### Determination of the Charge on an Electron

I. Pre-History

The charge on electron was first measured by J.J. Thomson and two co-workers (J.S.E. Townsend and H.A. Wilson), starting in 1897. Each used a slightly different method. Townsend's work will be described as an example.

Townsend's work depended on the fact that drops of water will grow around ions in humid air. Under the influence of gravity, the drop would fall, accelerating until it hit a constant speed.

Several items were measured in this experiment.

1. the mass of a water droplet (actually the average mass of many)
2. the total electric charge carried on all the droplets (this was done by absorbing the water into an acid and measuring the charge picked up.)
3. the velocity of the droplet
4. the total mass of all water droplets (found by measuring the acid's increase in weight)

He determined the e/m ratio of the droplets (2 divided by 4), then multiplied by the mass of one droplet to get the value for e.

Thomson, Townsend, and Wilson each obtained roughly the same value for the charge on positive and negative ions. It was about 1 x 10¯19 coulombs. This work continued until about 1901 or 1902.

II. Robert A. Millikan's Definitive Measurement

Robert A. Millikan started his work on electron charge in 1906 and continued for seven years. His 1913 article announcing the determination of the electron's charge is a classic and Millikan received the Nobel Prize for his efforts.

Here is a diagram of his apparatus, reproduced from his 1913 article:

Here is Millikan's description:

8. THE EXPERIMENTAL ARRANGEMENTS.

The experimental arrangements are shown in Fig. 1. The brass vessel D was built for work at all pressures up to 15 atmospheres but since the present observations have to do only with pressures from 76 cm. down these were measured with a very carefully made mercury manometer M which at atmospheric pressure gave precisely the same reading as a standard barometer. Complete stagnancy of the air between the condenser plates M and N was attained first by absorbing all of the heat rays from the arc A by means of a water cell w, 80 cm. long, and a cupric chloride cell d, and second by immersing the whole vessel D in a constant temperature bath G of gas-engine oil (40 liters) which permitted, in general, fluctuations of not more than .02° C. during an observation. This constant temperature bath was found essential if such consistency of measurement as is shown below was to be obtained. A long search for causes of slight irregularity revealed nothing so important as this and after the bath was installed all of the irregularities vanished. The atomizer A was blown by means of a puff of carefully dried and dust-free air introduced through the cock e. The air about the drop p was ionized when desired by means of Röntgen rays from X which readily passed through the glass window g. To the three windows g (two only are shown) in the brass vessel D correspond, of course, three windows in the ebonite strip c which encircles the condenser plates M and N. Through the third of these windows, set at an angle of about 18° from the line Xpa and in the same horizontal plane, the oil drop is observed.

This is a photo dating from the time of the experiment.

1. The two plates were 16 mm across, "correct to about .01 mm."
2. The hole bored in the top plate was very small.
3. The space between the plates was illuminated with a powerful beam of light.
4. He sprayed oil ("the highest grade of clock oil") with an atomizer that made drops one ten-thousandth of an inch in diameter.
5. One drop of oil would make it through the hole.
6. The plates were charged with 5,000 volts.
7. It took a drop with no charge about 30 seconds to fall across the opening between the plates.
8. He exposed the droplet to radiation while it was falling, which stripped electrons off.
9. The droplet would slow in its fall. The drops were too small to see. What he saw was a shining point of light.
10. By adjusting the current, he could freeze the drop in place and hold it there for hours. He could also make the drop move up and down many times.
11. Since the rate of ascent (or descent) was critical, he has a highly accurate scale inscribed onto the telescope used for droplet observation and he used a highly accurate clock, "which read to 0.002 second."

Millikan's Improvements over Thomson

1. Oil evaporated much slower than water, so the drops stayed essentially constant in mass.

2. Millikan could study one drop at a time, rather than a whole cloud.

3. In following the oil drop over many ascents and descents, he could measure the drop as it lost or gained electrons, sometimes only one at a time. Every time the drop gained or lost charge, it ALWAYS did so in a whole number multiple of the same charge.

The value as of 1991 (for the charge on the electron) is 1.60217733 (49) x 10¯19 coulombs. This is less than 1% higher than the value obtained by Millikan in 1913. The 49 in parenthesis shows the plus/minus range of the last two digits (the 33). It is unlikely that there will be much improvement of the accuracy in years to come.

Interesting Fact about Robert Millikan's Experiment

In "The Discovery of Subatomic Particles" by Steven Weinberg there appears a footnote on p. 97. It reads:

. . . . there appeared a remarkable posthumous memoir that throws some doubt on Millikan's leading role in these experiments. Harvey Fletcher (1884-1981), who was a graduate student at the University of Chicago, at Millikan's suggestion worked on the measurement of electronic charge for his doctoral thesis, and co-authored some of the early papers on this subject with Millikan. Fletcher left a manuscript with a friend with instructions that it be published after his death; the manuscript was published in Physics Today, June 1982, page 43. In it, Fletcher claims that he was the first to do the experiment with oil drops, was the first to measure charges on single droplets, and may have been the first to suggest the use of oil. According to Fletcher, he had expected to be co-author with Millikan on the crucial first article announcing the measurement of the electronic charge, but was talked out of this by Millikan.