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In CRYSTAL FIELD THEORY (CFT) for an OCTAHEDRAL complex, the five degenerate d-orbitals of the free metal ion split into
Atwo sets: $t_{2g}$ (3 orbitals, lower energy) and $e_g$ (2 orbitals, higher energy)
Btwo sets: $e_g$ (2 orbitals, lower energy) and $t_{2g}$ (3 orbitals, higher energy)
Cfive non-degenerate orbitals at all different energies
Da single degenerate set, unchanged from the free ion
Answer & Solution
Correct answer: A. two sets: $t_{2g}$ (3 orbitals, lower energy) and $e_g$ (2 orbitals, higher energy)
1. NCERT §5.6 (Crystal Field Theory): In an octahedral ligand field, the five d orbitals are no longer degenerate.
2. The orbitals pointing DIRECTLY toward the six ligands ($d_{z^2}, d_{x^2-y^2}$) — labelled $e_g$ — are RAISED in energy (more repulsion from ligand lone pairs).
3. The orbitals pointing BETWEEN ligand axes ($d_{xy}, d_{xz}, d_{yz}$) — labelled $t_{2g}$ — are LOWERED in energy.
4. So: $t_{2g}$ (3 orbitals) BELOW $e_g$ (2 orbitals). The splitting energy is denoted $\Delta_o$ (octahedral crystal field splitting).
5. Option B inverts the order. Option C splits too much. Option D contradicts the basic CFT picture.
_Source: NCERT Class 12 Chemistry Part 1, Ch 5, §5.6 (Crystal Field Theory — octahedral splitting), p. 10–12._
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