Physical Chemistry , 1st ed.

These three selection rules require several comments. First, a L0 tran-

sition is possible. This seemingly contradicts our earlier 1 selection

rule, but for multielectron atoms it is possible to have transitions where the

change in the approximate quantum number is 1 or 1 while the change

in the more rigorous Lquantum number is 0. Second, the selection rule

S0 is useful: electronic energy states that have different multiplicities

should not participate in allowed spectroscopic transitions. This allows us to

separate electronic spectra on the basis of multiplicity into systemsthat have

the same value ofS. Allowed transitions can occur only within a system. This

fact can be useful when trying to interpret an unknown spectrum. (Recall that

this is for allowed electronic transitions. Although transitions where S 0

are technically forbidden, they do occur. Phosphorescence is a process in which

such forbidden transitions do occur.)

There is an exception to the selection rule J0: an electronic state having

J0 will not participate in an allowed transition with another electronic state

that also has J0. This rule comes from the consideration of the symmetry of

wavefunctions for J0 states, and we will not go into detail about it here.

Finally, it should be understood that these selection rules of course apply only to

atomic systems where the Russell-Saunders coupling scheme is applicable. For

large atoms (approximately Z30, where Zis the atomic nuclear charge), this

coupling system breaks down and the j-jcoupling system is more appropriate.

Atomic spectra are occasionally displayed diagrammatically in what are

called Grotrian diagrams,after the scientist Walter Grotrian. Figures 15.6 and

15.5 Multiple Electrons: Term Symbols and Russell-Saunders Coupling 533

20,000

0

Energy, cm

^1

16,000

6 s

5 s

4 s

3 s

2 s

1 s

6 p

5 p

4 p

3 p

2 p

6 d

5 d

4 d

3 d

6 f

5 f

4 f

19,000

18,000

17,000

Figure 15.6 A partial Grotrian diagram for helium. Understand that these are not the only

possible transitions, only a few.Source: Physical Chemistryby Vemulapalli, G. K., © 1993. Adapted

by permission of Prentice-Hall, Inc., Upper Saddle River, NJ.