﻿2SQ Mr. E. J. Evans on the 



Fowler, in the absence of strict experimental proof, 

 considered that Rydberg's theoretical investigations justified 

 the conclusion that the three series of lines were due to 

 hydrogen, and the series represented by (4) was called the 

 second principal series of hydrogen. It is interesting to 

 note that with the observation of series (4) the supposed 

 analogy between the spectra of hydrogen and the alkali 

 metals breaks down, as the spectra of the latter are known 

 to have only one principal series. 



Recently the problem of the origin of the series in question 

 has been considered from the theoretical standpoint by 

 Dr. Bohr*, who has arrived at very interesting results. 

 Takino- as basis Sir E. Rutherford's f atom-model, he has 

 deduced with the aid of Planck's quantum hypothesis the 

 following formula for the spectrum emitted by an atomic 

 system consisting of a central positive nucleus and an electron 

 moving round it : 



_ 27r 2 e 2 Emm f 1 JH 

 V ~ 7i»(M+ m) \ ? h 2 ~ n 2 2 J ' ' • * W 



where e and m are the charge and mass of the electron, E 

 and M the charge and mass of the nucleus, and h is Planck's 

 constant. For a hydrogen atom according to Rutherford's 

 theory, E = — e, and the formula can be written 



v= ~~/ — s\T^"rjf .... (6) 



\ 1+ m) 



where the bracket multiplying li z is very nearly equal to 

 unity on account of the great mass of the nucleus compared 

 with that of the electron. It was shown by Bohr that the 

 above expression, on putting in the values of the constants, 

 agreed within the limits of experimental error with 

 formula (1). 



It will be seen that formula (G) does not include the lines 

 observed by Pickering and Fowler, and given by formulae 

 (2), (3), and (I). However, if in equation (5) E = — 2e, 

 which according to Rutherford represents the helium atom, 

 the following formula is obtained for the frequency of the 

 lines : 



2ttVwi r 1 1 , 



J TuTV^ ~ 7^2 • • • 0) 



V+S)W (!) 



* N. Bohr, Phil. Mas-, xxvi. pp. 1, 476, 857 (1913) ; xxvii. p. 506 

 (1914V 

 t Sir E. Rutherford, Phil. Mag. xxi. p. 669 (1911). 



