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LXXT. On tlu> Deduction ofRydberg i s Law from the Quantum 

 Theory of Spectral Emission. By Satyendra Nate Basu, 

 M.Sc, University Lecturer in Physics, University College of 

 Science, Calcutta*. 



IT is well known thai Rutherford's model of the atom lias 

 been fruitful in explaining many facts connected with 

 atomic radiation. In the simplest ease of hydrogen, with a 

 nucleus consisting of a single positive charge, and an 

 electron, Dr. Bohrf has successfully applied the quantum 

 theory to explain the Balmer series of hydrogen spectra. 

 The mathematical problem of finding the spectral series for 

 any atomic system has since been clearly formulated by 

 Sommerfeld J, and the quanta condition has been gene- 

 ralized in a. form suitable for systems with any number of 

 degrees of freedom. If q l9 q 2 , q$, ... q n are co-ordinates to 

 fix the position of the electron responsible for emission, and 

 Pu P2i Pzi ■■■ pn are the corresponding generalized momenta, 

 any statical path, according fco Sommerfeld, is characterized 

 by the conditions ^ p\dq l = n l ]i, \p. 2 dq2=n 2 h, \ /) a dq n = n r Ji, 

 where »*s are whole numbers and h is Planck's constant, 

 the integral being extended generally over the complete 

 orbit. The radiation # is supposed to take place when the 

 electron jumps from one statical path to another. The 

 difference in energy, at the same time, flows away in the 

 form of a homogeneous radiation of frequency v, which 

 can be calculated from the Bohr's equation hv = Wi — W s . 

 Sommerfeld has successfully applied this conception in 

 explaining the fine structure of hydrogen lines. It is 

 clear, however, that the problem of theoretically calculating 

 the spectrum of any atom other than hydrogen is beset 

 with difficulties of a formidable nature. It is exactly 

 analogous to the dynamical problem of " n " bodies, where 

 only in favourable c;ises we are able to find approxi- 

 mate solutions. Nevertheless, from a purely experimental 

 standpoint, we know that the visible radiation from any 

 element can be classified in definite series. The frequency 

 of any line in the series can be expressed as a difference of 



N 

 two terms, each of which hns the form — t~— 2, where 



m is a whole number and a. and ft are two constants 



* Communicated by the Author. 



t Bohr, Phil. Mag. July 1913. 



j Sommerfeld, Ann. der Phi/s/k, li. (lOlG). 



2 S 2 



