412 Dr. N. Bohr on the Quantum Theory of 



§ 4. The high frequency spectra of the elements. 



In paper II. it was shown that the assumption E led to an 

 estimate of the energy necessary to remove an electron from 

 the innermost ring of an atom which was in approximate 

 agreement with Whiddington's measurements of the mini- 

 mum kinetic energy of cathode rays required to produce the 

 characteristic Rontgen radiation of the K type. The value 

 calculated for this energy was equal to the expression (5) if 

 n = l. In the calculation the repulsion from the other 

 electrons in the ring was neglected. This must result in 

 making the value a little too large, but on account of the 

 complexity of the problem no attempt at that time was made- 

 to obtain a more exact determination of the energy. 



These considerations have obtained strong support through 

 Moseley's important researches on the high frequency spectra, 

 of the elements *. Moseley found that the frequency of the- 

 strongest lines in these spectra varied in a remarkably simple- 

 way with the atomic number of the corresponding element. 

 For the strongest line in the K radiation he found that 

 the frequency for a great number of elements was- 

 represented with considerable accuracy by the empirical 

 formula 



v=f(N-l) 2 K, (14} 



where K is the Rydberg constant in the hydrogen spectrum. 

 It will be seen that this result is in approximate agreement 

 with the calculation mentioned above if we assume that the 

 radiation is emitted as a quantum hv. 



Moseley pointed out the analogy between the formula (14); 

 and the formula (3) in section 2, and remarked that the 

 constant 3/4 was equal to the last factor in this formula, if 

 we put n 1 = l and n 2 = 2. He therefore proposed the ex- 

 planation of the formula (14), that the line was emitted' 

 during a transition of the innermost ring between two states 

 in which the angular momentum of each electron was equal 



to 2 — and — respectively. From the replacement of N 2: 



by (N — l) 2 he deduced that the number of electrons in the- 

 ring was equal to 4. This view, however, can hardly be 

 maintained. The approximate agreement mentioned above 

 with Whiddington's measurements for the energy necessary 

 to produce the characteristic radiation indicates very strongly 

 that the spectrum is due to a displacement of a single elec- 

 tron, and not to a whole ring. In the latter case the energy 



* Moseley, Phil. Mag. xxvi. p. 1024 (1913) ; and xxvii. p. 703 (1914). 



