Question

1. An excited state electron configuration of He is given by 2p'3d (a) Determine all the possible term symbols of this electron configurations. b) Now consider the following box notation (one way to arrange 2p 3d1). p-orbital d-orbital m,-+1 0 .1 m,: +2 +1 0-1 -2 (b-1) Write all the possible (valid) wavefunctions that match with the electron configuration in the above box notation. No need to determine the normalization constant. (b-2) Find all the possible term symbols in (a) that may come from the electron configuration in the above box notation.

Answer 1

1) a) Term symbol for 2p¹3d¹:

  $\bullet$ 2p¹ $\rightarrow$²P_1/2, ²P_3/2 ( S= 1/2, L=1, J=1/2,3/2)

  $\bullet$ 3d¹ $\rightarrow$²D_3/2, ²D_5/2 (S=1/2, L=2, J=3/2,5/2)

  $\bullet$ 2p¹3d¹$\rightarrow$ S_TOT = 0 or 1

  $\rightarrow$ L_TOT = 1 or 2 or 3

  $\rightarrow$¹P₁ + ³P₀, ³P₁, ³P₂

  $\rightarrow$¹D₂ + ³D_1, ³D_2, ³D₃

  _{$\rightarrow$}¹F₃ + ³F_2, ³F₃, ³F₄

[$\sum$(2J+1)= 3+ 1+ 3+ 5+ 5+ 3+ 5+ 7+ 7+ 5+ 7+ 9= 60]

If you want the solution of other parts also, then please let me know.