106 



of this system, the assumption presents itself, that the effect of the inner electrons 

 on the outer due to their great frequency of revolution in comparison with that of 

 the latter, to a high degree of approximation at any moment will be the same as 

 that of an electric charge — 2e distributed uniformly over a circle of radius equal 

 to that of the orbit of the inner electrons in the absence of the outer electron. If 

 we further would assume that the outer electron moves in the same plane as the 

 inner electrons, we meet therefore with a case which can be treated by means of 

 the simple theory of central systems. These assumptions have been used by Sommer- 

 feld^) in an attempt to explain the lithium spectrum, but apart from the interesting 

 general resemblance with the formula of Rydberg and Ritz mentioned in the former 

 section, no close agreement with the observations could be obtained for any choice 

 of the value of the radius of the orbit of the inner electrons. Thus the calculation 

 gives, that for any value of this radius 5>j-(n) should be smaller than unity for all 

 values of r, while the observed values of ff{n) are slightly larger than unit}' except 

 for r = 1. For the latter value of r the observed values for sPtC^) differ verj' con- 

 siderably from unity and would, for its explanation, on Sommerfeld's calculation 

 claim a value for the radius of the inner orbit which would be far greater than 

 that corresponding to the assumption mentioned above about the angular momenlum 

 of the inner electrons. These difficulties might arise from the mechanical instability 

 of the inner system which may lead to considerable perturbations on the orbits of 

 the inner electrons, especially in the case of r = 1, where the outer electron during 

 its motion passes close to these orbits. A possible explanation might also as remarked 

 by Sommerfeld be found in the assumption, that the electron would not move in 

 the same plane as the inner electrons. In that case a simple calculation shows, 

 that the outer electron would have a considerable perturbing effect on the orbit of 

 the inner electrons in continuously changing the plane of these orbits. For the fix- 

 ation of the stationary states for motions of these types the principles discussed in 

 the former parts, however, would apparently not suffice. In contrast to the case of 

 helium, no lithium spectra of higher orders have been hitherto observed. This may 

 be understood on the assumption, supported by observations on absorption in 

 vapours of alkali metals, that in the normal state of the lithium atom one of the 

 electrons moves in an orbit outside that of the two other electrons, and that there- 

 fore this electron is far more easily removed from the atom than the other electrons. 

 Under the exposure to a sufficiently intense discharge, however, we shall expect to 

 observe two separate series spectra of the second order and one of the third. The 

 first two spectra will correspond to transitions between stationary states in which 

 one electron is removed and in which a second electron moves at a distance from 

 the nucleus large compared with that of the third. These spectra may therefore be 

 expected to be closely analogous to the two helium series spectra of the first order. 

 The lithium spectrum of the third order will originate from atoms containing only 



') A. Sommerfeld, Ber. Akad. München, 1916, p. 160. 



