102 



of a positive charge, equal to that of the hydrogen nucleus multiplied by the "atomic 

 number" of the element under consideration, i. e. by the number of the element 

 in the periodic table. In considering the stationary states of such systems we 

 meet in general with problems of great complexity. From the analogy of the 

 series spectra of the elements with the hydrogen spectrum, however, we are at 

 once led to the conclusion that the ordinary spectra of these elements are due 

 to transitions between stationary states in which one of the electrons moves at 

 a distance from the nucleus large compared to the distance of the other electrons, 

 and in which this electron is therefore exposed to a force which differs only little 

 from the force on the electron in the hydrogen atom ^). In fact this suggests a simple 

 interpretation of the experimental result that in the ordinary series spectra of the 

 elements, the so-called "arc spectra", the function fj{ii) in formula (2) on page 3 

 can be written 



/T('0 = -^yr(") (88) 



where the constant A' with a high approximation is found to be the same as the 

 corresponding constant occurring in the formula (35) for the hydrogen spectrum and 

 where <pj{n) is a function which tends to unity when n becomes larger. In this way 

 we obtain moreover an interpretation of the fact that the frequencies of the lines 

 of the so called "spark spectra", which appear when the atoms of the elements 

 are subject to a condensed discharge, can be represented bj' a formula which differs 

 from the general formula holding for arc spectra only in the fact that the constant 

 K is replaced by a constant which is four times larger^). This is just what should 

 be expected if these spectra originated from atoms which have lost one electron 

 and in which another electron is removed at a large distance from the nucleus and 

 thus exposed to a force which differs only little from the force which would be 

 exerted by a single nucleus of double charge as that in the helium atom^). For 

 these reasons we shall in the following denote the arc spectra as series spectra of 

 the first order, spark spectra as series spectra of the second order, and in general 

 spectra in which the constant K is replaced by a constant m^ times larger, and 

 originating from transitions between stationary states in which the atom has lost 

 m — 1 electrons, while an m* electron is removed to a distance from the nucleus, 

 large compared with that of other electrons, as spectra of the m"* order. 



These simple considerations on the other hand give no explanation of the 

 characteristic difference between the hydrogen spectrum and the series spectra of 

 other elements, which consists in the fact that while in the hydrogen spectrum, when 

 the fine structure is neglected, there occurs only one function f^in) of the type (88) 

 corresponding to y (/?) = 1, there appear in the spectra of other elements several 

 such functions. On the basis of the general theory discussed in the preceding sect- 



') See N. Bohr, Phil. Mag. XXVI, p. 11 (igiS). 



^) See A. FowLEB, Phil. Trans. Roy. Soc. A. 214, p. 225, 1914. 



') See also N. Bohr, Phil. Mag. XXX, p. 407 (1915). 



