518 Quantum Mechanical Basis of Molecular Spectra /27 : 4 



In addition, in a weak magnetic field there is also the selection rule 



Am, = ±1,0 



whereas in a strong magnetic field 



Am t =±1,0 

 Am, = 



's 



For reasons which have far outlived their original meaning, the electrons 

 are designated by different letters according to their value of the orbital 

 quantum number /. These are 



/ = 1 2 3 4 5 6 and so on 

 letter = s p d f g h 



Notice that the letter s has been used both for the spin quantum 

 number and for an electron with no orbital angular momentum. It is 

 important not to confuse these two. (In naming the electrons, originally 

 s = sharp, p = principal, d = diffuse, and f = fundamental. These 

 words are devoid of anything but historical significance. This inappro- 

 priate ordering of letters to represent different values of / is, however, 

 employed by chemists and physicists alike. This situation is reminiscent 

 of some of their strongest criticisms of descriptive biology.) 



The five quantum numbers for an electron can be extended to a com- 

 plete atom. In so doing, one introduces more letters. The total 

 quantum number n must be specified for each electron. However, the 

 angular momenta of the various electrons can add vectorially. Both 

 the values of the individual momenta and some of their sums are quan- 

 tized. Capital letters are used for whole atom values corresponding to 

 the lower-case letters for single electrons. For instance, for two electrons, 

 in some cases 



S = Si ± s 2 



M L = -L,(-L+l),...(L-\),L 



M s = -1,0, +1 



J = {L-S),(L-S+l),---(L + S) 



In other cases, the orbital angular momentum and atomic spin are not 

 quantized but, instead, the total angular momentum is quantized. 

 Then one may write 



J = ( k ~ji)> (k ~ji + 1 ) , • • • (k +k) k > Ji 



Mj= -J,(-J + 1),...(J_1),J 



This last case is called j-j coupling and the former is called L-S or Russel- 



