1076 Mr. D. Coster on the Spectra of X-rays 



to remove an electron from the atom would arise from dif- 

 ferent orientations of the orbits of the remaining electrons 

 within the group concerned. In such levels it may be said 

 that the remaining electrons can have different screening 

 effects. This offers a simple explanation of a fact revealed 

 by an inspection of the measurements, that the energy- 

 differences between two such levels to a close approximation 

 vary linearly with the atomic number. Such a pair of levels 

 may therefore be termed " screening doublets " *. 



In this connexion, however, it must be pointed out, that 

 the numerical values of the screening constants for the 

 different levels calculated from the relativity doublets do not 

 agree with those calculated from the screening doublets f. 

 This is just what we might expect from Bohr's theory of 

 atomic structure. According to this theory the electrons 

 of the outer shells come during their revolution round the 

 nucleus wholly inside the orbits of the inner shells, so that 

 they are moving in a varying field of force. Now it is 

 easily seen, that the effect of the relativity change of mass on 

 the orbit of the electron is mainly due to that part of the 

 orbit which lies close to the nucleus, and where the velocity 

 is very great. We thus understand that the screening- 

 constant for these electrons appearing in the relativity term 

 of formula (2) has another value than that appearing in the 

 main term which in first approximation gives the whole 

 energy of the orbit. 



§ 5. In general, corresponding to a given pair of values 

 for n and k there exist two levels, of which one is of the type 

 denoted in the above diagram as an a-level, the other a 

 6-level. For the largest value of k corresponding to any 

 given value of n there appears, however, only one level. 

 I am indebted to Prof. Bohr for the remark that this 

 circumstance may be brought in suggestive connexion with 

 his theory of atomic structure, which rests upon a considera- 

 tion of the way in which an atom may be formed by the 

 successive binding of the electrons by the nucleus. In fact, 

 in such a process the subgroups corresponding to the highest 

 value of k will correspond to the elections bound during the 

 last stage of formation of the group, and, in contrast to the 

 removal of an electron from subgroups corresponding to 



* Sommerfeld divides the doublets into " regular " and " irregular " 

 doublets. As the screening doublets show no irregularity at all, these 

 names seem not to be well chosen. 



t Compare Sommerfeld and Wentzel, Zeitschrift fur Physik, vii. p. 86 

 (1921). 



