﻿624 Prof. 0. W. Richardson : Some Applications 



Differentiating (62) by 6 on the assumption that the 

 variation, if any, of e¥{y) with 6 can be neglected, one finds 



I^B^E + ^'N) (64) 



Differentiating (60) by assuming a constant gives 



8N ' 1 fE lW l 



a7=E3>U +N "> • • ' ' (65) 



whence y=J. Since E = 2NR0 this might be interpreted 

 by saying that on the average the light communicates to the 

 escaping electrons an amount of energy equal to that belonging 

 to each of the degrees of freedom. 



The above result depends on the identification of P 

 with w. P might be expected to be the same as iv if the 

 electrons expelled by photoelectric action have the full 

 kinetic energy corresponding to the temperature of the 

 metal before they are acted on by the light. This would be 

 the case if the electrons which are subject to photoelectric 

 action are free electrons or electrons which can become free, 

 or, in fact, any electrons which contribute their share to the 

 specific heat of the substance. 



It is, however, possible that the photoelectrically active 

 electrons are devoid of kinetic energy when inside the metal, 

 and I am not convinced that such an event would necessarily 

 involve a violation of the second law of thermodynamics. 

 I mean, of course, in the way in which the phenomena of 

 radioactivity may, loosely speaking, be said to violate the 

 law. In that case the proper assumption would be 

 V = w — §R#, §R# representing the kinetic energy of the 

 escaped particles. We should then have 7 = 1 and the whole 

 energy of the photoelectric electrons would come from the 

 light. According to the results of § 3, the same conclusion 



would follow if P were identified with w—6 =-^, an inter- 



pretation which might be justified by thermodynamic con- 

 siderations. The results would then be in accordance with 

 what, as I understand it, is Einstein's position. In any event, 

 it is clear that the view according to which the energy com- 

 municated to the electrons by light of a given frequency v is 

 equal to liv and that a constant amount P of this energy 

 is used up before the electrons can escape, is one which is 

 consistent with the equilibrium conditions interpreted in the 

 light of our present experimental knowledge of photoelectric 

 phenomena. 



