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and its Relation to the Quantum Theory. 847 



models possessing this property now appear to have been 

 weighed in the balance and found wanting, as thev lead to 

 impossible energy values. The conventional quantum theory 

 of atomic structure does not appear able to account for the 

 properties of even such a simple element as helium, and to 

 escape from this dilemma some radical modification in the 

 ordinary conceptions of the quantum theory or of the electron 

 may be necessary*. One such possibility is : 



Reformulation of the Quantum Conditions, 



Any reformulation of the quantum conditions which aims 

 to explain the anomaly of the helium atom by permitting 

 new energy values must yield results identical with those of 

 the ordinary Sommerfeld quantum integrals in the cases of 

 the hydrogen atom and a vibrating diatomic molecule, for in 

 these instances the Sommerfeld conditions are verified by a 

 mass of experimental evidence. 



Two very interesting suggestions on reformulation of the 

 quantum conditions have been made by Langmuir f . One of 

 these suggestions is that in a system with two negative 

 electrons the ordinary Sommerfeld integrals should be 

 replaced by the condition that the maximum angular 



momentum of a single electron be set equal to ^— . In 



Langmuir's semicircular helium atom (fig. 2), this maximum 



value — would be achieved when each electron is at the 



'ITT 



middle of its path, so that we may regard the atom as 

 having two quantum units of angular momentum circulating 

 about the nucleus in opposite directions. This new condition 

 for determining the constants of integration yields the 

 correct ionization potential for the semicircular model of 

 helium f, and therefore merits serious consideration. How- 

 ever, it appears to be a contradiction, rather than generaliza- 

 tion, of the Sommerfeld quantum conditions, for in the 



* The possibility of some asymmetrical model of normal helium 

 should perhaps not be entirely rejected, despite its apparent contra- 

 diction to the view of chemists on the symmetry of helium. In this 

 connexion it should be mentioned that the energies of the Lande 

 and the Franck and Keiche models are not computed directly, but are 

 obtained by extrapolation of spectral series terms. This extrapolation 

 pre-supposes the validity of the Lande theory of the helium spectrum. 

 Also the continuation of a curve can never be predicted with absolute 

 certainty by extrapolation. 



t Physical Review, vol. xvii. p. 339, vol. xviii. p. 104 (1921) ; also 

 Science, vol. lii. p. 434. 



