SPINNING ELECTRONS 
XVI. 2] 
219 
energy levels, but, as the arrows indicate, this spin splits each 
level into two, with the exception of the level K = |, which is 
only displaced. 
The symbols K and J used in Fig. 29 correspond to those 
used by Lande, but are somewhat old-fashioned. We should 
now replace K by / of the new mechanics, and J by j, the new 
quantum numbers being \ less than the old. 
Born has emphasized the fact that many of the difficulties 
k old K new j 
3 
2 
2 
1 
1 
Si 
Fig. 29.—Energy Levels. 
in explaining the existence of multiplets in spectra and the 
observations of the anomalous Zeeman effect have arisen from 
the use of an incorrect model, in which the electron was treated 
as a charged mass-point. If we assume with Uhlenbeck and 
Goudsmit * that the electron possesses angular momentum and 
a magnetic moment these difficulties may be removed. 
(2) Multiplets.—There is a remarkable analogy between the 
multiplet structure of optical spectra and the structure of X-ray 
* Goudsmit and Uhlenbeck, Zeits. f. Physik, vol. 35, p. 618, 1926.