In octahedral coordination entities:

The correct answer is Option (2) → t_2g set has lower energy than e_g set

In the crystal field theory, the ligands of an octahedral entity lie along the x, y and z axes. The two d orbitals that point towards them are raised in energy (the e_g set), and the three that point between the axes are lowered (the t_2g set). So t_2g lies below e_g, the gap being Δ_o. In a tetrahedral field the order is reversed and the sets are written e and t₂, without the subscript g, because a tetrahedron has no centre of symmetry.

• Option (1) t₂ set has lower energy than e_g set — Incorrect. The label t₂ belongs to the tetrahedral field; the octahedral sets are t_2g and e_g.

• Option (3) e_g set has lower energy than t₂ set — Incorrect. It mixes the labels of the two fields and also reverses the octahedral order.

• Option (4) e_g set has lower energy than t_2g set — Incorrect. It reverses the order; in an octahedral field e_g is the higher-energy set.

NCERT (2026-27 edition):
Crystal Field Splitting in Octahedral Coordination Entities – “In an octahedral coordination entity with six ligands surrounding the metal atom/ion, there will be repulsion between the electrons in metal d orbitals and the electrons (or negative charges) of the ligands. Such a repulsion is more when the metal d orbital is directed towards the ligand than when it is away from the ligand. Thus, the d_x²–y² and d_z² orbitals which point towards the axes along the direction of the ligand will experience more repulsion and will be raised in energy; and the d_xy, d_yz and d_xz orbitals which are directed between the axes will be lowered in energy relative to the average energy in the spherical crystal field. Thus, the degeneracy of the d orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, t_2g set and two orbitals of higher energy, e_g set.”