Question: The Pr 3+ ion has 91 microstates that can be grouped into six terms before spinorbit coupling is included: 1 D, 3 F, 1 G,

The Pr³⁺ ion has 91 microstates that can be grouped into six terms before spin–orbit coupling is included: ¹D, ³F, ¹G, ³H, ³P, ¹S.

(a) What is the electron configuration of Pr³⁺?

(b) What are the values of L and S for each of the six terms?

(b) Use Hund’s first two rules to arrange these six terms in order of increasing energy.

(c) Determine the allowed values of the total angular-momentum quantum number J for each of the six terms, and give the lowest-energy ⁽²^S+1⁾L_J term for each.

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