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?

▶ Run the simulationSee the measured result

Units: C (the elementary charge e)

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

Millikan oil-drop calculator: radius, charge & the quantum

Weigh an electron by watching a speck of oil fall. Nothing on this page stores the elementary charge as the answer: the drop’s radius is measured by its own terminal fall — no microscope ever sees it — the charge is measured off the speed the field steals, and the quantum arrives as a trial DIVISOR whose remainder decides it. The worked drop is a median 1.15 µm one from this lab’s own 0.6–1.7 µm population, built to carry exactly three of the MODULE’s recovered quantum rather than three CODATA e, which is why dividing it by the defined SI charge returns 2.973029168 and not 3 — the page inverts to what the instrument read, not to the textbook. Two charge routes that share no arithmetic land 2.0e-16 apart: the velocity route Millikan timed, and the balancing voltage that holds a drop still, which reads no v_E at all. The continuum is not a rival theory bolted on here but a limit of the same formula — turn the per-charge noise σ up and the remainder RMS climbs to 1/√12 = 0.288675135, which this page SUMS rather than types. And the systematic that made the original experiment famous is computed, not quoted: the charge goes as the 3/2 power of the assumed air viscosity, differenced out of this page’s own chain, so Millikan’s published value sitting 0.61% below the modern one is fully accounted for by a viscosity 0.41% low — LOW, which is the direction most often stated backwards. Four things this page will not do: model Cunningham slip for drops small enough to feel individual air molecules, handle non-spherical drops, run the multi-drop scan that actually settles the largest-divisor question, or correct the simulation’s own reading.