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Spectral terms provide a compact way of describing the quantum states of electrons in atoms. They summarize the total orbital angular momentum, spin, and multiplicity of a given electronic configuration.
A spectral term is written as:
$$^{2S+1}L_J$$
S, P, D, F, ... for L=0,1,2,3,...).L and S, ranging from
\( \lvert L+S \rvert \) to \( \lvert L-S \rvert \) in steps of 1.
The electron has spin \(S = \tfrac{1}{2}\) and orbital angular momentum \(L = 0\). Thus:
$$^{2}S_{1/2}$$
This represents a doublet-S state with total \(J = 1/2\).
For two electrons, spins can pair to form either:
This splitting explains why helium exhibits both singlet and triplet spectral series.
The multiplicity \(2S+1\) determines how many closely spaced energy levels appear. Higher multiplicity (like triplets) often correspond to lower energy due to electron exchange effects.
In short, spectral term notation provides a compact way to describe the structure of atomic energy levels.
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