The emission of electrons, usually into a vacuum, from a heated conductor. The emitted current density, J, is given by the Richardson (or Richardson–Dushman) equation, i.e. J = AT2exp(−W/kT), where T is the thermodynamic temperature of the emitter, W is its work function, k is the Boltzmann constant, and A is a constant. Thermionic emission is the basis of the thermionic valve and the electron gun in cathode-ray tubes. The equation was derived by the British physicist Sir Owen Richardson (1879–1959) from classical statistical mechanics and later modified by the Russian-born US physicist Saul Dushman (1883–1954) using quantum mechanics.