemption.</li>
</ol>

<h2>Prelab Preparation</h2>
<p>You will know from the posted schedule which experiment you will be doing. Before coming to do the experiment, you are expected to read the appropriate section of the manual. Be sure you understand the theory involved, consult your textbook, and plan your practical work. Most of the experiments contain prelab exercises which must be completed on a separate sheet of paper before you come to the lab. This preparation is most important. It is unlikely that you will be able to finish the experiment satisfactorily or learn from them if you do not prepare beforehand. There may be short, unannounced quizzes on the experiment during some labs.</p>

<h2>Lab Reports</h2>
<p>A sample lab report is included in the lab manual (appendix F). </p>
<p>We do not require you to write an elaborate report for each experiment. The report should include name, name of partner, title and date. The experimental data, whenever possible, should be summarized in the form of a table, with title, column headings, units and experimental errors. Graphs should have titles, axes labelled and units included. Errors of all measured quantities should be indicated on graphs in the form of error bars. Calculations should be shown and organized in a logical way, with short comments and explanations. Just formulas with substituted data are not acceptable.
Calculations of errors is an important part of the lab report (next section in the manual provides more information regarding error calculations and rounding of final result and its error). </p>
<p>You are encouraged to record in your report for future reference any comments regarding the theory or method or apparatus which enhance your understanding. Your report should resemble a research scientist's day-to-day experimental log rather than a polished scientific paper. </p>
<p>It is preferred that you write laboratory reports in notebooks, which encourage better organization and neatness. Do not tear pages out of the books, if a mistake is made, simply cross out the mistake neatly. Two books will be required to be used alternately throughout the year. Light weight coil notebooks are suitable. Put your name and lab time clearly on the outside. </p>
<p>The three-hour session should be sufficient for the taking of measurements and for calculations and conclusions, etc. Be punctual - latecomers will find it difficult to complete the assignment. All lab reports, finished or unfinished, must be handed in to your demonstrator by the end of the three-hour lab session.
Your report will be marked by the demonstrator whose name appears on the top of the attendance list which you sign. It will be your responsibility to collect your report from this demonstrator during your next laboratory session. At this time you should discuss with your demonstrator any matters concerning the report(s).</p>

<h2> Lab Marks</h2>
<p> Depending in which course you are enrolled (1010,1410,1420) the amount your lab marks contribute to your final mark can vary from 10%-20%. The course requires 11 labs, and your lowest of the 11 will be dropped when calculating your final lab mark. Your lab reports will be marked by the TA, with some fraction for the prelab, error analysis, results, answers to questions, neatness and completeness.</p>

<h2> Lab Partners</h2>
<p>Some students claim that they learn more while working with a lab partner; others prefer to work alone. For certain experiments where basic techniques, etc. are explored, you will be required to work individually - this will be stated in the lab outline for those particular experiments. For the other experiments we will try to provide sufficient apparatus so that you may work with another student who has been assigned the same experiment or alone, as you prefer. For a few of the experiments the mechanical work is so difficult that one person cannot perform the experiment satisfactorily. If two students work together, <b>each should take a turn at reading all the instruments and although both will have the same data, each student must submit an independent report, with independent calculations.</b> </p>

<p><b>Lab partners are randomly assigned.</b> This facilitates meeting many friends, promotes social skills as well as reduces the probability of dishonesty when doing lab work. The details of how lab partners are assigned will be explained in the first lab.</p>

<h2>Lab Safety</h2>
<p>Scientists very commonly live to a grand old age in spite of their daily encounters with many hazards. The main reason for this is that a scientist doing an experiment is paying very close attention to everything that happens, is expecting the unknown and can react quickly to it. Your best protection against accidents in the lab is a constant thoughtful alertness which never permits your actions to become "mechanical" and "reflex". </p>
<p>Specific hazards which exist in particular experiments will be stressed in the respective lab outline. Please pay very careful attention to these warnings and act accordingly. </p>
<p> Notify the TA or lab coordinator of any accident or injury no matter how insignificant it may seem. </p>
<p>In the case of a fire, at the sound of the fire alarm in the building, the university stipulates that everyone must leave the building. In the case of a fire in the lab, the TA is responsible for taking the appropriate action to curb it, but the students must leave the building immediately. </p>

<b> A 24-hour Emergency Services Telephone Centre operates on York Campus and can be alerted by calling 33333 on all campus telephones or 736-2100 Ext. 33333 on public telephones.
Health services are located in York Lanes. </b>

<h2>Academic Honesty</h2>
<p>Students will certainly discuss and talk about their studies with their friends and this can be very useful; but any work that you hand in must have been done by yourself. This is the only way to test your own competence and to prepare yourself for positions of responsibility after graduation. If scientists are dishonest, they are useless.</p>
<p><b>THE UNIVERSITY CONSIDERS ALL FORMS OF COPYING AND CHEATING TO BE SERIOUS OFFENCES. </b>[[http://www.yorku.ca/secretariat/policies/index-policies.html YorkU Policy on Academic Honesty]].</p>

<ul>
<li>[[LAB INFORMATION|LAB INFORMATION]] </li>
<li>[[MEASUREMENTS AND ERRORS|MEASUREMENTS AND ERRORS]] </li>
<li>[[MEASURING LENGTH|MEASURING LENGTH]] </li>
<li>[[GRAPHS|GRAPHS]] </li>
</ul>

PHYS 1010, 1410 & 1420

2015-04-07T15:03:12Z

Mgeorge:

<h1> Special Note </h1>
<p><b> The strike is over, please carefully follow the revised schedule below. Thank you to our fantastic TAs who continued to offer their services during the strike ensuring student's learning was only minimally interrupted. For students who missed labs during the strike, opportunities to perform Exp 10 and Exp 11 will be offered during the week of April 13 to April 18- see below.</b></p>

<h1> Remediation Option </h1>
<p> The following sessions are offered as remediation to any student in any course who missed Experiment 10 or Experiment 11. Please note, you are obliged to complete Experiment 10 and Experiment 11. Please simply show up to any of the sessions listed below to complete your experiments.</p>
<ul>
<li>Tuesday April 14th, 9:30am - 12:30pm </li>
<li>Tuesday April 14th, 2:30pm - 5:30pm </li>
<li>Wednesday April 15th, 2:30pm - 5:30pm </li>
<li>Thursday April 16th, 2:30pm - 5:30pm </li>
<li>Friday April 17th, 2:30pm - 5:30pm </li>
</ul>

<h1> REVISED LAB SCHEDULE </h1>
<ul>
<li> [[PHYS1010 Schedule|SECTION X PHYS1010 Schedule (and PHYS1420 Lab sections 9,12,16)]] </li>
<li> [[PHYS1410 Schedule|SECTION Y PHYS1410 Schedule]] </li>
<li> [[PHYS1420 Schedule|SECTION Z PHYS1420 Schedule (all sections except 9,12,16)]] </li>
</ul>

<h2> General Information </h2>

<p> These labs serve as the practical teaching experience for PHYS 1010, PHYS 1410, and PHYS 1420. The labs are located in '''102C''' and '''102D''' Bethune College.Select your course below to view your lab schedule. The schedule also appears in the Lab Manual which you can pick up from the York Bookstore.</p>

<p><b>NOTE:</b> Be sure to pick up a copy of the lab manual from the bookstore, and preform the prelab exercise for Experiment 1 ''before'' coming to your first lab.</p>
<p> Check the schedule carefully to see which weeks you have experiments, and in which order you will be performing them.</p>

<h2>Lab Coordinator</h2>
<p> The lab coordinator is responsible for the administration of these labs. Should you have issues such as- you wish to change lab sections, you have missed your scheduled lab time, or other matters for which the TA cannot assist, please see the lab coordinator during the office hours listed below.</p>
<table>
<tr><td>'''Lab Coordinator'''</td><td>Matthew George</td></tr>
<tr><td>'''Office Hours'''</td><td> MW 4:30pm 5:30pm</td></tr>
<tr><td>'''Location'''</td><td> Bethune 102 C</td> </tr>
<tr><td>'''Email'''</td><td>mgeorge (at) yorku.ca</td></tr>
</table>

<h2>Teaching Assistants</h2>
<p> The Teaching Assistant is responsible for providing you the physics knowledge, and the practical know-how required in order to complete these experiments successfully in a timely manner. You should pay careful attention to what they have to say, and heed their advice. They will also be responsible for marking your lab report. They have the authority to deny entry or remove from the lab any student they feel is: acting in an unsafe manner, arriving more than 15 minutes late, grossly unprepared, causing major disruptions, or attempting to stay beyond the 3 hour limit.</p>

<h2> Help Sessions</h2>
<p>There will be help sessions everyday from 1:00pm to 2:00pm in room 102C and/or 102D Bethune. Drop by and get expert help with your prelab exercises, get a sneak peak at the apparatus for your next experiment, and get prepared. The detailed schedule of TA coverage for the session is [[Media:15WinterHelpv3.pdf |here]]. </p>



<h2> Lab Rules </h2>
<ol>
<li> Lab safety is the number one priority. If you are unsure on how to operate the equipment, or believe you may be doing something which might cause harm to you or your classmates, stop and and ask the TA for clarification.</li>
<li> If you are purposely misusing the equipment in a manner which is obviously unsafe, you will be told to leave, and receive a mark of zero for this experiment.</li>
<li> Show up on time- the TA will give a short presentation at the beginning of each lab, where you will learn some very useful information. If you show up late, you will miss this. If you show up more than 15 mintues late, the TA can forbid you from performing the experiment, and you will receive a mark of zero.</li>
<li><b> You must leave the workstation as you have found it! All the equipment must be exactly in the manner in which you found it. All scraps of paper, eraser bits, and other garbage must be cleaned from the station before you leave. Failure to do so will result in a loss of up to 30% for that lab.</b></li>
<li> Each lab session is 3 hours, there are no provisions made for extra time. 15 minutes before the end of the lab, you should start cleaning up you workstation, and leave the room by the end of the lab session.</li>
<li> Report broken or damaged equipment to the TA immediately. You are not responsible for broken equipment, you will not be charged, and your mark will not suffer. We need to know of broken equipment so we can fix or replace it before the next lab session.</li>
<li> No more than two students working together as lab partners is allowed.</li>
<li> A valid medical note is the only acceptable reason for missing a lab. This must be presented to the lab coordinator in order to be considered for scheduling or an exemption.</li>
</ol>

<h2>Prelab Preparation</h2>
<p>You will know from the posted schedule which experiment you will be doing. Before coming to do the experiment, you are expected to read the appropriate section of the manual. Be sure you understand the theory involved, consult your textbook, and plan your practical work. Most of the experiments contain prelab exercises which must be completed on a separate sheet of paper before you come to the lab. This preparation is most important. It is unlikely that you will be able to finish the experiment satisfactorily or learn from them if you do not prepare beforehand. There may be short, unannounced quizzes on the experiment during some labs.</p>

<h2>Lab Reports</h2>
<p>A sample lab report is included in the lab manual (appendix F). </p>
<p>We do not require you to write an elaborate report for each experiment. The report should include name, name of partner, title and date. The experimental data, whenever possible, should be summarized in the form of a table, with title, column headings, units and experimental errors. Graphs should have titles, axes labelled and units included. Errors of all measured quantities should be indicated on graphs in the form of error bars. Calculations should be shown and organized in a logical way, with short comments and explanations. Just formulas with substituted data are not acceptable.
Calculations of errors is an important part of the lab report (next section in the manual provides more information regarding error calculations and rounding of final result and its error). </p>
<p>You are encouraged to record in your report for future reference any comments regarding the theory or method or apparatus which enhance your understanding. Your report should resemble a research scientist's day-to-day experimental log rather than a polished scientific paper. </p>
<p>It is preferred that you write laboratory reports in notebooks, which encourage better organization and neatness. Do not tear pages out of the books, if a mistake is made, simply cross out the mistake neatly. Two books will be required to be used alternately throughout the year. Light weight coil notebooks are suitable. Put your name and lab time clearly on the outside. </p>
<p>The three-hour session should be sufficient for the taking of measurements and for calculations and conclusions, etc. Be punctual - latecomers will find it difficult to complete the assignment. All lab reports, finished or unfinished, must be handed in to your demonstrator by the end of the three-hour lab session.
Your report will be marked by the demonstrator whose name appears on the top of the attendance list which you sign. It will be your responsibility to collect your report from this demonstrator during your next laboratory session. At this time you should discuss with your demonstrator any matters concerning the report(s).</p>

<h2> Lab Marks</h2>
<p> Depending in which course you are enrolled (1010,1410,1420) the amount your lab marks contribute to your final mark can vary from 10%-20%. The course requires 11 labs, and your lowest of the 11 will be dropped when calculating your final lab mark. Your lab reports will be marked by the TA, with some fraction for the prelab, error analysis, results, answers to questions, neatness and completeness.</p>

<h2> Lab Partners</h2>
<p>Some students claim that they learn more while working with a lab partner; others prefer to work alone. For certain experiments where basic techniques, etc. are explored, you will be required to work individually - this will be stated in the lab outline for those particular experiments. For the other experiments we will try to provide sufficient apparatus so that you may work with another student who has been assigned the same experiment or alone, as you prefer. For a few of the experiments the mechanical work is so difficult that one person cannot perform the experiment satisfactorily. If two students work together, <b>each should take a turn at reading all the instruments and although both will have the same data, each student must submit an independent report, with independent calculations.</b> </p>

<p><b>Lab partners are randomly assigned.</b> This facilitates meeting many friends, promotes social skills as well as reduces the probability of dishonesty when doing lab work. The details of how lab partners are assigned will be explained in the first lab.</p>

<h2>Lab Safety</h2>
<p>Scientists very commonly live to a grand old age in spite of their daily encounters with many hazards. The main reason for this is that a scientist doing an experiment is paying very close attention to everything that happens, is expecting the unknown and can react quickly to it. Your best protection against accidents in the lab is a constant thoughtful alertness which never permits your actions to become "mechanical" and "reflex". </p>
<p>Specific hazards which exist in particular experiments will be stressed in the respective lab outline. Please pay very careful attention to these warnings and act accordingly. </p>
<p> Notify the TA or lab coordinator of any accident or injury no matter how insignificant it may seem. </p>
<p>In the case of a fire, at the sound of the fire alarm in the building, the university stipulates that everyone must leave the building. In the case of a fire in the lab, the TA is responsible for taking the appropriate action to curb it, but the students must leave the building immediately. </p>

<b> A 24-hour Emergency Services Telephone Centre operates on York Campus and can be alerted by calling 33333 on all campus telephones or 736-2100 Ext. 33333 on public telephones.
Health services are located in York Lanes. </b>

<h2>Academic Honesty</h2>
<p>Students will certainly discuss and talk about their studies with their friends and this can be very useful; but any work that you hand in must have been done by yourself. This is the only way to test your own competence and to prepare yourself for positions of responsibility after graduation. If scientists are dishonest, they are useless.</p>
<p><b>THE UNIVERSITY CONSIDERS ALL FORMS OF COPYING AND CHEATING TO BE SERIOUS OFFENCES. </b>[[http://www.yorku.ca/secretariat/policies/index-policies.html YorkU Policy on Academic Honesty]].</p>

<ul>
<li>[[LAB INFORMATION|LAB INFORMATION]] </li>
<li>[[MEASUREMENTS AND ERRORS|MEASUREMENTS AND ERRORS]] </li>
<li>[[MEASURING LENGTH|MEASURING LENGTH]] </li>
<li>[[GRAPHS|GRAPHS]] </li>
</ul>

PHYS 1010, 1410 & 1420

2015-04-01T12:46:05Z

Mgeorge:

<h1> Special Note </h1>
<p><b> The strike is over, please carefully follow the revised schedule below. Thank you to our fantastic TAs who continued to offer their services during the strike ensuring student's learning was only minimally interrupted. For students who missed labs during the strike, opportunities to perform Exp 10 and Exp 11 will be offered during the week of April 13 to April 18 (and perhaps other times)- Details available soon.</b></p>

<h1> REVISED LAB SCHEDULE </h1>
<ul>
<li> [[PHYS1010 Schedule|SECTION X PHYS1010 Schedule (and PHYS1420 Lab sections 9,12,16)]] </li>
<li> [[PHYS1410 Schedule|SECTION Y PHYS1410 Schedule]] </li>
<li> [[PHYS1420 Schedule|SECTION Z PHYS1420 Schedule (all sections except 9,12,16)]] </li>
</ul>

<h2> General Information </h2>

<p> These labs serve as the practical teaching experience for PHYS 1010, PHYS 1410, and PHYS 1420. The labs are located in '''102C''' and '''102D''' Bethune College.Select your course below to view your lab schedule. The schedule also appears in the Lab Manual which you can pick up from the York Bookstore.</p>

<p><b>NOTE:</b> Be sure to pick up a copy of the lab manual from the bookstore, and preform the prelab exercise for Experiment 1 ''before'' coming to your first lab.</p>
<p> Check the schedule carefully to see which weeks you have experiments, and in which order you will be performing them.</p>

<h2>Lab Coordinator</h2>
<p> The lab coordinator is responsible for the administration of these labs. Should you have issues such as- you wish to change lab sections, you have missed your scheduled lab time, or other matters for which the TA cannot assist, please see the lab coordinator during the office hours listed below.</p>
<table>
<tr><td>'''Lab Coordinator'''</td><td>Matthew George</td></tr>
<tr><td>'''Office Hours'''</td><td> MW 4:30pm 5:30pm</td></tr>
<tr><td>'''Location'''</td><td> Bethune 102 C</td> </tr>
<tr><td>'''Email'''</td><td>mgeorge (at) yorku.ca</td></tr>
</table>

<h2>Teaching Assistants</h2>
<p> The Teaching Assistant is responsible for providing you the physics knowledge, and the practical know-how required in order to complete these experiments successfully in a timely manner. You should pay careful attention to what they have to say, and heed their advice. They will also be responsible for marking your lab report. They have the authority to deny entry or remove from the lab any student they feel is: acting in an unsafe manner, arriving more than 15 minutes late, grossly unprepared, causing major disruptions, or attempting to stay beyond the 3 hour limit.</p>

<h2> Help Sessions</h2>
<p>There will be help sessions everyday from 1:00pm to 2:00pm in room 102C and/or 102D Bethune. Drop by and get expert help with your prelab exercises, get a sneak peak at the apparatus for your next experiment, and get prepared. The detailed schedule of TA coverage for the session is [[Media:15WinterHelpv3.pdf |here]]. </p>



<h2> Lab Rules </h2>
<ol>
<li> Lab safety is the number one priority. If you are unsure on how to operate the equipment, or believe you may be doing something which might cause harm to you or your classmates, stop and and ask the TA for clarification.</li>
<li> If you are purposely misusing the equipment in a manner which is obviously unsafe, you will be told to leave, and receive a mark of zero for this experiment.</li>
<li> Show up on time- the TA will give a short presentation at the beginning of each lab, where you will learn some very useful information. If you show up late, you will miss this. If you show up more than 15 mintues late, the TA can forbid you from performing the experiment, and you will receive a mark of zero.</li>
<li><b> You must leave the workstation as you have found it! All the equipment must be exactly in the manner in which you found it. All scraps of paper, eraser bits, and other garbage must be cleaned from the station before you leave. Failure to do so will result in a loss of up to 30% for that lab.</b></li>
<li> Each lab session is 3 hours, there are no provisions made for extra time. 15 minutes before the end of the lab, you should start cleaning up you workstation, and leave the room by the end of the lab session.</li>
<li> Report broken or damaged equipment to the TA immediately. You are not responsible for broken equipment, you will not be charged, and your mark will not suffer. We need to know of broken equipment so we can fix or replace it before the next lab session.</li>
<li> No more than two students working together as lab partners is allowed.</li>
<li> A valid medical note is the only acceptable reason for missing a lab. This must be presented to the lab coordinator in order to be considered for scheduling or an exemption.</li>
</ol>

<h2>Prelab Preparation</h2>
<p>You will know from the posted schedule which experiment you will be doing. Before coming to do the experiment, you are expected to read the appropriate section of the manual. Be sure you understand the theory involved, consult your textbook, and plan your practical work. Most of the experiments contain prelab exercises which must be completed on a separate sheet of paper before you come to the lab. This preparation is most important. It is unlikely that you will be able to finish the experiment satisfactorily or learn from them if you do not prepare beforehand. There may be short, unannounced quizzes on the experiment during some labs.</p>

<h2>Lab Reports</h2>
<p>A sample lab report is included in the lab manual (appendix F). </p>
<p>We do not require you to write an elaborate report for each experiment. The report should include name, name of partner, title and date. The experimental data, whenever possible, should be summarized in the form of a table, with title, column headings, units and experimental errors. Graphs should have titles, axes labelled and units included. Errors of all measured quantities should be indicated on graphs in the form of error bars. Calculations should be shown and organized in a logical way, with short comments and explanations. Just formulas with substituted data are not acceptable.
Calculations of errors is an important part of the lab report (next section in the manual provides more information regarding error calculations and rounding of final result and its error). </p>
<p>You are encouraged to record in your report for future reference any comments regarding the theory or method or apparatus which enhance your understanding. Your report should resemble a research scientist's day-to-day experimental log rather than a polished scientific paper. </p>
<p>It is preferred that you write laboratory reports in notebooks, which encourage better organization and neatness. Do not tear pages out of the books, if a mistake is made, simply cross out the mistake neatly. Two books will be required to be used alternately throughout the year. Light weight coil notebooks are suitable. Put your name and lab time clearly on the outside. </p>
<p>The three-hour session should be sufficient for the taking of measurements and for calculations and conclusions, etc. Be punctual - latecomers will find it difficult to complete the assignment. All lab reports, finished or unfinished, must be handed in to your demonstrator by the end of the three-hour lab session.
Your report will be marked by the demonstrator whose name appears on the top of the attendance list which you sign. It will be your responsibility to collect your report from this demonstrator during your next laboratory session. At this time you should discuss with your demonstrator any matters concerning the report(s).</p>

<h2> Lab Marks</h2>
<p> Depending in which course you are enrolled (1010,1410,1420) the amount your lab marks contribute to your final mark can vary from 10%-20%. The course requires 11 labs, and your lowest of the 11 will be dropped when calculating your final lab mark. Your lab reports will be marked by the TA, with some fraction for the prelab, error analysis, results, answers to questions, neatness and completeness.</p>

<h2> Lab Partners</h2>
<p>Some students claim that they learn more while working with a lab partner; others prefer to work alone. For certain experiments where basic techniques, etc. are explored, you will be required to work individually - this will be stated in the lab outline for those particular experiments. For the other experiments we will try to provide sufficient apparatus so that you may work with another student who has been assigned the same experiment or alone, as you prefer. For a few of the experiments the mechanical work is so difficult that one person cannot perform the experiment satisfactorily. If two students work together, <b>each should take a turn at reading all the instruments and although both will have the same data, each student must submit an independent report, with independent calculations.</b> </p>

<p><b>Lab partners are randomly assigned.</b> This facilitates meeting many friends, promotes social skills as well as reduces the probability of dishonesty when doing lab work. The details of how lab partners are assigned will be explained in the first lab.</p>

<h2>Lab Safety</h2>
<p>Scientists very commonly live to a grand old age in spite of their daily encounters with many hazards. The main reason for this is that a scientist doing an experiment is paying very close attention to everything that happens, is expecting the unknown and can react quickly to it. Your best protection against accidents in the lab is a constant thoughtful alertness which never permits your actions to become "mechanical" and "reflex". </p>
<p>Specific hazards which exist in particular experiments will be stressed in the respective lab outline. Please pay very careful attention to these warnings and act accordingly. </p>
<p> Notify the TA or lab coordinator of any accident or injury no matter how insignificant it may seem. </p>
<p>In the case of a fire, at the sound of the fire alarm in the building, the university stipulates that everyone must leave the building. In the case of a fire in the lab, the TA is responsible for taking the appropriate action to curb it, but the students must leave the building immediately. </p>

<b> A 24-hour Emergency Services Telephone Centre operates on York Campus and can be alerted by calling 33333 on all campus telephones or 736-2100 Ext. 33333 on public telephones.
Health services are located in York Lanes. </b>

<h2>Academic Honesty</h2>
<p>Students will certainly discuss and talk about their studies with their friends and this can be very useful; but any work that you hand in must have been done by yourself. This is the only way to test your own competence and to prepare yourself for positions of responsibility after graduation. If scientists are dishonest, they are useless.</p>
<p><b>THE UNIVERSITY CONSIDERS ALL FORMS OF COPYING AND CHEATING TO BE SERIOUS OFFENCES. </b>[[http://www.yorku.ca/secretariat/policies/index-policies.html YorkU Policy on Academic Honesty]].</p>

<ul>
<li>[[LAB INFORMATION|LAB INFORMATION]] </li>
<li>[[MEASUREMENTS AND ERRORS|MEASUREMENTS AND ERRORS]] </li>
<li>[[MEASURING LENGTH|MEASURING LENGTH]] </li>
<li>[[GRAPHS|GRAPHS]] </li>
</ul>

PHYS1420 Schedule

2015-03-30T19:33:03Z

Mgeorge:

<p>Lab sections 9, 12, and 16 follow the [[PHYS1010 Schedule|PHYS1010 Schedule]] </p>

<h2> Lab Sections 1,2,3,4,5,6,7,8,11,15</h2>
<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 29-Oct 3 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 20-24 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 3-7 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 10-14 </td><td>4. Elasticity</td></tr>
<tr><td>Jan 26-30 </td><td>6. DC Electricity</td></tr>
<tr><td>Feb 9-13 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Mar 2-6 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Mar 17-20 </td><td>9. Speed of Sound</td></tr>
<tr><td>Mar 23-27 </td><td>11. Diffraction of Light/ Spectroscopy</td></tr>
<tr><td>Mar 30-Apr 2, Apr13 </td><td>10. Polarization of Light/Lenses</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li> Only Monday sessions performed Experiment 8, and Monday sessions will not perform Experiment 9.</li>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li> PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
<li>There will be no Labs on April 3 (Good Friday), they are rescheduled for Monday April 13.</li>
</ul>

PHYS1410 Schedule

2015-03-25T15:27:36Z

Mgeorge:

<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 22-26 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 20-24 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 10-14 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 24-28 </td><td>4. Elasticity</td></tr>
<tr><td>Jan 19-23 </td><td>6. DC Electricity</td></tr>
<tr><td>Feb 2-6 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Feb 23-27 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Mar 2-6 </td><td>9. Speed of Sound (not all sessions)</td></tr>
<tr><td>Mar 23-27 </td><td>10. Polarization of Light/Lenses</td></tr>
<tr><td>Apr 6- 10 </td><td>11. Diffraction of Light/ Spectroscopy</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li> Only Monday sessions performed Experiment 9. Other sessions will not perform Experiment 9.</li>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li> PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
</ul>

PHYS1410 Schedule

2015-03-25T15:26:59Z

Mgeorge:

PHYS1410 Schedule

2015-03-16T20:35:48Z

Mgeorge:

PHYS1420 Schedule

2015-03-16T20:34:47Z

Mgeorge:

<h2>Lab sections 9, 12, and 16 </h2>
<p>follow the [[PHYS1010 Schedule|PHYS1010 Schedule]] </p>

<h2> Lab Sections 1,2,3,4,5,6,7,8,11,15</h2>
<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 29-Oct 3 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 20-24 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 3-7 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 10-14 </td><td>4. Elasticity</td></tr>
<tr><td>Jan 26-30 </td><td>6. DC Electricity</td></tr>
<tr><td>Feb 9-13 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Mar 2-6 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Mar 17-20 </td><td>9. Speed of Sound</td></tr>
<tr><td>Mar 23-27 </td><td>11. Diffraction of Light/ Spectroscopy</td></tr>
<tr><td>Mar 30-Apr 2, Apr13 </td><td>10. Polarization of Light/Lenses</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li> Only Monday sessions performed Experiment 8, and Monday sessions will not perform Experiment 9.</li>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li> PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
<li>There will be no Labs on April 3 (Good Friday), they are rescheduled for Monday April 13.</li>
</ul>

PHYS1420 Schedule

2015-03-16T20:33:33Z

Mgeorge:

<h2>Lab sections 9, 12, and 16 </h2>
<p>follow the [[PHYS1010 Schedule|PHYS1010 Schedule]] </p>

<h2> Lab Sections 1,2,3,4,5,6,7,8,11,15</h2>
<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 29-Oct 3 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 20-24 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 3-7 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 10-14 </td><td>4. Elasticity</td></tr>
<tr><td>Jan 26-30 </td><td>6. DC Electricity</td></tr>
<tr><td>Feb 9-13 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Mar 2-6 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Mar 17-20 </td><td>9. Speed of Sound</td></tr>
<tr><td>Mar 23-27 </td><td>11. Diffraction of Light/ Spectroscopy</td></tr>
<tr><td>Mar 30-Apr 2, Apr13 </td><td>10. Polarization of Light/Lenses</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li> PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
<li>There will be no Labs on April 3 (Good Friday), they are rescheduled for Monday April 13.</li>
</ul>

PHYS1010 Schedule

2015-03-16T20:33:21Z

Mgeorge:

<h2>For PHYS1010 Students, as well as PHYS1420 students of Lab sections 9,12 & 16.</h2>

<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 22-26 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 14-17,27 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 3-7 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 17-21 </td><td>4. Elasticity</td></tr>
<tr><td>Nov 24-28 </td><td>5. Thermal Physics (PHYS1010 students only)</td></tr>
<tr><td>Jan 12-16 </td><td>6. DC Electricity</td></tr>
<tr><td>Jan 26-30 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Feb 9-13 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Feb 23-27 </td><td>9. Speed of Sound</td></tr>
<tr><td>Mar 30-Apr 2, Apr13 </td><td>11. Diffraction of Light/Spectroscopy</td></tr>
<tr><td>Apr 6-10 </td><td>10. Polarization of Light/Lenses</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li>PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
<li>There are no labs on Monday October 13 (Thanksgiving Holiday), this is rescheduled for October 27.</li>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li>There will be no Labs on April 3 (Good Friday), they are rescheduled for Monday April 13.</li>
</ul>

PHYS1410 Schedule

2015-03-16T20:32:52Z

Mgeorge:

<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 22-26 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 20-24 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 10-14 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 24-28 </td><td>4. Elasticity</td></tr>
<tr><td>Jan 19-23 </td><td>6. DC Electricity</td></tr>
<tr><td>Feb 2-6 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Feb 23-27 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Mar 2-6 </td><td>9. Speed of Sound (not all sessions)</td></tr>
<tr><td>Mar 23-27 </td><td>10. Polarization of Light/Lenses</td></tr>
<tr><td>Apr 6- 10 </td><td>11. Diffraction of Light/ Spectroscopy</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li> PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
<li>There will be no Labs on April 3 (Good Friday), they are rescheduled for Monday April 6.</li>
</ul>

PHYS1420 Schedule

2015-03-16T20:32:01Z

Mgeorge:

<h2>Lab sections 9, 12, and 16 </h2>
<p>follow the [[PHYS1010 Schedule|PHYS1010 Schedule]] </p>

<h2> Lab Sections 1,2,3,4,5,6,7,8,11,15</h2>
<table class="wikitable">
<tr><td width="100"><b>Week</b></td><td width="300"><b>Experiment</b></td></tr>
<tr><td>Sept 29-Oct 3 </td><td>1. Linear Motion</td></tr>
<tr><td>Oct 20-24 </td><td>3. Oscillatory Motion</td></tr>
<tr><td>Nov 3-7 </td><td>2. Centripetal Force/ Rotational Inertia</td></tr>
<tr><td>Nov 10-14 </td><td>4. Elasticity</td></tr>
<tr><td>Jan 26-30 </td><td>6. DC Electricity</td></tr>
<tr><td>Feb 9-13 </td><td>7. RC Circuits, Oscilloscope</td></tr>
<tr><td>Mar 2-6 </td><td>8. Charge-to-Mass ratio of electron/ Electromagnetic Induction</td></tr>
<tr><td>Mar 17-20 </td><td>9. Speed of Sound</td></tr>
<tr><td>Mar 23-27 </td><td>11. Diffraction of Light/ Spectroscopy</td></tr>
<tr><td>Mar 30-Apr 2, Apr13 </td><td>10. Polarization of Light/Lenses</td></tr>
</table>

<h2> Notes:</h2>
<ul>
<li>You do not necessarily perform the experiments in the order of the lab manual.</li>
<li> PHYS1410 and PHYS1420 students do not perform Experiment 5.</li>
</ul>