Part II. 

 On the hydrogen spectrum. 



§ 1. The simple theory of the series spectrum of hydrogen. 



As well known, the frequencies of the lines of the series spectrum of hydrogen 

 may, if we look apart from the fine structure of the single lines i-evealed by instru- 

 ments of high dispersive power, be represented by the formula 



' = «(^--r-). 



(35) 



where K is a constant, and n' and n" a set of two entire numbers, different for the 

 different lines of the spectrum. According to the general principles of the quantum 

 theory of line spectra discussed in the first section of Part I, we shall therefore 

 expect that this spectrum is emitted by a system which possesses a series of sta- 

 tionary states in which the numerical value of the energy in the ;)"' stale, omit- 

 ting an arbitrary constant, with a high degree of approximation is given by 



l^n|=^Î, (36) 



where h is Planck's constant which enters in the fundamental relation (1). 



Now according to Rutherford's theory of atomic structure, a neutral hydrogen 

 atom must be expected to consist of an electron and a positive nucleus of a mass 

 very large compared with that of the electron, which move under the influence of 

 a mutual attraction inversely proportional to the square of the distance apart. As- 

 suming that the motion in the stationary states may be determined by ordinary 

 mechanics, and neglecting for the moment the small modifications claimed by the 

 theory of relativity, we find that each of the particles will describe an elliptical 

 orbit with their common centre of gravity at one of the foci, and from the well 

 known laws for a Keplerian motion we have that the frequency of revolution w 

 and the major axis 2 a of the relative orbit of the particles, quite independent of 

 the degree of eccentricity of this orbit, are given by 



=v^ 





N^éMm ' W 



where W is the work necessary to remove the electron to infinite distance from the 

 nucleus, while Ne and M are the charge and the mass of the nucleus, and — e and 

 m the charge and the mass of the electron. 



D. K. D. Vldensk. Selsk. Skr., naturvidensk. og mathem. Aid., S. Række, IV. 1. 6 



