What is an excited state of scandium?

Well, the ground-state electron configuration of `"Sc"` is

`[Ar] 3d^1 4s^2`

`"Sc"` has many excited states, but let's choose an intuitive one... one where a valence electron is promoted to a clearly higher energy level.

We'll assume the `4s -> 4p` transition. That would give one of the excited states as:

`[Ar] 3d^1 4s^color(red)(2) -> barul(|stackrel(" ")(" "[Ar] 3d^1 4s^1 4p^color(red)(1)" ")|)`

(There are other lower-lying states, but we are ignoring them for simplicity.)

Due to spin-orbit coupling...

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(Notice how the `""^3` states have three energy levels.)

...the destination state (a `""^4 F`), which was quadruply-degenerate in the absence of a magnetic field, now splits into four energy levels of this same configuration, with term symbols `""^4 F_(3//2)`, `""^4 F_(5//2)`, `""^4 F_(7//2)`, and `""^4 F_(9//2)`, in order of increasing energy.

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Assuming we start at the ground-state energy level of `"0 cm"^(-1)`, this transition thus requires an input of any of the following frequencies:

`"15 672.58 cm"^(-1)`

`"15 756.57 cm"^(-1)`

`"15 881.75 cm"^(-1)`

`"16 026.62 cm"^(-1)`