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)#