IQ20. No, 2. ON THE X-RAY SPECTRA. 



Later on I found, that if we give up the assumption that it is only 

 tlie energychanges of 7. and 7 , which are engaged in the production of 

 the ./'-ray Hne, the assumption of preservation of angular momentum can 

 be made to agree wiih Kossel's relation. 



During recombination the rings between <j . and <j will undergo a 

 change of energy because the effective nucleus charge is diminished by 

 one elementary unit and we might assume ih(d also fJie chaivje of energy 

 of the intermediate rings enters into tJie energy quantum of radiation 

 ivhich is emitted during the process of recombination . 



On this assumption the expression for the frequency takes the form : 



l=k-l 



i = ifi 



Let us now suppose, that another time the electron recombines from 

 a ring (j -, where i<ij<.h\ to the same ring q^. Then we get another 



frequency ( X^j • 



Finally we imagine the electron to be removed from the / — ring, 

 and that the recombining electron comes from the /i-ring; then we get 

 k 



a frequency [ij] 



Applying equation (5a) in all cases we easily deduce the identity 



tX - (IX ^ (X-A . ... (61 



R). \H): \R).^ 



Applied to the Kß, h\^ and L^ lines this equation is identical with 

 (i), and Kossel's relation is fulfilled. 



The general etjuation for the frequency we get by incerting into 

 equation (5a) the expression for ]' — (equations 3). 



Instead of using the exact expression (3 a) we ma)' take (3 c), which 

 with the first approximation takes into account the variation of the mass 

 with velocity. The expression for the frequency then takes the form : 



