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## Homework Statement

An atom with an excited-state configuration

1s

^{2}2s

^{2}2p

^{6}3s

^{2}3p

^{6}4s

^{2}3d

^{1}4p

^{1}

With residual electron-electron interactions are taken into account, this configuration splits into atomic terms. List these terms labelled by thier L and S quantum numbers

## Homework Equations

L=|l

_{1}-l

_{2}|, |l

_{1}-l

_{2}|+1,..., l

_{1}+l

_{2}-1, l

_{1}+l

_{2}

S=|s

_{1}-s

_{2}|, |s

_{1}-s

_{2}|+1,..., s

_{1}+s

_{2}-1, s

_{1}+s

_{2}

## The Attempt at a Solution

With 3d

_{1}4p

_{1}open would give l

_{1}=2 s

_{1}=1/2 and l

_{2}=1 s

_{1}=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?

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