Dual-purpose Millikan experiment with polystyrene spheres

Abstract

A common complaint leveled against the Millikan oil drop experiment, as ususally performed in the undergraduate physics laboratory, is that it often yields values of the electronic charge with inexplicably gross errors. Both students and instructors find such in-the-ballpark values of e highly unsatisfactory. The chief purpose of this article, as far as the value of the electronic charge is concerned, is to show that acceptable values of e are obtainable when polystyrene spheres of specified uniform diameter and density are substituted for oil drops in the experiment. This substitution eliminates the errors associated with the use of oil drops of unknown and variable size and removes much of the guesswork involved in assigning proper index integers to the observed charges, a likely source of error in the oil drop experiment. Because the size of the spheres is given in advance, we can make two independent determinations of the value of e, one with the use of Stokes’s law and a second without its use. Finally, because of the small size of the spheres, we can also make an estimate of the value of the Boltzmann constant, using the effects of Brownian motion on the dispersions of the sets of time measurements taken in the experiment.