702 BELL SYSTEM TECHNICAL JOURNAL 



we set the volume of the piece of metal — a decision which is tanta- 

 mount to ignoring the atoms, to supposing the metal a vacuum 

 inhabited by free electrons only. So remarkable an assumption, 

 even though it be made only in approximation, requires some excuse. 

 Its strangeness may be mitigated by recalling, first, that slow electrons 

 may go through atoms (at least through certain kinds of atoms) 

 as imperturbably as if the atoms were not there; and second, that a 

 wave-train may go without being scattered at all through a crowd 

 of particles individually quite able to scatter it, provided that the 

 particles are arranged in a regular lattice having a spacing smaller 

 than the wave-length of the waves. The speeds attributed to electrons 

 in metals are so low and their wave-lengths are so great, that perhaps 

 they do behave in such a way. 



The "wall " is the agency which prevents the electrons from escaping; 

 it is commonly imagined as a sharp and sudden gradation of potential 

 at the surface of the metal. Any electron moving towards it from 

 within, with a velocity of which the component normal to the bounding 

 surface may be denoted by «, is supposed to be driven back into the 

 body of the metal if the corresponding "component of kinetic energy" 

 ^mu^ is less than a certain constant Wa ; while if ^mu'^ > Wa the electron 

 escapes, but with its kinetic energy diminished by Wa- According 

 to newer ideas electrons may sometimes escape even when their 

 values of |wm- are smaller than Wa, and may sometimes fail to escape 

 in the contrary case; but the earlier and simpler conception remains 

 approximately valid, and I will abide by it for a time. The constant 

 Wa may be named the work-function. 



Like the constant N, the work-function figures as a disposable 

 constant in the theory. It is an ambition of physicists to explain 

 as many as possible of the differences between different metals, by 

 varying only the values of these two constants. Later we shall find 

 it necessary to introduce others, beginning with the one which in the 

 older theories appeared as the mean free path of the electrons; but 

 there are several results of value which can be obtained with no other 

 but these two. 



I repeat now from (60) the Fermi formula for the distribution-in- 

 energy of an assemblage of N particles in volume Fat temperature T, 

 with two changes made to bring the notation into harmony with that 

 of Sommerfeld: 



Here the symbol 1/^ replaces e^, and a factor G to which we shall 



