Millikan's oil drop experiment proved charge is quantised

Turning Points in Physics | AQA A-Level Physics

Key Definition

Quantisation of charge: Electric charge exists only in integer multiples of the elementary charge, $e = 1.60 \times 10^{-19}$ C. You cannot have a fraction of $e$.

The experimental setup

Oil drops are sprayed into a chamber between two horizontal parallel plates. As they pass through the nozzle, friction charges them (they pick up or lose electrons).
The drops are observed through a microscope. Without an electric field, they fall under gravity, reaching terminal velocityThe constant velocity reached when the driving force (here, gravity) is exactly balanced by resistive forces (here, viscous drag). At terminal velocity, acceleration is zero. when the drag force equals their weight.
A voltage is applied across the plates, creating a uniform vertical electric field. The p.d. is adjusted until a selected drop is held stationary.

The stationary condition

When the drop is stationary, the upward electric force exactly balances the downward gravitational force:

$$QE = mg \quad \Rightarrow \quad Q\frac{V}{d} = mg \quad \Rightarrow \quad Q = \frac{mgd}{V}$$

The mass $m$ of the drop is found separately using Stokes' law (see Note 06).
The plate separation $d$ and applied voltage $V$ are measured directly.

Quantisation

Millikan repeated this for hundreds of drops and found that every measured charge was an integer multiple of $1.60 \times 10^{-19}$ C.
Typical results: $Q = 1.59 \times 10^{-19}$ C, $3.21 \times 10^{-19}$ C, $4.80 \times 10^{-19}$ C, corresponding to 1$e$, 2$e$, 3$e$.
Crucially, no charge smaller than $e$ was ever observed. This proved that charge is quantised and that $e$ is the fundamental unit of charge.
Combined with Thomson's value of $e/m_e$, Millikan's measurement of $e$ allowed the electron mass to be calculated for the first time.

Common Mistake

The stationary drop condition $QE = mg$ only applies when the drop is held perfectly still. If the drop is moving (even slowly), there is also a drag force and the equation does not hold. Make sure you state that the drop is stationary before using this relationship.