626 Mr. S. N. Basil on the Deduction of Rydbercf s Law 



value, whereas the radial quanta can have all values from 

 to oo ; he thus shows that in s, p, and d terms the azimuthal 

 quanta generally have values 1, 2, and 3 respectively. 



Making the above assumptions in our formula, we see that 



.. ' . ... t NA 



the expression or the energy comes out as — . — : — . 2 



in the same form as required hy the Rydberg formula. The 

 constant A, however, depends only upon n 1 and n 2 ; it 

 diminishes for increasing values of the azimuthal quanta ; 

 so that they decrease progressively in the s, p, and d terms. 

 Moreover, our form shows that A depends upon « 2 and n 2 

 separately, so that for the same value of % + n 2 we may 

 have different values of the constant. Thus, if we suppose 

 n±+n 2 = l, we have two values corresponding to the values 

 1, and 0, 1 ; for ?i 1 -\-n 2 = 2 we have three values ; and so on. 

 Thus we see, even on Sommerfeld's assumption, for the con- 

 stancy of the azimuthal quanta we shall have two different s, 

 three different p, four different d terms. At least two dif- 

 ferent values of p and three different values of d seem to be 

 required by the series formula, which is essential for the 

 explanation of doublets and triplets of constant frequency 

 difference *. We thus see that our model serves at least 

 as a qualitative explanation of the following facts : — 



(1) The progressive decrease of the characteristic numbers 



in the s, p, and d terms. 



(2) The existence of different sets of s, p, and d terms 



for the same element. 



It is clear, however, that our simplified assumption will not 

 fit in any actual case exactly. The complex nature of the 

 internal field can in no case be properly represented by 



a simple term, -j— , in the Potential. Moreover, we 



have reason to believe that the internal arrangement of 

 the electrons itself will be influenced, in a large measure, 

 by the motion of the outer electron, which we have neglected 

 in our formula. In fact, Lande f has tried in a recent 

 paper to take account of this disturbance in the comparative 

 simple case of the helium series. But at the same time, 

 it is hoped that the calculation, in this comparatively simple 



* If we exclude the case n 2 = 0—i. e., if we assume that the motion in 

 a plane containing the axis of the doublet is excluded — we get the 

 proper number of s^p, and d terms as observed in the case of the alkali 

 metals and the doublet system of alkaline earths. 



f Lande, Phys. Zeit. 1919. 



