Thomson measured the electron’s charge-to-mass ratio, but clearly it was desirable to measure the charge q directly. This was done in 1906 by the American scientist Robert Millikan. The Millikan oil-drop experiment is illustrated in FIGURE 37.14. A squeeze-bulb atomizer sprayed out a very fine mist of oil droplets. Millikan found that some of these droplets were charged from friction in the sprayer. The charged droplets slowly settled toward a horizontal pair of parallel-plate electrodes, where a few droplets passed through a small hole in the top plate. Millikan observed the drops by shining a bright light between the plates and using an eyepiece to see the droplets’ reflections. He then established an electric field by applying a voltage to the plates.

FIGURE 37.14 Millikan’s oil-drop apparatus to measure the fundamental unit of charge.

A drop will remain suspended between the plates, moving neither up nor down, if the electric field exerts an upward force on a charged drop that exactly balances the downward gravitational force. The forces balance when

and thus the charge on the drop is measured to be

Notice that m and q are the mass and charge of the oil droplet, not of an electron. But because the droplet is charged by acquiring (or losing) electrons, the charge of the droplet should be related to the electron’s charge.

The field strength E could be determined accurately from the voltage applied to the plates, so the limiting factor in measuring $q_{\text{drop}}$ was Millikan’s ability to determine the mass of these small drops. Ideally, the mass could be found by measuring a drop’s diameter and using the known density of the oil. However, the drops were too small $(\approx 1\mu \text{m})$ to measure accurately by viewing through the eyepiece.

Instead, Millikan devised an ingenious method to find the size of the droplets. Objects this small are not in free fall. The air resistance forces are so large that the drops fall with a very small but constant speed. The motion of a sphere through a viscous medium is a problem that had been solved in the 19th century, and it was known that the sphere’s terminal speed depends on its radius and on the viscosity of air. By timing the droplets’ fall, then using the known viscosity of air, Millikan could calculate their radii, compute their masses, and, finally, arrive at a value for their charge. Although it was a somewhat roundabout procedure, Millikan was able to measure the charge on a droplet with an accuracy of $\pm 0.1\text{\%}$.

Millikan measured many hundreds of droplets under a wide variety of conditions. He found that some of his droplets were positively charged and some negatively charged, but all had charges that were integer multiples of a certain minimum charge value. Millikan concluded that “the electric charges found on ions all have either exactly the same value or else some small exact multiple of that value.” That value, the fundamental unit of charge that we now call e, is measured to be

We can then combine the measured e with the measured charge-to-mass ratio $e\text{/}m$ to find that the mass of the electron is

Taken together, the experiments of Thomson, Millikan, and others provided overwhelming evidence that electric charge comes in discrete units and that all charges found in nature are multiples of a fundamental unit of charge we call e.