Question

Among the term symbols \(4S_1\), \(2D_{7/2}\), \(3S_1\), and \(2D_{5/2}\), choose the option(s) possible in the LS coupling notation.

• A. \(4S_1\)
• B. \(2D_{7/2}\)
• C. \(3S_1\)
• D. \(2D_{5/2}\)

Hint:

In LS coupling, the term symbols follow the form \(^{2S+1}L_J\) where \(S\) and \(L\) are combined to give the total angular momentum \(J\).

Answer 1

The Correct Option is C, D

In the LS coupling (Russell-Saunders coupling) scheme, the term symbols represent the combined total orbital angular momentum (\(L\)) and total spin angular momentum (\(S\)) of an atom. The term symbol is written as \(^{2S+1}L_J\), where: - \(^{2S+1}\) is the multiplicity (indicating the total number of spin states), - \(L\) is the orbital angular momentum quantum number (denoted by letter: S, P, D, F,...), - \(J\) is the total angular momentum quantum number (\(J = L + S\)). The only term symbol that is valid in LS coupling is \(2D_{5/2}\) because it follows the correct rules for combining orbital and spin angular momenta, with a possible value for \(L\) corresponding to the \(D\)-orbital (\(L = 2\)) and \(S = 1/2\). Thus, the correct answer is (D) \(2D_{5/2}\).