Millikan oil drop · charge is quantized

Is electric charge a continuous quantity you can have any amount of, or does it come in indivisible lumps — and if so, how big is the lump?

How the lab tests it

Suspend charged oil drops between two horizontal plates. With the field OFF a drop falls at the terminal speed where gravity (buoyancy-corrected) balances Stokes drag, m'g = 6πη a v_f — so its own fall speed MEASURES its radius, a = √(9η v_f/2(ρ−ρ_air)g). With the field ON the electric force qE shifts the terminal velocity to v_E = v_f − qE/6πη a, giving the charge q = 6πη a (v_f−v_E)/E. Forward-model a population of 60 drops (each carrying some integer number of electrons, realistic 1.5% velocity noise, seeded), recover q for every one, and look at the distribution.

What it checks

the elementary charge e = 1.602×10⁻¹⁹ C — the recovered charges do not form a continuum; they land on equally-spaced bands at integer multiples n·e. The lab recovers the common unit WITHOUT being told it (a 1-D scan for the divisor that best fits every charge, then a least-squares refine e = Σ(n·q)/Σ(n²)). Control: if charge were continuous the drops' fractional remainders would scatter uniformly (RMS ≈ 0.289); instead they cluster near zero. Millikan & Fletcher's 1909–1913 result (Nobel 1923) — the proof that charge is quantized and the first precise value of e, the seventh pillar of early quantum theory after Rutherford's nucleus