CONTEMPORARY ADVANCES IN PHYSICS, XXIX 293 



this last, the strongest argument is furnished by the vaUdity of the 

 verifiable formula for the g-factors of various atoms in various states, 

 which we shall presently be deriving. For, inasmuch as in nearly 

 every state of an atom there are both electron-spins and electron- 

 orbits, and the net magnetic moment and net angular momentum of 

 the atom are sorts of resultants of these, the g-factor of the atom-as-a- 

 whole varies from state to state and from one kind of atom to another 

 in a remarkable fashion, which imposes a stringent test on the con- 

 temporary atom-model. 



In explaining how this test is satisfied, I can no longer postpone 

 specific numerical statements about the angular momenta of electron- 

 orbits and electron-spins and the atoms into which these enter. 

 These statements will be made confusing by the fact that to each one 

 of these angular momenta it will be necessary to assign two diliferent 

 numbers. This is one of the impediments which are unavoidable in 

 fitting visualizable atom-models to the results of quantum-mechanical 

 theory, and which to avoid, some theorists would be willing to forego 

 models altogether. 



Were it not for this impediment, I could say quite simply that in 

 every P-state of the sodium atom, the valence-electron has a spin, 

 with angular momentum ^(/i/2x), and is moving in an orbit with 

 angular momentum {hllir) ; that as regards the two members of each 

 of the aforesaid pairs of P-states, these two angular momenta are 

 oriented parallel for on€ member and anti-parallel for the other, so that 

 the net angular momentum of the atom-as-a-whole is \{hl2Tr) in one 

 case and ^{hjlir) in the other; that when an atom with a net angular 

 momentum of ^{h/Iir) is exposed to an applied magnetic field, it 

 orients itself either parallel or anti-parallel to the field, so that the 

 projection of its angular momentum upon the field-direction is either 

 -f |(/i/27r) or — ^(h/lw) ; that when an atom with a net angular 

 momentum of ^{h/lir) is exposed to an applied magnetic field, it 

 orients itself in one or another of four permitted ways so that the 

 projection of its angular momentum upon the field-direction is either 

 + 3/2 or -f 1/2 or - 1/2 or - 3/2 times h/lw. 



This sort of thing is frequently said in the literature, and one must 

 realize its limitations. The trouble is, that quantum mechanics 

 prescribes for these angular momenta (but not for their projections on 

 the field-direction!) magnitudes which differ from those which I 

 have been giving. For the spin 5 of the electron, it substitutes 

 -\/l/2-3/2(/?/27r) for ^{h/lw) ; for the orbital motion / in the present case, 

 it substitues Vl-2 for the factor unity whereby {h/lir) was multiplied; 

 in the two values ;' and j" of angular momentum of the atom-as-a- 



