658 BELL SYSTEM TECHNICAL JOURNAL 



expressed by these three equations are correct also. Are these conse- 

 quences impressive enough to prove the suppositions true? 



The answer to this question depends on our degree of success, or 

 rather on the degree of success attained by Sommerfeld and Bohr and 

 their followers, in generalizing these equations to other and more com- 

 plex cases. Usually the process of generalizing will involve difficult 

 labours of orbit-tracing. But it is possible to make a significant com- 

 parison between the spectra of hydrogen and of ionized helium, witli- 

 out additional studies of orbits. 



I. Rklations Bf.twken the Spectrum of Hydrogen and the 

 Spectrum of Ionized Helium 



To make trial of the validil\- of the foregoing ideas about the origin 

 of the hydrogen spectrum, one naturally applies them to whatever 

 other spectra may reasonably be ascribed to an atom consisting of a 

 nucleus and a single electron. As according to the view adopted in 

 this article the atom of the nih element in the Periodic Table con- 

 sists of a nucleus and w electrons, the only way to produce such a 

 spectrum is to produce a sufficient number of atoms of some element 

 or other, each atom lacking all but one of its electrons; helium atoms 

 deprived each of one electron or "once-ionized," lithium atoms de- 

 prived each of two or "twice-ionized," beryllium atoms depri\ed 

 each of three electrons, or in general atoms of the nth element of the 

 Periodic Table divested each of («— 1) electrons. This we should 

 expect to require violent electrical or thermal stimulation of the 

 vapor of the element, more violent the more electrons have to be 

 remi ved. Hence it is not surprising that the spectrum of once- 

 ionized helium is the easiest of these spectra to produce; but it is 

 more than a little strange that this is not merely the easiest but the 

 only spectrum of this kind which has ever been obtained. Even the 

 spectrum of twice-ionized lithium has not been generated, in spite of 

 efforts quite commensurate with the value it would have.* The 

 sjiectrum of once-ionized helium remains the only companion of tlie 

 spectrum of hydrogen; these arc the onlj' two known spectra which 

 are ascribed to atoms consisting of a nucleus and a single electron. 



We have seen that if we imagine that the electron of the hydrogen 

 atom can revolve, without spending energy by radiation, in and 

 only in those circular orbits for which the angular momentum of the 



atom is equal to h/2ir, 2h/2ir, '6h/2ir nh/2v then the 



energy of the atom-mcxlel can assume only the values —Rli, —Rli/i, 



•Consult for iiibtancc tlic article by .^ngcrcr, ZS. f. Pliysik, 18, pp. IK? IT. 



