PHYSICS 365 



Turning now to the photo-electric effect, we have the famous 

 equation of Einstein deduced by an appHcation of the quantum 

 hypothesis which will hardly bear very strict investigation. 

 Yet, although its theoretical foundations are extremely weak, 

 the work of A. LI. Hughes and of Millikan and his pupils have 

 established its experimental validity to an extremely high 

 order of accuracy. The equation relates to the maximum 

 velocity with which an electron can escape from a body when 

 the surface is illuminated with monochromatic light of frequency 

 V. If V is this maximum velocity, then 



I niv' = hv — p, 



where h is Planck's constant, so that hv is the energy quantum 

 for light of this frequency and the kinetic energy with which 

 the electron escapes is equal to the balance of energy left out of 

 this hv after work against surface forces has been done, the 

 least possible amount of work being p. Richardson, in the 

 Phil. Mag., 23, p. 61$, and 24, p. 570 (1912), considerably 

 strengthened the theoretical basis of this equation, and also 

 identified Einstein's p quantity with the w quantity of his own 

 thermionic result given above. 



Admitting, therefore, the existence of this surface-work 

 term as an intrinsic property of the body, let us proceed to show 

 its relation to contact potentials. Consider two metallic bodies 

 placed in a vacuous enclosure maintained at constant tempera- 

 ture T. Let w and w^ refer to the work functions corresponding 

 to the escape of electrons through the surfaces of each body 

 respectively. Let V and V^ be the potentials in the space just 

 outside the surfaces of the metals. The work required to remove 

 an electron from the first body, transport it across the space 

 between and carry it into the second metal isw + {V— V^) e — w^. 

 [N.B., the electronic charge is negative, but e is regarded 

 here as its mere magnitude, i.e. as a positive number, so that 

 (V — V^) e is work done on the electron in travelling from the 

 place where the potential is V to the place where it is V^] 

 Now, by a well-known result in electronic theory, this work 

 must also be equal to kT log n/«\ where n and n^ are con- 

 centrations of conduction electrons in each metal. Hence 



V-V' ^{w''-w + kT log w/«')/e (i ) 



= ^* — <^ + kTje- log w/w^ 



Suppose now, that the two metals are placed in contact, 

 then from the values of electric conductivity and thermo- 

 electric measurements we are justified in assuming that n and 

 n^ become, under these circumstances, numbers of the same 

 order of magnitude, and the term kTfe • log nfn^ is found to 

 lead to comparatively small E.M.F.s of the order of magnitude 



