Physics 1913

On the Elementary Electrical Charge and the Avogadro Constant

Robert A. Millikan

He caught charged oil drops in mid-air and showed electric charge comes only in whole multiples of e.

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In depth · the introduction

How do you weigh a single piece of electricity, far too small to ever see? Millikan caught it on a speck of oil floating in the air.

The big idea

Electric charge does not come in any amount you like. It comes in identical grains — and every grain is the charge of a single electron. Millikan measured the size of one grain.

His trick was to make a tiny drop of oil hover between two metal plates. Gravity pulls the drop down; turning on a voltage between the plates pushes the charged drop up. Tune the voltage just right and the drop hangs perfectly still — and from how hard you had to push to hold it, you can work out exactly how much charge it carries. Do this for drop after drop, and the charges always come out as 1, 2, 3… times the same little number. That number is e, the charge of one electron.

How it came about

The work was done at the University of Chicago between 1909 and 1913. Earlier experimenters had tried watching clouds of charged water droplets, but the water evaporated before anyone could finish measuring. Millikan — working closely with his graduate student Harvey Fletcher, whose part in the breakthrough was long under-credited — switched to oil from an ordinary perfume atomizer, which does not dry up.

Then came the patience: watching a single glowing speck through a telescope for hours, nudging the voltage, recording each tiny jump as the drop caught a passing ion. The charges always changed in equal steps. Millikan announced his value for e in 1913 and won the Nobel Prize in 1923. Decades later, historians studying his notebooks would also raise a hard question about which drops he chose to publish.

Why it mattered

This was the direct proof that electricity is made of countable units, and the first really precise measurement of how big one unit is. Combined with Thomson's earlier discovery of the electron, it pinned down the electron's mass. And by counting charge, Millikan could also count atoms — his number for e gives Avogadro's number, the staggering count of atoms in a everyday lump of matter.

A way to picture it

Imagine you may only weigh sealed bags of identical coins, never a coin on its own. One bag weighs 3 grams, another 5, another 8, another 11. You never see a bag weighing 3.5 or 4.2. The only way that works is if each coin weighs exactly 1 gram, and the bags simply hold 3, 5, 8, 11 coins. Millikan's drops were the bags; the equal-step charges told him each "coin" — each electron — carries the very same e.

Where it sits

In 1897 J. J. Thomson (thomson-1897) had found the electron and measured its charge-to-mass ratio, but not the charge by itself. Millikan supplied the missing number. Together they handed the next generation — Rutherford (rutherford-1911) and Bohr (bohr-1913) — a particle of known charge and mass to build the atom from. The grainy nature of charge his drops revealed is now woven into all of physics, and his e is one of the constants the modern system of units is literally built upon.

The original document

Original source text

R. A. Millikan · Physical Review, Series II, 2 (1913): 109–143 · Ryerson Physical Laboratory, University of Chicago

§ The question

[Annotation] Is electric charge built from indivisible grains — exact multiples of one elementary unit — or can a body carry any amount at all? J. J. Thomson had measured the electron's charge-to-mass ratio in 1897, but the charge itself was known only roughly, and Felix Ehrenhaft was claiming to see fractional "sub-electrons." Millikan set out to measure the charge directly, on the smallest objects he could isolate.

§ The oil-drop method

[Annotation] A fine mist of oil is blown from an atomizer into a chamber above a pair of horizontal brass plates. Friction in the nozzle (and X-rays passing through the air) leaves each tiny drop with a few excess or missing electrons. A single drop is watched through a short telescope: with the field off it falls under gravity at a steady terminal speed; with the field switched on it can be driven back up, or held perfectly still. From the fall speed Millikan gets the drop's radius; from the balance of forces he gets its charge.

§ The correction of Stokes's law

[Annotation] His drops are only about a micron across — comparable to the average distance an air molecule travels between collisions — so the smooth-fluid drag law of Stokes slightly overestimates the resistance. Millikan's earlier (1911) paper, "The Isolation of an Ion, a Precision Measurement of its Charge, and the Correction of Stokes's Law," introduced the slip correction that made the result precise. This refinement, more than the apparatus, is what carried the measurement to a fraction of a percent.

§ The result

[Annotation] Whenever a drop suddenly caught or lost an ion, its charge changed by a jump — and every jump, and every total, was an exact whole-number multiple of one unit. Millikan's figure for that unit was e ≈ 4.774 × 10⁻¹⁰ electrostatic units, i.e. about 1.59 × 10⁻¹⁹ coulombs — within roughly a percent of today's value. Dividing the Faraday constant of electrolysis by e then gives the number of atoms in a mole, the Avogadro constant.

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Ryerson Physical Laboratory, University of Chicago · 1913