Open AccessThe photo-electric threshold frequency and the thermionic work function
Publication year - 1928
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1928.0047
Subject(s) - thermionic emission , work function , electron , fermi gas , atomic physics , work (physics) , saturation (graph theory) , physics , metal , condensed matter physics , quantum mechanics , chemistry , mathematics , electrode , combinatorics , organic chemistry
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 potentialX 0 /ε positive relative to free space, so that the workX 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 cm2 ., I = 120(1 —r ) T2 e -x /k T. (1) In this formular is the fraction of electrons incident on the metal from outside which are reflected at the surface, andX is the customary thermionic work function. It is related toX 0 by the formulaX =X 0 -h 2 /2m (3n̅ /4πg )⅔ . (2)