and the Theory of Atomic Structure. 1075 



Taking into account the variation of mass with velocity 

 required by the theory of relativity, the energy necessary for 

 the removal of the electron from one of the stationary states 

 is, to a first approximation, given by Somuierfeld's formula, 



WhcR . WhcUu/n 3 



W=-I_^ + 



(H> • • ■ ^ 



where k is the azimuthal quantum number and a. a numerical 

 constant small compared with unity, the theoretical value of 

 which is given by 



Formula (1) gives an interpretation of the general laws 

 which had been revealed by Moseley's fundamental dis- 

 coveries. According to these laws the energies of the 

 observed levels are closely proportional to the square of the 

 atomic number, the energies of the K-, L-, and M-levels 

 being approximate^ represented by the formulae 



■ ■ • (3) 



where a&, «l, and a^ are constants which are different for 

 the different levels. The appearance of these constants in 

 formula (3) is simply explained by taking into consideration 

 the interaction of the electrons in the atom ; the main effect 

 of these is virtually to reduce the attractive influence of the 

 nucleus on the electron whose removal corresponds to the 

 level under consideration. The constant a is therefore often 

 termed the " screening-constant " belonging to the level; 

 and the quantity (N T — a) may be called the effective nucleus 

 charge. 



Fro.n formula (2) we obtain an explanation of the circum- 

 stance that certain pairs of energy-levels corresponding to 

 the same value of n vary to a close approximation as the 

 fourth power of the atomic number. Following the notation 

 of Sommerfeld, such pairs of levels may be termed " relativity 

 doublets/'' since the energy-difference between the two orbits 

 is due to the differential effect of the relativity modification 

 on orbits having the same value of n but different values of k. 

 In the diagrams these pairs of levels are denoted by {. 



As stated above, for levels having the same values of n and 

 k we should expect that differences in the energy necessary 



3Z2 



