THERMIONIC ELECTRON EMISSION 



437 



or the decrease in the work function due to an appHed field is equal to 

 the decrease in the maximum of the potential energy-distance curve. 

 Since P depends on F, the true field (applied + contact potential field), 



10.0 



9.9 



9.8 



9.7 



o 



> 9.6 



Z 



-0,1 



-0.2 



-0.3 



50 100 150 200 250 300 350 400 450 X lO"^ 



Z— DISTANCE FROM CATHODE IN CENTIMETERS 



Fig. 7 — Potential energy versus distance from cathode surface for image force and 

 applied fields of zero or 40,000 volts/cm. 



it will be convenient to designate values for curve 1 for which F = 

 by the subscript 0. Then 



and 



P = Po - Fez, 

 dP/dz = dPo/dz - Fe. 



(48) 

 (49) 



At the maximum in the P versus z curve, dP/dz — and z = Zc- 

 Hence 



(dPo/dz) I ,^ = Fe. (50) 



We require an expression for AP„,, the decrease in P„, due to the field F. 

 From Fig. 7 it is clear that 



AP„, = distance A + distance B = P,„o - Po\z, + Fez, (51) 



d(AP,„)/dF = - dP,/dF\,=., + FeidzJdF) + ez,. (52) 



