Measuring the Electron: e/m and e

Two classic experiments measured the electron: Thomson found its charge-to-mass ratio in 1897, and Millikan its charge about fifteen years later. Together they gave its mass.

The discovery of the electron#

Discharge-tube experiments in the late 1800s convinced physicists that cathode rays were tiny negative particles. J J Thomson is credited with discovering the electron, not because he was first to run such experiments, but because he measured their properties and proposed that electrons are a part of every atom.

Thomson’s measurement of e/m#

Electrons from the cathode C are accelerated through a potential difference V to the anode A; a narrow beam passes through holes in A and A′, between deflecting plates D₁ (+) and D₂ (−), and hits a fluorescent screen. The plates’ field E pushes the beam up. Coils C₁, C₂ add a magnetic field B, perpendicular to both E and the beam, pushing it down.

Adjust the fields until the spot returns to its undeflected position. Then eE = evB, so v = E/B. The speed also follows from the accelerating voltage, ½mv² = eV:

Millikan’s oil-drop experiment#

Two accurately parallel plates a few millimetres apart sit in a glass-walled chamber. Oil droplets sprayed in through a hole in the top plate pick up charge by friction (X-rays or a radioactive source can help); lit from the side, each looks like a star through a telescope. A drop of mass m and charge q feels its weight mg, the electric force qE, buoyancy and viscous drag.

Most drops are negative, so with E downward the electric force is upward. Adjust E until a chosen drop hangs still (no drag then):

Switch the field off: the drop falls and soon reaches a steady speed v, when Stokes drag 6πηrv plus buoyancy balance its weight. That gives the radius, and then the charge:

Over thousands of drops, every charge was a small whole-number multiple of one value: e = 1.6 × 10⁻¹⁹ C, the charge of the electron. Millikan won the 1923 Nobel Prize for this work.