274 Dr. Megh Nad Saha on- the Problems of 



«3. 



At the present time,. the electrodynaniical part, — i. e., the 

 manner in which the lines of an element originate from the 

 quantum-vibrations of the constituent electrons of the atomic 

 system — has been worked up in the case of the H-atom 

 alone. For the other atoms, it is only in the process of 

 making"*. But the thermodynamical part of the problem — 

 that is, how the proportion of different possible stable orbits 

 varies according to temperature, and how the orbits change 

 from one into the other giving rise to line-radiations — 

 has not even been clear-ly formulated. In his interesting 

 development of the quantum theory applied to systems with 

 more than one degree of freedom, Planckf has laid the 

 foundations of a new method for dealing with the statistical 

 aspect of the question. The second aspect — namely radiation 

 following as a result of mutual interchange of stable orbits — 

 has been dealt with by Einstein J. But there are still many 

 difficulties to overcome. When this is done, a new and fruit- 

 ful chapter — that of line radiation of gases — will be added to 

 thermodynamics. 



We may provisionally proceed along the following lines : — 

 Let us suppose that the orbits having the rotational quanta 

 1, 2, ... . m . . . vary as a geometric progression 



(i-/)[i,/,/ 2 ,/ 3 ...], 



where f is a fraction and a function of temperature and 

 concentration. Similarly, let us suppose that the orbits 

 having the radial quanta 0, 1, 2, 3, etc., vary according to the 

 terms of the geometric progression 



(i-#)[i,^y,# 3 ....], 



where g is a similar fraction. 



Then at any instant the proportion of orbits with the 

 rotational quantum number n+1 and the radial quantum 

 number n' is 



/Y'(i -/)(!-.<?), 



since at low temperatures and high concentrations almost 

 the whole number of atoms is in the state (1, s) corresponding 

 to n = l, n' = 0. 



We see that /and g are very small quantities under these 



* Sommerfeld, Atombau und Spektvalanalyse. 



+ Planck, Verh. d. D. Phys. Ges. vol. xrii. p. 407 (1915) ; Ann. d. Phys. 

 vol. 50. p. 385 (1916). 



% Einstein, Verh. d. 2). Phys. Ges. vol. x.viii. p. 318 (1916) ; Phys. Zeit. 

 1918, p. 124. 



