---
title: "Thermionic emission: a hot surface sets a current limit"
description: "How did Richardson separate electrons leaving a hot metal from currents caused by gas?"
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Materials · Measurements · Explanation

# Thermionic emission: a hot surface sets a current limit

How did Richardson separate electrons leaving a hot metal from currents caused by gas?

Sandbox Physics · 2026-10-23

Nobel contribution: 1928-1

1. Heat a clean metal
2. Remove residual gas
3. Measure the saturation current
4. Compare its temperature dependence

The temperature law describes emission-limited current from a specified surface. Extraction can impose a different limit.

## Pumping was part of the evidence

Richardson heated wires in evacuated tubes and waited for the current to stabilize. Gas released by hot walls could mimic emission, so repeated heating and pumping tested whether the effect survived after that contamination diminished.

His 1901 platinum measurements connected a limited electron supply to the surface temperature. The 1928 award recognized the thermionic work and its law, not a newly invented electron in that year.

Sources: [1]

## Temperature opens the route out of the metal

Thermal electrons need enough energy to escape the surface work function. The equation below uses the modern Richardson–Dushman form; it is not a transcription of Richardson’s earliest 1901 formula. It combines a temperature-dependent supply with a strong exponential factor. Comparing several temperatures is more informative than measuring one bright cathode.

$$
J=A_{\mathrm R}T^2\exp\!\left(-\frac{\Phi}{k_{\mathrm B}T}\right)
$$

Sources: [1]

## A collected current can be limited after emission

A weak extraction field allows the emitted charge to repel later electrons. Then the anode current probes space charge as well as the surface. Surface films also change the effective work function, so material preparation must accompany a quoted emission constant.

Sources: [1]

## The electron gun makes that distinction visible

The related electron gun lets temperature change the source and voltage change extraction. It is useful for asking which stage limits the beam. Its simplified cathode is a teaching source; Richardson’s historical case depended on vacuum controls and repeatable temperature measurements.

Sources: [1] [2]

Continue with the physics

## Try the related models

### [Thermionic electron gun](https://sandboxphysics.com/labs/electron-gun/)

Change cathode temperature and inspect the extracted beam.

The source model illustrates emission and extraction; it does not reproduce Richardson’s original vacuum experiment.

## Sources and reading notes

1. [Richardson: Thermionic phenomena (Nobel lecture 1929; prize 1928)](https://www.nobelprize.org/uploads/2018/06/richardson-lecture.pdf)

   Richardson describes removing residual-gas effects and the temperature law for emission-limited current.

2. [Nobel Prize in Physics 1928: official award](https://www.nobelprize.org/prizes/physics/1928/summary/)

   Official attribution and award year. The observation or theoretical paper may be much earlier.

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