508 Dr. N. Bohr on the Effect of 



The spectrum of hydrogen observed in ordinary vacuum- 

 tubes * is represented by (2) and (3) by putting 



fr(n) = ft(ii)=...=l. .... (4) 



Accordingly we shall assume that this spectrum is emitted 

 by a system possessing a series of stationary states in which, 

 corresponding to the nih state, the energy, omitting the 

 arbitrary constant, is given by 



A»=-7i? (5) 



According to Rutherford's theory, the atom of an element 

 consists of a central positive nucleus surrounded by electrons 

 rotating in closed orbits. Concordant evidence, obtained in 

 very different ways, indicates that the number of electrons in 

 the neutral atom is equal to the number of the corresponding 

 element in the periodic table f. 



On this theory the structure of the neutral hydrogen atom 

 is of extreme simplicity ; it consists of an electron rotating 

 round a positive nucleus of opposite charge. In such a 

 system we get on the ordinary mechanics the following equa- 

 tions for the frequency of revolution co and the major axis 2a 

 of the relative orbit of the particles 



2W 3 (M + m) 9 _f! 

 TrVmM ' ~ a ~ W 



(6) 



where e and — e are the charges, M and m the masses of the 

 nucleus and the electron respectively, and where W is the 

 amount of energy to be transferred to the system in order to 

 remove the electron to an infinite distance from the nucleus. 

 It may be noticed that the expressions are independent of the 

 degree of eceentricity of the orbits. 



In order to obtain a mechanical interpretation of the 

 above-mentioned stationary states, let us now in (6) put 

 W»=— A\ This gives 



w JiK 2 2/* 3 K 3 (M+™) _ehr> m 



According to this view, a line of the hydrogen spectrum 

 is emitted during the passage of the atom between two 



* A series of lines, first observed by Pickering in stellar spectra and 

 recently by Fowler in vacuum-tubes containing a mixture of hydrogen 

 and helium, is generally also ascribed to hydrogen. These lines, however, 

 can be accounted for on the present theory, if we ascribe them to helium. 

 (Phil. Mag. loc. cit. p. 10 : comp. also ' Nature,' xcii. p. 231 (1913).) 



+ Comp. A. v. d. Broek, Phys. Zeitschr. xiv. p. 32 (1913), comp, also 

 several recent contributions to ' Nature.' 



