364 



80 



perturbed atom, corresponding to the different possible values of it (ii == 1,2, . . . n.^), 

 l)ut the displacements of these components from their original posi- 

 tions will only be small quantities proportional to the square of the 

 electric field (the displacements being represented by small terms containing 

 the factor F''jo. Compare note 3 on page 77). 



Let us now proceed to discuss the influence of the electric field on the inten- 

 sities of the fine structure components. On Bohr's theory this influence may be 

 discussed by considering the amplitudes of the harmonic vibrations in which the 

 motion of the electron in the perturbed system may be resolved. Now for the un- 

 disturbed hydrogen atom there appear in the motion, as mentioned above, only 

 vibrations of frequencies aw^j^w^' where a is a positive integer, and from this the 

 conclusion was drawn that only such transitions were possible for which — n'^ 

 was equal to 4: 1, i- e. for which the angular momentum of the electron round the 

 nucleus decreased or increased by ft 'i-. In the motion of the perturbed system, 

 however, there appear vibrations of frequencies which did not appear in the origi- 

 nal motion. Thus, identifying for the moment co,, and Wj, we see from the calcula- 

 tions in § 4 that there will occur vibrations in the motion of the perturbed system 

 the amplitudes of which are small quantities proportional to f'/o , and the frequen- 

 cies of which are equal to aw^ and aca^ ±_ 2 a».,, where a is an integer. On the other 

 hand the amplitudes of the vibrations of the original frequencies which appeared 

 already in the motion of the undisturbed atom are, as far as small quantities of 

 this order are concerned, not influenced by the perturbing field. From these facts 

 we may, with reference to the formal connection between the quantum theory and 

 the ordinary theory of radiation, directly conclude that under the influence 

 of the electric field there will appear new components in the fine 

 structure o f t h e hydrogen lines corresponding to transitions between 

 an initial state {n\, n'j and a final state (n", n'^) for which n'„ — n" = 

 or /I'jj — /i'^' -= 4; 2, i. e. for which the angular momentum of the electron 

 round the nucleus remains unchanged, or decreases or increases by 

 2 •'» 2- (compare Bohr, loc. cit. Part II, p. 69). The intensities with which these 

 new components appear will be of the same order as the square of the amplitudes 

 of the vibrations corresponding to the new frequencies aw^ and awj^2w^, i. e. 

 they will be represented by small quantities proportional to ( ^/o) 



We may summarise the results of the preceding discussion by saying that 

 the presence of a small homogeneous electric field of force in first 

 approximation will leave the frequencies and relative intensities of 

 the original fine structure components of the hydrogen lines unal- 

 tered, but will give rise to the appearance of new components, the 

 frequencies of which are equal to the sum or to the difference of two 

 of the original components. This affords a general interpretation of the fact 

 mentioned above that the appearance and intensity of the fine structure components 

 appearing on Paschen's photographs seem to depend on the experimental conditions 



