[C^b'J 



Normal State of the Helium Atom. 125 



metals (lithium, sodium, potassium, &c.) absorb the principal 

 series of doublets, the conventional formula for which is 



v = (l,s)-(m,p)*. 



The frequency of the limit of this series, which we have 

 indicated by the symbol (1, s). fits the empirical formula for 

 the terms of the sharp series (m, s), and we conclude that, 

 the normal state of each of these atoms is simply that stationary 

 state of the sharp series which has the least radial quantum 

 number (presumably zero). 



Several suggestions have been made regarding the orbits 

 of the electrons in the normal helium atom. Bohr's model 

 consisting of two electrons revolving about a common circular 

 orbit, is the simplest, but gives the wrong ionization potential. 

 The Lande model f, which identifies the normal atom with 

 the stationary state corresponding to the one quantum sharp 

 series coplanar orbit term (1, s), must be discarded for the 

 same reason. The writer has recently applied the Sommerfeld 

 quantum conditions to the Langmuir model, which consists 

 of two electrons which oscillate in symmetrical arcs on opposite 

 sides of the nucleus, and has shown that if these quantum 

 conditions are correct, this model also has the wrong energy j. 



There remains the suggestion of Franck and Reiche § that 

 the normal state of the helium atom is identical with the one 

 quantum sharp series state (1, S) of the crossed orbit (single- 

 line) system. In a very interesting and suggestive paper, 

 Franck and Reiche have shown that this hypothesis leads at 

 once to the conclusion that the stationary state (2, s) of the 

 coplanar system constitutes a metastable modification of the 

 helium atom. The experimental evidence presented by them 

 and by Franck and Knipping || seems definitely to establish this 

 conclusion, but gives no direct confirmation of the original 

 hypothesis. On the contrary, it is the writer's purpose to 

 show that the normal state of the helium atom cannot be 

 identical with the state (1, S). This paper contains in 



* In this paper the symbols used for the various series terms and the 

 corresponding stationary states are the same as those used by Sommerfeld 

 and Lande except in the case of the sharp series, where (m, s) is sub- 

 stituted for the customary (m+5,5). m is in each case given the theo- 

 retical value of the sum of the azimuthal and radial quantum numbers 

 for the corresponding stationary state. Small letters s } p, d are used in 

 designating terms of the sharp, principal, and diffuse series of the doublet 

 system, and capital letters S, P, D are used to designate terms of the 

 corresponding series of the single line-system. 



t A. Lande, /. c. 



X E. C. Kemble, i Science,' n. s. lii. p. 581 (1920). 



§ Franck & Reiche, Zeits.f. Phys. i. 2, p. 154(1920). 



|| Franck & Knipping, Zeits.f. 'Phys. i. 4, p. 320 ( L920), 



