The photo-electric threshold frequency and the thermionic work function

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 X 0 /ε positive relative to free space, so that the work X 0 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 cm 2 ., I = 120(1 — r ) T 2 e - x / k T . (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 X 0 by the formula X = X 0 - h 2 /2 m (3 n̅ /4π g ) ⅔ . (2)