Theory of Photoelectric Action. 573 



which is absorbed. For equilibrium we have therefore 



E = £ . 2NR0 (7) 



If we neglect the effects of reflexion, by putting 



and substitute the value of N from (2), making the same 

 proximations as before, we obtain from (6) and (7) 



a P. 



hv 



( dv.T v e¥{v)hv*e U0 = 2A 1 R6> 3 e 

 J° 



Subject to 



h 



RO 



6~F(v) = from v = to v = W 



and 



l'W=^(l- r J from ,= T to , = «e 



the solution of this is 



T„=7ii> — u'o when w < 7iv < co . ... (8) 



For values of 7tv which lie between and it' U5 T„ has no 

 meaning, as the corresponding electrons have no external 

 existence. 



The solution (8) is dependent on the assumption that the 

 reflexion of electrons can be neglected. This is equivalent 

 to assuming that effects which arise from the collisions of 

 the electrons may be disregarded. But if we consider this 

 from the point of view of the electrons emitted under the 

 influence of the light, we see that neglecting the effects of 

 collisions is tantamount to assuming that the only energy 

 lost by the electrons is used up in overcoming the work w of 

 the forces which tend to retain them within the interior of 

 the substance. Under these circumstances the kinetic energy 

 of the escaped electrons will be equal to that which they 

 acquire by the action of the light (not necessarily from the 

 light directly) minus the work ic which they have to do to 

 escape. It is clear that the energy which they acquire under 

 the influence of light is hv where h is Planck's constant. It 

 evidently has the same value for all the electrons liberated 

 by light of the same frequency ; any difference in the energy 

 of the electrons liberated by monochromatic light must there- 

 fore be attributed to the effect of collisions of the escaping 

 electrons in the interior of the substance. 



We can take account of the reflexion of electrons tenta- 

 tively by putting /3 = sa. Then, instead of (8), we get 



T„ = s r hv — w Q ) when w <7w<ao . ... (9) 



