Q1(b). Ground terms by L-S coupling

Answer in brief

Free-ion parent terms: Cr³⁺ (d³), ⁴F; Mn³⁺ (d⁴), ⁵D. Their octahedral ground states are ⁴A₂g and high-spin ⁵Eg, respectively.

Key points

• Both metals are in oxidation state +3: Cr³⁺ is 3d³ and Mn³⁺ is 3d⁴.
• Apply Hund's rules: maximise total spin S, then total orbital angular momentum L within that spin multiplicity.
• For d³, parallel spins in ml = 2, 1, 0 give S = 3/2 and L = 3 (F). Thus ⁴F; the free-ion lowest J is 3/2.
• For d⁴, parallel spins in ml = 2, 1, 0, −1 give S = 2 and L = 2 (D). Thus ⁵D; the free-ion lowest J is 0.
• In an octahedral field, d³ (t₂g³) is ⁴A₂g; aqua Mn(III) is high-spin t₂g³eg¹, ⁵Eg, Jahn-Teller distorted.