﻿Magnetic Field of an Atom. 45 



In Bohr's theory W is capable of being expressed by the 

 equation 



where a is an 

 Let us now 



integ( 

 put 



W 

 >r. 



O-Jifj) 

















u= 



r 









(6) 









— 



Ee 1 , 



; a> 2 + 



Mea) 



T 



• 





Then 



by means 



of (1) 



we find 



that 



u 



reduces 



to 



~mr 2 o) 2 , which is the kinetic energy of the electron. 

 Making use of (2) we see that 



U = ^ (7) 



4tt v } 



When there is no magnetic field present r and a become 

 identical and U = W. In the presence of the magnetic field 

 we have to take into account the small term Mem/r, We 

 proceed to find the approximate relation between t and a in 

 this case. 



Combining (6) and (7) we find 



rh(0 (T/lCO Mtfft) 



47r " 4tt + r 



aha) 47r 2 mME6 2 ft> 



+ 



4tt t t 2 A 2 

 Hence r = a + ^ , .... (8) 



or, approximately, 



16V 3 mME6 2 



where 



-*+?• (9) 



s 167r 3 mME^ 2 



8 = ~hT • 

 The value of W may be expressed in a form more 

 convenient for our purpose as follows : 



4tt 



= -^L(Ma> + E) a (10) 



4 77 A v 



