292 BELL SYSTEM TECHNICAL JOURNAL 



and the angular momentum of the rotation.-^ This ratio is the one 

 enclosed in parentheses in equation (7) : we may therefore write: 



U = ojp cos a. (8) 



The precession of which co is the angular velocity is known as the 

 Larmor precession. To keep this precession in mind as a feature of the 

 atom-model is usually desirable, though not constantly necessary. It 

 must be supposed to occur not only when an atom is immersed in an 

 extraneous magnetic field, but also when two of the subatomic magnets 

 within a single atom are influencing one another. 



We have treated the (non-existent) extreme case in which there is 

 nothing but the angular momentum and the magnetic moment of the 

 orbital motion of a single electron to be taken account of; we turn now 

 to the other extreme in which there is nothing but the spin of a single 

 electron to be taken into account. Were we still confined to the 

 original atom-model of Bohr, this case would be equally non-existent; 

 for no electron-orbit could have a vanishing angular momentum unless 

 it were a straight line passing to and fro through the nucleus, and this 

 was formerly excluded as unthinkable. Quantum mechanics, how- 

 ever, assigns the value zero to the angular momentum of a valence- 

 electron in a state of the S sequence (to which the normal state of the 

 sodium atom belongs). Whether the student prefers to visualize a 

 straight-line "orbit" for such a case, or a spherical cloud of charge or of 

 "probability-of -charge," is to some extent a matter of taste, though 

 usually the latter is the better policy. For such a state, there is no 

 angular momentum and there is no magnetic moment save those of the 

 electron-spin itself. 



To this spin of the electron — whether isolated as in this extreme 

 example, or compounded with an orbital motion into a resultant — 

 we are compelled by various reasons to assign the value 2{e/2mc) for 

 that important ratio of magnetic moment to angular momentum. 

 Otherwise expressed : the spin of the electron is characterized by the value 

 2 for the g-f actor. 



There is a classical argument for this assertion, based on an evalua- 

 tion of the ratio in question for a sphere of homogeneous charge rotating 

 about an axis passing through its centre. There is a more powerful 

 quantum-mechanical argument, based on the fact that when Schroed- 

 inger's fundamental equation of wave-mechanics was amended by 

 Dirac to be conformable with relativity, there appeared in it a term 

 attributable to a whirling charge with a ^-factor of 2. Apart from 



•■' Slater and Frank, "Introduction to Theoretical Ph>sics," Chapter X. 



