How did Millikan show the electron charge to be quantized?

[Signifier]

In all of the physics books I have, the story is Millikan, in measuring (calculating) the charge found on tiny oil drops, "found them all to be integer multiples of a single, fundamental unit", the electron charge -e. The question I have is, HOW did he show them to all be multiples of a fundamental unit - that is, how did he show charge to be quantized?

I can dream up some very "soft" ways of "showing" this - IE, dividing each calculated charge by the smallest difference between charges, and then playing around with this smallest difference value until each charge divided by the value is very close to an integer, perhaps doing a least squares type of fitting. But there must be a more formal way to show that, given a (large) set of data, each element in the set is essentially an integer multiple of some constant, and then determining that constant.

This would be related to the neat little experiment I've seen a few places in physics education literature, where the oil drop experiment is simulated with a bunch of envelopes each containing random numbers of identical ball bearings. The idea is to measure the mass of each of the many envelopes, and then to determine the mass of a single ball bearing, analagous to the fundamental charge of the electron.

In this case, I imagine dividing all the differences between bags of similar mass by the smallest difference between two bags, and trying once again to get integer values. But this would only work if the difference in mass between two of the bags was just one ball bearing, which may not be the case.

Any suggestions or revelations would be greatly appreciated. I'm stumped. Thanks.

 

[NeoDevin]

I believe he made the drops small enough that he could expect there to be a charge of one or two electrons... I don't know all the reasoning that went into it though, hopefully someone else can help out.

 

[AcidBathSDMF]

When you divide any charge into another it would be very near an integer. If you're looking for a proof that they're integer multiples of e, I'm not sure.

 

[rbj]

I believe he made the drops small enough that he could expect there to be a charge of one or two electrons... I don't know all the reasoning that went into it though, hopefully someone else can help out.

it could have been 5 or 6 or even maybe a dozen elementary charges per droplet. but whatever it was, when the charge of each droplet was measured. i don't know how, but somehow he established that the size (and mass) of the droplets where all the same.

IIRC, the droplets were sprayed into a chamber with oppositely charged plates on the bottom and top and the voltage between the plates was adjusted until a particular subset of the drops were "frozen" (neither fell nor went up). he did this for many different droplets, but the voltage required always (to within some experimental error) took on a finite set of values (the reciprocals of the voltage were always an integer times a common value), each voltage value corresponded to an integer number of a common amount of electric charge which was believed to be the elementary charge.

 

[Meir Achuz]

The experiment is repeated in good UG labs.
With a small number of electrons on a drop, and a radiating source nearby,
you can actually observe a small (1 or 2) jump in the electrons on the drop.
This affects the subsequent motion of the same drop, as the suspending E field is changed.
It has to be done for the same drop.