Residual electron-electron interactions, atomic terms

[klw289]

Homework Statement

An atom with an excited-state configuration
1s²2s²2p⁶3s²3p⁶4s²3d¹4p¹
With residual electron-electron interactions are taken into account, this configuration splits into atomic terms. List these terms labelled by their L and S quantum numbers

Homework Equations

L=|l₁-l₂|, |l₁-l₂|+1,..., l₁+l₂-1, l₁+l₂
S=|s₁-s₂|, |s₁-s₂|+1,..., s₁+s₂-1, s₁+s₂

The Attempt at a Solution

With 3d₁4p₁open would give l₁=2 s₁=1/2 and l₂=1 s₁=1/2
Thus L = 1, 2 and 3 and S = 0 and 1. Which give the pairs

(1,0)
(1,1)
(2,0)
(2,1)
(3,0)
(3,1)

Is this correct?

If these are correct then I looked at the degeneracy of each of the terms above and total degenerate states would be 60. How can I confirm that this agrees with the number expected from the l and s quantum numbers of the two valence electrons in the configuration above?

 

[klw289]

From my question above can I look at (2L+1)(2S+1)? Is there another way from l and s