1074 Mr. D. Coster on the Spectra of X-rays 



on measurements for elements of atomic number preceding 

 or following that of niton (86) *. 



Comparing this diagram with the above table representing 

 the results of Bohr's theory, we see that it has been possible 

 to characterize the levels by the same quantum-numbers as 

 those which in the niton atom characterize the different 

 groups and subgroups. We may now assume that the 

 existence of the levels indicated in diagram I. is connected 

 with the appearance of the various subgroups of electrons in 

 the atom. Further, we may assume that in those cases where 

 more than one level is characterized by the same quantum 

 numbers, we witness different processes of removal of an 

 electron from the same subgroup, the remaining electrons 

 in the group arranging themselves afterwards in different 

 ways. 



§ 4. These conclusions obtain strong support from an 

 inspection of the way in which the energy differences of the 

 levels corresponding to the various values of n and k vary 

 with the atomic number N of the element. The considera- 

 tions in question rest upon a comparison with the theory of 

 the stationary states of an atom consisting of a single 

 electron revolving round a positive nucleus. In the first 

 approximation, where the motion of the electron is calculated 

 according to Newtonian mechanics, the energy necessary to 

 remove the electron from one of these states to an infinite 

 distance from the nucleus depends only on the total quantum 

 number n. This energy is given by Bohr's formula, 



W=N»^?, ...... (1) 



where N is the number of unit charges on the nucleus, h 

 Planck's constant, c the velocity of light, and R a universal 

 constant appearing in the theory of spectra and called the 

 Rydberg constant. The theoretical value of the latter 

 constant is given by the relation 



%7T^e 171 



R= — j3~ t — =109737, (number of wave-lengths per cm.), 



where e is the charge of the electron and m its mass for 

 velocities small compared with the velocity of light. 



* As to the nomenclature of the lines, which often differs very much 

 with different authors, I have in this paper in general used that 

 proposed by Prof. Siegbahn. Still, for a theoretical discussion it may be 

 advantageous to use sometimes another nomenclature analogous to that 

 used for the visible region. According to this latter one, e. g., the lines 

 K# 2 and L-y^ may be called KL 2 and L 3 N 5 respectively. 



