71 



355 



the properties of the motion of the electron in the atom, but can obviously not be 

 found from an examination of the a-priori probabilities of the stationary states, 

 although of course these quantities must be taken into account in the detailed 

 discussion of the intensities. 



/. The relatiue intensities of the components of the fine structure of the lines of the 

 spectrum of the nndistnrlwd hijdroqen atom. 



In order to discuss the interpretation of the observed intensities whicli can be 

 obtained from the considerations in § 5, let us first suppose that the hydrogen atom 

 is entirely uninfluenced by external forces. In that case the motion of the electron 

 will take place in a plane; moreover the position of this plane would remain un- 

 altered if the electron emitted radiation according to the laws of ordinary electro- 

 dynamics. From the formal connection with ordinary electrodynamics in the limit 

 of large n"s we must therefore expect that also on the quantum theory the plane 

 of the motion remains unaltered during a transition between two stationary states 

 and that the emitted radiation is polarised in this plane. On the other hand the 

 total radiation emitted by a large number of atoms will show no characteristic 

 polarisation, since the position in space of the plane of the orbit in the stationary 

 states is undetermined. Further we have seen in § 2 (compare the formulae (37) 

 and (38)) that the motion of the electron may be considered as a superposition of 

 a number of circular harmonic vibrations of frequencies riWi + ß'j > where ö;, and 

 (o., are the frequency of the radial motion and the mean frequency of the angular 

 motion respectively, while Tj is an integer which may assume all positive and 

 negative values including zero. According to the considerations in § 5 it is there- 

 fore necessary to assume that only such transitions between stationary states will 

 be possible for which n^ decreases or increases by 1, i. e. for which the angular 

 momentum of the electron round the nucleus decreases or increases by ''/2rr, and 

 that the emitted radiation will be circularly polarised in a direction which is the 

 same as or the opposite of that of the direction of revolution of the electron in its 

 orbit respectively.^) It is thus seen that a large number of the ensemble of the 

 n' X n" imaginable components of the fine structure of a line (n' — n") will corres- 

 pond to transitions which must be regarded as physically imposible, the a-priori 

 probability for their spontaneous occurence being equal to zero, and that we may 

 only expect the appearance of 2n" — 1 components, n" of which correspond to 

 /J'o — n,' = 1 and n" — 1 of which to n, — /»,' = — 1. 



In order to discuss the intensities with which, according to Bonn's theory, 

 these components may be expected to appear, it will first of all be necessary to 

 discuss the modifications which on account of the degenerate character of Ihe 

 system in question must be introduced in the considerations of j? 5 in order that 

 they may be applied in the present case. As a consequence of the degeneration the 



'i Compare Hohh. loc. cit. l'ai t II. p. (iS. 



