352 



68 



nents, because the theoretical intensities of the parallel components at J = 6 and the 

 parallel component at J = are of the same order of magnitude. It is therefore 

 of interest to note that Stark (see loc. cit., p. 575) only has observed a single, very 

 weak, diflfuse component, and that he from analogy with the character of the 

 Stark effect of for small intensity of the electric force, has suspected this 

 component to consist of two symmetrical components. 



In connection with the above considerations it may be of interest to emphasize 

 that a comparison of the observations on the Stark effect of the helium lines in 

 question with the results to be expected on the quantum theory could not have 

 been obtained by a direct consideration of the frequencies of the components, cal- 

 culated by means of relation (1) from the values of the energy in the stationary 

 slates of the atom, but that it was of essential importance for the above comparison 

 that we were able to obtain an estimate of the relative intensities of these compo- 

 nents by means of a closer consideration of the motion of the electron in the atom. 



In this chapter we will give, from the point of view of Bohr's theory, a dis- 

 cussion of the intensities of the components of the fine structure of the hydrogen 

 lines and of the analogous helium lines, and it will be shown thai it is possible to 

 account in a suggestive way for the observations, especially in the case of the helium 

 lines, the fine structure of which has been carefully investigated by Paschen Let us 

 first consider the general expression for the frequency of the radiation which may 

 be emitted from a hydrogen atom which is uninfluenced by external forces and in 

 which the motion of the particles is assumed to be governed by the laws of rela- 

 livistic mechanics. According lo (99) the stationary states of the atom are fixed by 

 putting the quantities /, and U_, defined by (23) in § 2, equal to entire multiples of 

 Planck's constant h (compare page 39) : 



While /?, may take one of the values 0, 1, 2 . it must be assumed that ii., 

 ran only take one of the values 1, 2, 3 ... In fact, = would correspond to a 

 motion in which the angular momentum of the electron round the nucleus would 

 be equal to zero, but such a motion can obviously not correspond to a stationary 

 state of the atom because the electron would collide with the nucleus. Introducing 

 (117) in (24) and writing /?^-|- /j^ = n we get, with neglect of small quantities of the 

 same order of magnitude as the second and higher powers of ("/c)-, for the total 

 energy of the atom in the stationary states 



§ 7. The fine structure of the hydrogen lines. 



(117) 



E = ~ 



27r-A/-e' 



m 



(118) 



') F. Paschen, Ann. d. Phys. L., p. 901 ,1916). 



