# How do they ensure there is one electron on an oil drop in Millikan's oil drop experiment?

Since air is ionized using X-rays, in the 'observation chamber', there must be several electrons in the chamber, so the oil drops are exposed to several electrons so it seems intuitive that a single oil drop should catch more than one electron.

Then why is it that there's just one electron on a droplet or do they selectively choose those droplets which have a single electron residing on them?

• And, more to the point, they can only catch an integer number of electrons. – Jon Custer Dec 24 '17 at 8:19
• Perhaps even more to the point, did Millikan ignore droplets which apparently had fractional charges? – matt_black Dec 24 '17 at 17:04
• @DavidRicherby the point is that, unless you know the answer, you can’t use this experiment to prove it. And even when you do know the answer, there are experimental errors. Questions have been raised about whether Millikan ignored some actual observations to make his results look better. – matt_black Dec 24 '17 at 18:38
• You can overcome experimental errors with a sufficient body of data, using statistical techniques to show a tendency in favor of integer multiples of some factor. @andselisk in his reference also suggests that Millikan effectively got more than one data point per drop by observing drops over time. – Oscar Lanzi Dec 25 '17 at 14:09
• If only it were somehow possible to reproduce the experiment and verify the results... Oh wait. – barbecue Dec 25 '17 at 17:44

There does not have to be just one electron per drop. Say you have a drop which, in reality, picked up four electrons, another with five and a third drop with seven. None has one electronic charge, but when you measure charges you find they have a common factor; the first drop has four times that factor, the second has five times that factor and the third drop shows a multiplier of seven. It was this common factor, not necessarily the charge on any specific drop, that was recognized as one electronic charge.

The experiment showed all the drops had discrete amounts of charge. That means, the charges weren't all over the place (any random value). They only had specific values. Some had $2$ or $3$ or $4$ times the charge of others, but it was always some specific value that they had multiples of.

The conclusion was that oil drops didn't seem to pick up "any random amount" of charge, and the reason seemed likely to be because electric charge couldn't be just "any value". There seemed to be some basic unit of a "single electric charge", the smallest value that was found. Some oil drops had $1\times$ or $2\times$ or $5\times$ that charge, but no oil drops had (say) $3.77\times$ or $1.628\times$ that value.

• Actually, the initial formula $(1)$ that was employed in the experiment $$e'= 9\unicode[Times]{x3c0}\frac{v_0+v_E}{E}\sqrt{\frac{2\eta^3v_0}{g(\rho-\rho_0)}}\tag1$$ failed to give a constant common divisor, and Stokes law was consequently corrected for radii near the mean free path of a gas particle. $|$doi.org/10.1103/PhysRev.2.109 (Slightly different notation, here I used subscript '$0$' to denote having to do with air, and dropped subscript $n$ in the paper for an apostrophe.) – Linear Christmas Dec 27 '17 at 13:51

This is my absolute favorite physics experiment; I actually wrote a miniature essay on my lab report containing, in essence, the following:

Millikan's experiment is amazingly indirect. You don't directly measure the charge of the electron, nor do you compute it from an equation (like, say, the one relating electrostatic force to charge, though you do use this equation to deduce the non-unit charge on each oil drop). You don't even deduce it by fitting a curve to a set of data points. You do deduce it from a frequency graph, but it is, again, not any kind of fitting of the actual frequency data; rather, you identify spikes in the frequency counts and mark off the corresponding charges. Then you find their greatest common divisor and argue that your data was random enough that this must be the charge of one electron (since it is vanishingly unlikely after enough droplets that each one contained only, say, even numbers of electrons). It is actually a simple form of image recognition.

You don't need to luck into one-electron droplets. You just need to keep measuring until you have an unambiguous set of frequency spikes at sufficiently many different charges and apply (what?!) a number-theoretic computation.