240 Dr. L. Vegard on the X-Ray Spectra 



If we suppose the angular momentum to be kept the 

 energy of the ring after the removal of an internal electron 

 willbeC-W(n,p-l,gr). 



The correctness of this statement is evident from the fact 

 that the formula (2) gives the energy of the ring when each 



electron has an angular momentum of — and an effective 



° 27T 



nucleus charge (N— p)e. The expulsion of an electron from 

 an interior system will change the effective nucleus charge 

 of the ring to (N — (p — 1) )e. 



When the momentum is maintained the expulsion of an 

 electron is accompanied by a sudden change of energy of all 

 the ring-systems outside the broken one. As a matter 

 of fact, the energy of such a ring is diminished, and by 

 the amount 



AB = W{n,p-l,q)-W(n,p,q). 



This energy might either disappear in the form of 

 radiation or it might be spent on the escaping electron 

 on its wav out of the atom. 



The Frequency Formula. 



§ 3. The general expression for the frequency on the 

 assumption of conservation of energy was given in my 

 previous paper, and we easily see that KossePs relations 

 are fulfilled. 



On the second assumption of conservation of momentum 

 the matter is not quite so simple. 



Let the ring-systems — beginning from the nucleus — be 

 indicated by the indices 1, 2, 3, .... Let the broken ring- 

 have an index i and the ring from which recombination 

 takes place be k. The effective nucleus charge of any 

 ring i is (N—p^e, where 



p i= q l + q 2+m , m g i _ 1 (4) 



Now originally I supposed that it was only the energies 

 of the rings qi and q k , between which recombination took 

 place, which were engaged in the production of an X-ray 

 line. On this assumption we get for the frequency : 



gr = V(ni,Pi, qi)—V(ni,pi, Qi — 1) —ViWfc, pk-1, qk) 



+ V{n h p h £*— 1). 



