406 Dr. N. Bohr on the Quantum Theory oj 



out in my previous papers that a simple interpretation can 

 be given of the fact that in every series <f>(n) approaches 

 unity for large values of n. It was assumed that in the 

 stationary states corresponding to such values of n, one of 

 the electrons in the atom moves at a distance from the 

 nucleus large compared with the distance of the other 

 electrons. If the atom is neutral, the outer electron will be 

 subject to very nearly the same forces as the electron in the 

 hydrogen atom, arid the formula (13) indicates the presence 

 of a number of series of stationary states of the atom in 

 which the configuration of the inner electrons is very nearly 

 the same for all states in one series, while the configuration 

 of the outer electron changes from state to state in the series 

 approximately in the same way as the electron in the 

 hydrogen atom. From the considerations in the former 

 sections it will therefore appear that the frequency calcu- 

 lated from the relations (1) and (13) for the radiation emitted 

 during the transition between successive stationary states 

 within each series will approach that to be expected on 

 ordinary electrodynamics in the region of slow vibrations*. 

 From (13) it follows that for high values of n the con- 

 figuration of the inner electrons possesses the same energy 

 in all the series of stationary states corresponding to the 

 same spectrum (11). The different series of stationary states 

 must therefore correspond to different types of orbits of the 

 ■outer electron, involving different relations between energy 

 and frequency. In order to fix our ideas, let us for a 

 moment consider the helium atom. This atom contains only 

 two electrons, and in the previous papers it was assumed 

 that in the normal state of the atom the electrons rotate in a 

 circular ring round a nucleus. Now the helium spectrum 

 contains two complete systems of series given by formulae of 



* On this view we should expect the Rydberg constant in (13) 

 -to be not exactly the same for all elements, since the expression (5) 

 depends to a certain extent on the mass of the nucleus. The correction 

 is very small ; the difference in passing from hydrogen to an element of 

 high atomic weight being only 0'05 per cent, (see IV. p. 512). In a 

 Tecent paper (Proc. Roy. Soc. A. xci. p. 255, 1915), Nicholson has con- 

 cluded that this consequence of the theory is inconsistent with the 

 measurements of the ordinary helium spectrum. It seems doubtful, 

 however, if the measurements are accurate enough for such a conclusion. 

 It must be remembered that it is only for high values of n that the 

 theory indicates values of <£ very nearly unity ; but for such values of n, 

 the terms in question are very small, and the relative accuracy in the 

 experimental determination not very high. The only spectra for which 

 a sufficiently accurate determination of K seems possible at present are 

 the ordinary hydrogen spectrum and the helium spectrum considered in 

 the former section, and in these cases the measurements agree very 

 closely with calculation. 



