Part II. 



Discussion of the intensities of the connponents of the 

 hydrogen lines. 



§ 5. Application of the quantum theory to the problem of the intensity of 



spectral lines. 



According to Rutherford's theory of atomic structure the atom of an element 

 consists of a number of electrons surrounding a positive nucleus, the mass of which 

 is very large compared with that of the electrons and the charge of which is equal 

 to Ne, where N is an integer and where — e denotes the charge of an electron. In 

 the simple case where the atom consists of a nucleus and one electron only, viz. 

 for a neutral hydrogen atom (A' = 1), a helium atom which has lost one electron 

 {N = 2), a lithium atom which has lost two electrons {N = 3), etc. it has been 

 possible to develop methods which allow us to fix the stationary states, not only when 

 the atom is undisturbed by external influences, but also when it is exposed to the 

 influence of constant small external forces. In special cases, where the external field 

 is of such a character that the perturbed atom allows of separation of variables, 

 the stationary states will, according to the theory developed by Sommerfeld and 

 by Epstein, be given by 



= n,,h, {k = \, . ... s) (99) 



where /j, ... are the quantities defined by (6), and where /ij, .... ;i, are a set 

 of positive integers, while h is Planck's constant i). For instance, in the case of a 

 hydrogen atom (positively charged helium atom, etc.) which is exposed to a homo- 

 geneous electric field of force, the intensity of which is so large that its influence 

 on the motion of the electron is large, compared to that which is due to the modi- 

 fications in the laws of Newtonian mechanics claimed by the theory of relativity, the 

 stationary states will be fixed by the conditions /j = n^h, = n^h, /g = n^h, where 

 /j, /j, /g are the quantities defined by (45) in § 3. If, however, the system is degenerate 



') Compare P. Epstein, Ann. d. Phys. L . p. 489 (1916). A method which allows us to treat the 

 problem of the stationary states of a perturbed hydrogen atom in more general cases has been deve- 

 loped in Part II of Bohr's often mentioned paper. This theory will, from the point of view of introduc 

 tion of angle variables, be discussed in the paper mentioned in the beginning of § 4, in which it will 

 especially be applied to the problem of the simultaneous effect of the relativity modifications and of a 

 homogeneous electric field on the li3'drogen spectrum, which ])roblem cannot be treated by means of the 

 method of separation of variables. 



