Electron Emission from Metals as a Function of Temperature

Electron emission from metals as a function of temperature.—(1) General equation. The emission of electrons from a metal may be considered as thermodynamically equivalent to the evaporation of a monatomic gas, for which an equation is derived on the basis of the Nernst heat theorem. If it is assumed that the specific heat of free electrons in the metal is negligible while the specific heat of the evaporated electrons is the same as that of a monatomic gas, the equation assumes the simple form $I=A{T}^2{\epsilon }^{\frac{-b_0}{T}}$, where $b_0=\frac{{\varphi }_{0}e}{k}$ ($e$ is electronic charge, $k$ is the Boltzmann constant, and ${\varphi }_0=\frac{\varphi -\frac{3}{2}\mathrm{kT}}{e}$, where $\varphi$ is the Richardson work function). An equation of this form has been suggested before but not on the same theoretical grounds and a different value of $A$ has been obtained. Its chief advantage over the usual Richardson equation, $I=A_1{T}^{\frac{1}{2}}{\epsilon }^{\frac{-b}{T}}$, where $b=\frac{\varphi e}{k}$, is that $A$ is theoretically a universal constant. (2) The value of the universal emission constant $A$ is computed in two ways. Using the Sackur-Tetrode equation for the chemical constant $i_0$, $A$ comes out 60.2 amp./${\mathrm{cm}}^2$ ${\mathrm{deg}.\mathrm{}}^2$, while the theory of rational units of Lewis, Gibson and Latimer gives 50.2 amp./${\mathrm{cm}}^2$ ${\mathrm{deg}.\mathrm{}}^2$. Recent experimental results of Davisson and Germer, and of Schlichter as well as data obtained by the writer agree with the new equation as well or better than with the old, but the temperature scale is not sufficiently accurately known to distinguish experimentally between the two values of $A$. (3) The relation between A and the chemical constant $i_0$ (or $C_0$) is derived.