SURFACES OF DISCONTINUITY - 681 



further out, a negative charge (either in the form of a surface 

 charge or in a more or less diffuse layer) not actually coincident 

 with the positive charge. 



We can now give the theoretical connection between electron 

 affinities and contact potentials quite simply if the reader will 

 recall the few remarks on statistical conditions in subsection (9) 

 of this article. Conceive a metal body to be in a vacuum in 

 an enclosure. Electrons escape from it and gradually the metal 

 will become positively charged. (At room temperatures this 

 process would be very slow, but this does not affect the validity 

 of the calculations which are concerned with the ultimate state 

 of equilibrium, attainable of course at much greater speed at 

 high temperatures.) A state of equilibrium is reached (anal- 

 ogous to that of an evaporating liquid in an enclosed space) 

 when as many electrons return to the metal body as leave it in 

 unit time. There is no difference of potential between the 

 metal and a point just outside, but there does exist a difference 

 between the metal and a distant point, since the metal is 

 charged. Let the electron concentration in the metal be n and 

 that in the space adjacent to the metal surface n'; then we have 

 by a well-known statistical relation 



n 



= exp 



i-t) 



11 

 or 



kt(\og n — log n') = e<t>. 



If an electron travels from a point near the surface to a point 

 P in the "space charge" where the potential is V p, the electron 

 loses kinetic energy of an amount e{V — V p) where V is the 

 potential of the metal body and also the potential at a point 

 just outside it. (It would gain that amount if the electron were 

 charged positively.*) This follows from the strict definition 

 of potential; for it is assumed that by the time the electron has 

 travelled a physically small distance from the surface the 



* Observe that e is treated here as a number without sign; the numeri- 

 cal value 4.8 X 10""" of the electron charge. 



