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The ground state energy term for [Co(ox)₃]⁴⁻ is ⁴A₂g. Here's why:
1. Cobalt(II) Ion: The central metal ion is Co²⁺, which has a d⁷ electron configuration.
2. Octahedral Geometry: The complex has an octahedral geometry due to the three bidentate oxalate ligands (ox).
3. Crystal Field Splitting: In an octahedral field, the d orbitals split into two sets: the lower energy t₂g set (dxy, dyz, dxz) and the higher energy eg set (dx²-y², dz²).
4. Electron Filling: With 7 electrons, the t₂g set is filled with 5 electrons (↑↓ ↑↓ ↑) and the eg set has 2 electrons (↑). This gives a high-spin configuration.
5. Term Symbol: The ground state term symbol is determined using Hund's rules. The total spin multiplicity is 2S+1 = 4 (S=3/2), and the orbital angular momentum is L=0 (A term). The subscript 'g' indicates that the complex has a center of symmetry. Therefore, the ground state term is ⁴A₂g.