Beyond electronic configurations terms, levels, states

6 Beyond electronic configurations terms, levels, states 

The spin-orbit interaction considered in the study of monoelectronic atoms also plays an important role in polyelectronic atoms, with the exception of closed-shell configurations for which the total orbital angular momentum and the total spin angular momentum vanish. 

As the core electrons are a closed sub-shell, the magnetic moments associated with their orbital and spin angular momenta cancel out, and therefore only the valence electrons need be considered. For atoms with just one valence electron, the situation is similar to that for monoelectronic atoms. For example, for the excited configuration of 19K, [Ar], 4p we have 

There are two possibilities for the spin-orbit interactions, corresponding to two values of the total angular momentum quantum number j. Therefore, two energy levels exist for such a configuration  

The superscript on the left of P is the number of values /Wj, (2s +1 = 2) (spin multiplicity) and the remaining indices have the same meaning as on page 69. The spin-orbit sphtting is larger for K than for Na it is roughly dependent on Z.  

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