Energy levels and terms schemes of many-electron atoms

1 Energy levels and term schemes of many-electron atoms 

Atom Symbol Configuration Ion Configuration f electron configuration 

In order to obtain the value of S for three electrons, 5(3), the value for two electrons, 5(2), is added to the spin quantum number of the third electron, 53 thus  

This procedure is called the Clebsch-Gordon rule. It is used to obtain the 5 values for increasing numbers of spins. It is found that for an even number of electrons, 5 values are integers for an odd number of electrons, 5 values are half-integers. 

The total angular momentum quantum number, L, is obtained in a similar fashion. For two electrons with individual angular momentum quantum numbers li and I2, the total angular momentum quantum number, L(2) is  

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