(a) In octahedral crystal field, energies of which d-orbitals will be raised when ligands approach the central metal atom/ion? Give reason in support of your answer.

Concept

Crystal Field Theory treats ligands as point negative charges. In the free ion all five d-orbitals are degenerate, but an octahedral arrangement of ligand charges lifts that degeneracy.

• Orbitals pointing at the ligands ($e_g$: $d(x^2-y^2)$, $d(z^2)$) are destabilised — energy raised.
• Orbitals pointing between the ligands ($t_{2g}$: $d(xy)$, $d(yz)$, $d(zx)$) are relatively stabilised — energy lowered.

The energy gap between the two sets is the crystal field splitting energy, $\Delta_0$.

Exam trap

A common slip is to name the wrong pair. Remember: 'along the axes → raised ($e_g$)'. The subscript in $d(x^2-y^2)$ and $d(z^2)$ is the memory hook because these expressions contain the axes directly.

Real-world

This splitting explains the colour of transition-metal complexes (d–d transitions across $\Delta_0$) and their magnetic behaviour (high-spin vs low-spin).