132 Mr. E. C. Kemble on the Probable 



of lines in the spectrum due to atoms jumping to the normal 

 state from the closely-allied series of stationary states (m,p), 

 which have each three units of angular momentum. It would 

 therefore appear that if the application of the Bohr principle 

 of selection to the transfer of atoms from the outer stationary 

 states to the normal state is legitimate, the resultant angular 

 momentum of the normal atom must be zero. This conclusion 

 is very satisfactory from the standpoint of the theory of mag- 

 netism, but leads to difficulties, as we shall see. 



The Probable Normal State of the Helium Atom. 



If the resultant angular momentum of the normal helium 

 atom is zero, the two electrons must move in a common plane 

 with equal and opposite angular momenta. The average 

 angular momentum of each electron will be zero or h/2ir. In 

 the former case the net area enclosed by each orbit must be 

 zero, for the angular momentum is a measure of the area 

 swept out per unit time by a radios vector from the centre 

 of mass to the electron. Ruling out the fantastic possibility 

 of paths of the form of a figure eight, we must in this case 

 assume that the orbit degenerates into an unclosed line along 

 which the electron oscillates, and so arrive at the Langmuir 

 model. 



If each of the electrons has one unit of angular momentum, 

 they must execute coplanar orbital motions with opposite 

 directions of rotation. The only system of orbits o£ this type 

 which does not involve a good deal of radial motion is that 

 in which the two paths are approximate concentric circles 

 of unequal radii. The corresponding model is like that of 

 Lande except that the directions of rotation of the two 

 electrons are opposite. The energy of this model has not 

 yet been calculated, but there is an initial presumption 

 against it from the chemical point of view, owing to the lack 

 of symmetry. 



In view of the unsatisfactory character of the alternative 

 models to which the hypothesis of zero resultant angular 

 momentum for the normal helium atom has led us, w^e may, 

 perhaps, seek a way out in the abandonment of the Bohr 

 principle of selection as applied to the transfer of atoms from 

 the stationary states of higher energy to the normal state, 

 A symmetrical model of a type not hitherto considered may 

 be devised'by introducing the assumption that the co-ordinates 

 of the two electrons x ± , y ls z x and x 2 , y 2 , * 2 > respectively, 

 satisfy the conditio 



liS 



= — X 



1 3 



J/2 = ~ III 



z 2 == Z l> 



