﻿Emission of Electrons by X-Rays. 799 



In the first place, let it be assumed that the number of 

 electrons escaping from the radiator falls off exponentially 

 with the depth from which they come. If I is the initial 

 intensity of the X-rays, S the area bombarded, n the number 

 of electrons liberated per unit volume per unit time per- 

 unit intensity, and yu-j and jjl 2 the absorption coefficients of the 

 X-rays and electrons in the radiator, then the number of 

 electrons from a layer die at a depth ,v which actually 

 escapes is 



dn' = n.$.I e-^ +M)x dx. 



The total number escaping is therefore 



ri = nSI /(/Ai 4- fi 2 ). 

 Hence, since /j.i is small compared with //, 2 > 



If, on the other hand, it is assumed that the number 

 escaping falls off exponentially with the distance traversed 

 by the electrons in the radiator, the following expression is 

 obtained : 



n' = wSI /4/a 2 * 



where /jl 2 is the exponential coefficient of absorption for the 

 electrons. 



Whichever of these tw r o absorption laws is taken, it follows 

 that the number of electrons liberated per unit volume 

 is proportional to /jl 2 times the number actually escaping. 

 From this the number liberated per atom can easily be 

 derived. 



If A is the atomic weight of the radiator, m the mass of 

 the hydrogen atom, and p the density, the number of atoms 



* The actual expression for n is 



-which, on evaluation, gives 



»'=i«SlJl— (*lo*(l+&)"|. 



If this is expanded in terms of ^1 ( and^ is neglected, it gives the result 

 quoted above. P- ^ 2 



