﻿84:6 Mr. J. H. Van Vleck on the normal Helium Atom 



their cylindrical coordinates are 



I. R, Z, </>, II. R, Z, c£ + 7r, 



the Z axis being that o£ symmetry. This model may be 

 regarded as a sort of hybrid of the Bohr and Langmuir 

 models. The constant angular momentum, which the elec- 

 trons possess about the axis of: symmetry, reminds one of 

 the Bohr model, and the projection of the motion on the 

 plane Z = 0, which is normal to the axis of symmetry, is 

 a sort of precessing ellipse. The type of motion in the 

 RZ plane can be seen by returning to fig. 2. This motion 

 is of an oscillatory character, and is similar to that of the 

 Langmuir semicircular model, except for the effect of a 

 centrifugal force term introduced by the rotation of the 

 RZ plane about the axis of symmetry as the coordinate (j> 

 steadily increases. The motion may be approximately 

 described as the projection of a sine curve on a barrel-shaped 

 surface of revolution, the two electrons always being on 

 opposite sides of the barrel. 



Rough preliminary calculations for this model indicated 

 approximate agreement of the computed and observed 

 ionization potentials, and it was therefore necessary to carry 

 through a more accurate solution of the dynamical problem, 

 which took almost six months. The orbits of the electrons 

 in the helium atom were determined as power series in a 

 constant of integration, a mathematical method often used by 

 astronomers in the three body problems of the solar system. 

 A more detailed description of the mathematics used in 

 solving the dynamical problem, as well as the method used 

 to check the accuracy of solution, is. given in Part II. 



After solution of the dynamical problem, the constants of 

 integration were determined by the quantum conditions (see 

 Part III.), and the ionization potential was then computed, 

 which proved to be 20 '7 volts for the removal of one electron 

 or 71*9 volts for the removal of both electrons. This does 

 not agree with the experimental value of 25'4+ *25 volts *, 

 but the discrepancy is only slightly larger than for the Bohr 

 model, which yields 28*8 volts, the closest agreement 

 obtained by any model based purely on the Sommerfeld 

 quantum conditions. 



The Dilemma of the Helium Atom. 



As already mentioned, the extraordinary chemical stability 

 of helium indicates that the arrangement of its pair of 

 electrons is particularly simple and symmetrical, but all 



* Franck and Knipping, Phys. Zeit. xx. p. 481 (1919). 



