In an octahedral crystal field, which of the following d orbitals doe…

The correct answer is Option (4) → d_z²

In an octahedral complex the six ligands lie along the x, y and z axes. The d orbitals that point between the axes are lowered in energy and form the t_2g set; the two that point along the axes are raised and form the e_g set.

Option (1) d_xy — Belongs to the t_2g set. It lies in the xy plane between the x and y axes.

Option (2) d_yz — Belongs to the t_2g set. It lies in the yz plane between the y and z axes.

Option (3) d_xz — Belongs to the t_2g set. It lies in the xz plane between the x and z axes.

Option (4) d_z² — Does not belong to the t_2g set. It points along the z axis, straight at two ligands, so it belongs to the e_g set.

NCERT (2026-27 edition):
(a) Crystal field splitting in octahedral coordination entities – “… 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.”