THERMIONIC ELECTRON EMISSION 



431 



potential energy of an electron at various distances between the 

 cathode and anode when the anode is Vr volts negative to the cathode. 

 It is tentatively assumed that the anode work function (pa is the same 

 as the cathode work function <pc\ this is another way of saying that 



Fig. 4 — Potential distribution between parallel plates; Pa = Pc- 



the contact potential is zero. When F^ = nearly all the space 

 between the cathode and anode is field free as shown in curve 2 ; only 

 in the immediate neighborhood of the cathode or the anode is the 

 electron subjected to any forces. When a retarding potential is 

 applied the electrons must have sufficient energy to pass over the 

 maximum in curve 1, Fig. 4, in order to reach the anode. 



To determine the number of electrons that can reach the anode we 

 integrate equation (10) or (20), from ti = Ua to u — oo where Ua is 

 given by equation (39) or (40), respectively. Whether we use the 

 classical or the quantum-mechanical statistics we arrive at the same 

 result. 



i = Ne = U exp. (- Vre/kT), (41a) 



or 



log i = log io — (e/2.3kT)Vr, 



(41b) 



where io — i when Vr — 0. The slope of the straight line in Fig. 3 

 should thus be e/l.ZkT. 



If (pa and ifc are not equal, the field between anode and cathode will 

 not be zero when the applied potential is zero ; a contact potential or 

 Volta potential Vv will exist between a point just outside the cathode 

 and a point just outside the anode. To produce zero field a potential 



