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The free ion term symbol for a Cr⁴⁺ ion with all electrons paired is ¹S₀. Here's why:
Electronic Configuration: Cr⁴⁺ has an electronic configuration of [Ar]3d².
Pairing: All electrons are paired, meaning each orbital within the 3d subshell has two electrons with opposite spins.
Term Symbol: The term symbol is derived from the total spin angular momentum (S), the total orbital angular momentum (L), and the total angular momentum (J).
S = 0 (all electrons paired)
L = 0 (all orbitals are filled or half-filled, so the sum of the individual orbital angular momenta is zero)
J = 0 (since S and L are both 0)
The term symbol is written as ²S+¹Lⱼ, where the superscript is 2S+1. Therefore, for Cr⁴⁺ with all electrons paired, the term symbol is ¹S₀.