Main Page/PHYS 3220/Millikan

Abstract

In this experiment charged droplets of oil, in air, moving under gravitational and electric fields are observed to verify the quantization of charge. The electric charge unit is determined to a few-percent accuracy. From the Brownian motion of the oil droplets one also obtains an estimate of Boltzmann’s constant.

Introduction

Millikan's determination of e, the charge of the electron (1909), proved that electric charges are quantized, i.e., occur as integer multiples of a unit. The measurement is performed on oil droplets that are ionized by the process of vaporization. To the present day it is true that for all elementary particles that can be freely observed, their electric charge is given as an integer multiple of a unit, i.e., q = n e. There exist, however, confined particles (quarks) that carry fractional charges of 1/3 and 2/3 of e.

The experiment makes use of an atomizer that generates oil droplets, some small fraction of which acquire positive or negative charges during the atomizing process. An electric condenser that can be charged to several hundreds of volts, and an illumination device as well as a telescope are included to observe the motion of the oil droplets. (Note that a radioactive source was used by Millikan to change the charge of droplets).

Under gravity the droplets move downwards. However, they are not in free-fall as a result of the viscosity of air, and the forces due to viscosity is described by Stokes' law. This frictional force results in a constant terminal velocity. Knowledge of the density and viscosity allows us to determine the mass of the droplet from the measured terminal velocity. The size of the droplet can be calculated by knowing the density of the oil.

Using an electric field of the right direction and magnitude Vh it is possible to counterbalance the gravitational force, i.e., to suspend the droplet (viscosity is irrelevant for a stationary droplet). This permits us to determine the charge of the droplet after the mass has been determined in the previous step.

An alternative method involves a measurement of the terminal velocity for a fixed voltage V that counteracts gravity. This was used by Millikan who did not have a continuously adjustable power supply to dial up the correct voltage for any given droplet, i.e. Vh. Both methods are used independently in this experiment.

A correction (due to Millikan) for the fact that the viscosity becomes smaller for droplets of a size comparable to the mean free path of air molecules has to be introduced for an accurate determination of the charge unit.

Theory

A charge q, situated in an electric field E experiences a force F = q E. If a potential difference V is applied to two parallel plates separated by a distance d, the constant electric field between the plates is perpendicular to the plane defined by the plates and its magnitude is given as E=V/d. Thus, by changing the voltage it is possible to counteract the gravitational acceleration g and hence to suspend a macroscopic particle of mass m with charge q according to