Millikan's Oil Drop Experiment: Measuring the Charge of an Electron

By 1897, J.J. Thomson had shown that electrons exist and had measured the ratio of their charge to their mass. But the charge itself remained unknown. Was electric charge continuous, like water, or did it come in fixed packets? And if so, how big was the packet? Between 1909 and 1913, the American physicist Robert Millikan, working with his graduate student Harvey Fletcher, answered both questions using nothing more exotic than tiny drops of oil, an electric field and extraordinary patience.

Why the charge mattered

Thomson’s experiments gave e/m, the charge-to-mass ratio of the electron. Knowing e would immediately give the electron’s mass. It would also give a new, independent value for Avogadro’s number, because the charge needed to deposit one mole of a singly charged ion in electrolysis (the Faraday constant, about 96,500 C/mol) equals N_A × e. See Avogadro’s number.

Earlier attempts to measure e by watching clouds of charged water droplets fall had given rough answers, but the droplets evaporated too quickly for precise work. Millikan’s key improvement was to use oil, which barely evaporates, and to watch individual droplets.

The apparatus

1. A fine spray of oil droplets was produced by an atomiser, like a perfume sprayer.
2. Some droplets drifted through a small hole into the space between two horizontal metal plates, a few millimetres apart.
3. The droplets picked up small electric charges, from friction in the atomiser or from air ionised by X-rays.
4. A voltage could be applied across the plates, creating a uniform electric field.
5. A light illuminated the droplets, and Millikan watched them through a small telescope with a scale, timing their motion with a stopwatch.

The physics: balancing forces

Each droplet experiences:

• Gravity pulling it down: weight = mg
• Air resistance opposing its motion
• Electric force from the field between the plates: F = qE, where q is the droplet’s charge and E = V/d (voltage ÷ plate separation)

Step 1: find the droplet’s mass

With the field off, a droplet falls and quickly reaches a steady terminal velocity, when air resistance balances its weight. Using Stokes’ law for air resistance on a small sphere, Millikan could calculate the droplet’s radius from its terminal velocity, and from the radius and the density of the oil, its mass.

Step 2: find its charge

With the field on, the voltage can be adjusted until the droplet hangs motionless. At that point, the upward electric force exactly balances the weight:

qE = mg → q = mgd ÷ V

(Millikan actually used a more precise method, timing droplets moving up and down under the field, but the balancing method shows the principle clearly.)

The discovery: charge comes in packets

Millikan measured the charges on many droplets, sometimes watching a single droplet for hours as it gained or lost charge. When he looked at the results, a pattern appeared: every charge was a whole-number multiple of one smallest value.

Worked example with illustrative data

Suppose five droplets give these charges:

Droplet	Charge (× 10⁻¹⁹ C)
A	3.20
B	4.81
C	1.60
D	8.00
E	6.41

Looking for a common factor:

• The differences between charges (for example, 4.81 − 3.20 = 1.61; 3.20 − 1.60 = 1.60) cluster around 1.60 × 10⁻¹⁹ C.
• Dividing each charge by 1.60 × 10⁻¹⁹ gives 2.00, 3.01, 1.00, 5.00 and 4.01: all whole numbers, within experimental error.

So the fundamental unit of charge is about 1.60 × 10⁻¹⁹ C, and droplet A carries 2 extra electrons, B carries 3, C carries 1, D carries 5 and E carries 4.

Millikan’s published value (1913) was about 1.592 × 10⁻¹⁹ C, within about 0.6% of today’s exact value, e = 1.602176634 × 10⁻¹⁹ C. (The small error came mostly from a slightly inaccurate value for the viscosity of air.)

What followed immediately

• Mass of the electron: combining e with Thomson’s e/m gives m ≈ 9.1 × 10⁻³¹ kg, about 1/1836 of a proton’s mass. See the electron.
• Avogadro’s constant: N_A = F ÷ e ≈ 96,485 ÷ 1.602 × 10⁻¹⁹ ≈ 6.02 × 10²³ mol⁻¹.

What made it so difficult

The experiment sounds simple, but it demanded remarkable care. The droplets were only about a micrometre across, visible only as tiny points of light. Air currents, temperature changes and evaporation all disturbed them. Millikan had to keep the apparatus at constant temperature, time each droplet’s motion many times over the same distance, and correct Stokes’ law for droplets so small that they were comparable to the spacing between air molecules. A single measurement could take hours of continuous observation through the telescope.

Why it was so important

The experiment proved that electric charge is quantised: it always comes in whole-number multiples of e. There’s no such thing as half an electron’s charge on a droplet. (Quarks inside protons and neutrons carry fractional charges of ±⅓e and ±⅔e, but they’re never found alone.)

Millikan received the Nobel Prize in Physics in 1923, for this work and for his experiments confirming Einstein’s equation for the photoelectric effect.

The controversy

Millikan’s reputation took a knock decades later, when historians examined his laboratory notebooks. His 1913 paper stated that the results came from all the droplets studied “during 60 consecutive days”. The notebooks showed he had observed many more droplets and excluded some from the published data.

The debate continues:

• Critics argue that selecting data, and claiming otherwise, was poor scientific practice.
• Defenders point out that many excluded runs had clear experimental problems (unstable droplets, faulty conditions), that including them wouldn’t have changed his value of e significantly, and that experienced scientists routinely judge which runs are reliable.

There’s also a lesson in what happened afterwards. Later measurements of e crept upwards gradually towards the true value, rather than jumping. The physicist Richard Feynman suggested that researchers who got values far from Millikan’s may have searched harder for errors than those who got similar values, an example of confirmation bias. It’s a useful reminder that good scientists report all their data and methods transparently. See experimental errors.

Legacy

• The elementary charge e is now one of the defining constants of the International System of Units (SI). Since 2019, it has had an exact fixed value, used to define the ampere.
• Millikan’s approach, measuring many individual events and looking for a pattern, inspired later experiments searching for fractional charges.
• Versions of the oil drop experiment are still performed in university teaching labs, giving students first-hand evidence that charge comes in packets.

Key takeaways

• Millikan and Fletcher measured the charge on individual oil droplets held in an electric field between 1909 and 1913.
• Balancing the electric force against gravity gives q = mgd/V; the droplet’s mass comes from its terminal velocity.
• Every charge was a whole-number multiple of about 1.6 × 10⁻¹⁹ C, proving charge is quantised.
• Combined with Thomson’s e/m, this gave the electron’s mass; with the Faraday constant, it gave Avogadro’s number.
• Questions about Millikan’s data selection make the experiment a lasting lesson in honest reporting of results.