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)
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25 articles.
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