The photo-electric threshold frequency and the thermionic work function

Abstract

Abstract 1. Sommerfeld’s revived electron theory of metals has already had marked successes, and gives a convincing account of all their equilibrium thermoelectric properties. It is based, of course, on a greatly simplified model of the interior of a metal as a region of uniform potential X0/ε positive relative to free space, so that the work X0 is required to extract an electron from rest in the metal to rest at infinity. The electrons, however, are not all at rest, but form practically a perfect gas—a gas, however, at such a concentration that they are almost tight-packed, and obey the Ferni-Dirac statistics. The theory also yields, as I have shown in a recent note, the remarkably satisfactory formula for I, the thermionic saturation current at temperature T in amperes per cm2., I = 120(1 — r) T2e-x/kT. (1) In this formula r is the fraction of electrons incident on the metal from outside which are reflected at the surface, and X is the customary thermionic work function. It is related to X0 by the formula X = X0 -h2/2m (3n̅/4πg)⅔. (2)