﻿Hydrogen and the Structure of the Atom. 141 



In a paper in the Philosophical Magazine on the magnetic 

 field of an atom in relation to theories o£ spectral series *, I 

 have shown that a formula of the type given by Ritz can be 

 deduced by the methods of Bohr's theory if the magnetic 

 field of the atom be taken into account. Formula 17 of 

 that paper gives the frequency in the form 



27r 2 me 2 E 2 \ 1 1 



{ 



IP ) r BT r B 



h+d 0+j?J 



(3) 



where B=- ^ (4) 



Seeing that Bohr's theory of spectral series has achieved 

 its greatest success in dealing with the hydrogen spectrum, 

 it appeared that it would be of special interest to determine 

 whether the inclusion of the effect of a magnetic field would 

 lead to results consistent with observation in this case. 



In the case of hydrogen E, the charge on the nucleus, is 

 equal to e, the charge on the electron, and the factor outside 

 the bracket becomes equal to 27r 2 /??e 4 //i 3 , which is equivalent 

 to Rydberg's constant. It has been pointed out by Bohr t 

 and Fowler % that a correcting factor must be introduced 

 involving the mass of the electron and that of the core. 



In order to test the applicability of the formula to the 



hydrogen series, we may put a 2 = 2, <r 1 = m (where 



m = o, 4, . . .)_, B in the first bracket = and B in the 



, , ' 167r 3 mMe 3 



second bracket = ^ . 



nr 



It must be noted here that this implies a slight modifi- 

 cation of the scheme suggested in the previous paper. For 

 by assigning different values to B in the two brackets we 

 suppose that the magnetic moment of the core (M) has 

 different values in the two types of steady states of motion, 

 the emission taking place in the passage between these 

 types. 



The inequality in the order of magnitude of p and p in 

 Ihe formula of Curtis indicates that the two types of state 

 concerned are in some way different. 



The formula for the wave-number may now be written 



w = N-< 4 



1 ) 



* Sir pre), p. 40. 



t Bohr, Phil. Mag. vol. xxvii. p. 509, March 1914. 



| Fowler, Bakerian Lecture, Royal Society, 1014. 



