THE PHYSICAL BASIS OF FERROMAGNETISM 33 



assigned to this spin of the electron about its own center was equal to 

 one Bohr magneton which by definition is that of the smallest electron 

 orbit on the Bohr theory. 



eh 

 MB = -^^^ = 9.2 X 10-21 erg/gauss. 



The unit of angular momentum was taken as one-half of that for the 

 smallest Bohr orbit or as 



47r 



The ratio for the spin motion, denoted by ps, is 



Js inc pn 

 liB e I 



and is thus twice the gyromagnetic ratio for the orbital motion of the 

 electron. Dirac has shown that these results are consequences of 

 relativistic quantum theory. 

 In general the ratio M jJ is 



mc 2 



^ = Ti 



where g is known as the Lande splitting factor. For spin moment, 

 g = 2\ for orbital moment, g = \. When the moment of an atom 

 is the resultant of finite spin and orbital moments, g may be found 

 in terms of the quantum numbers, 5 and /, expressing the angular 

 momenta of the spin and orbital components: 



« = 3/2 +-^(^+ "-'('+') 



Vij + 1) 



Here 5 may have any of the half-integral values 0, 1/2, 1, 3/2, • • • and 

 / any of the integral values 0, 1, 2 • • • , while the number, j, representing 

 the angular momentum of the resultant may be any positive number 

 equal to the sum or difference of 5 and /. (The actual value of the 

 resultant angular momentum is 



j-^ vjcTm), 



LIT 



and that of the magnetic moment is 



