620 Mr. S. N. Basu on tlie Deduction of Rydberg'' s Laiv 



depending upon the element and the nature of the series. 

 So that it we are to explain the formation of the series from 

 theoretical considerations following Bohr and Sommerfeld, 

 we must look upon each member multiplied by "h" as 

 giving the energy of the atomic system when the radiating 

 electron moves in a definite statical path. The complexity 

 of the inner atomic field under which the radiating electron 

 moves is to be looked upon as bringing in the terms 

 involving a and /3. So it seems interesting to see what 

 will be the corresponding expression for energy in a system 

 by which the complex nature of the internal field may be 

 approximately represented. In the case of any atom we 

 have, in general, a condensed nuclear charge of + ne (where 

 n is the atomic number) surrounded by rings of electron 

 at different distances. The number of electrons in total 

 must be also equal to n in order to secure that the atom is 

 electrically neutral in the ordinary state. 



In X-ray emission the electron displaced comes from the 

 inner rings ; in the case of visible radiation, however, we 

 have reasons to think that the displaced electron responsible 

 for radiation comes from the outermost ring — the valency 

 electrons, as they have been designated by Sommerfeld. 

 When excited for radiation, we can suppose that the electron 

 in the outermost ring is removed to a greater distance 

 from the centre than the others, so that the force actino- 

 upon it may be regarded as the resultant of the various forces 

 exerted by the central charge and the remaining electrons. 

 The potential at any point can be regarded as given by 



\-e 2 Z — , where r is the distance from the centre 



and r s is the distance from the 5-th electron. If we neglect 

 the influence of the moving electron upon the arrangement 

 of the others surrounding the nucleus, it is clear that the 



potential can be approximately represented as — — + °° S 



r r 2 



The resultant field might be looked upon as due to a single 

 positive charge, together with a doublet of strength L 

 in a certain fixed direction, which we take as our 2-axis. 

 If we neglect the disturbing effect of the outer electron, 

 L may be taken to be approximately fixed in direction 

 and in magnitude in the small interval of time durino- which 

 the active emission takes place. 



We may, therefore, take as our model a system consistino- 

 of a positive charge and a doublet of strength L. We 

 proceed to calculate the energy in a statical path on the 

 above simplified hypothesis, 



