Theory of X Rays and Photoelectric Hays. 549 



whole of the energy given to it in the ^>th oscillation. Its 

 velocity y x will be such that 



• • • (24) 



On the other hand, if at the pth maximum the electron 

 has only barely enough energy to escape, it will just succeed 

 in crawling away with practically zero velocity. The average 

 value of the velocity with which the electron escapes will 

 thus be of an order given by 



. 2 _{2p-l)/Y eY 



8 



-' (±A (25) 



\mn J v y 



From (20) we have 



1 /Y e\ 2 

 x = 77- (- — j t sin 2 2irnt* 

 2c\ in J ' 



leading on integration between the limits zero and t to 

 1 /Y A 2 f 9 t . A 1 ' . . ^ 1 



X ~ T7~ ( V" ~> Sln k* nt + A 9 9 sin ^ nt V • 



bc\m J (. Zirn ^irrr ) 



After a few oscillations the first term becomes all important, 

 and at the pth maximum of y we have 



w = (#) = V - A — £_( _JL I _.^_/_L_) approximately. (26) 



v '* be \mnj bc\mnj 



Thus from (25) and {26) 



u 



V 



- =£v f27) 



v 2c v J 



The energy E which has been absorbed is approximately 

 the energy which the electron has absorbed in the p oscilla- 

 tions, i. e. the kinetic energy of the electron at its pth 

 maximum is 



B m/pYoe\* 



o \ mn J 



so that we have from (25) 



* 



v 2 = - — = — approximately. . . (29) 

 mp mp y 



Suppose we take &) for a certain electron as corresponding 

 to the energy absorbed by the ionic charge in a fall through 



