In an octahedral weak ligand field, each t2g electron lowers the ener…

The correct answer is Option (2) → A-r, B-p, C-q, D-s

• In an octahedral field the d orbitals split into a lower t_2g set and a higher e_g set. The (2/5)Δ_o and (3/5)Δ_o are the 0.4Δ_o and 0.6Δ_o given here, so the crystal field stabilisation energy is:

      \( \displaystyle \text{CFSE}=(-0.4\,n_{t_{2g}}+0.6\,n_{e_g})\,\Delta_o \)

• In a weak ligand field \( \Delta_o \lt P \), so the electrons fill all five orbitals singly before any pairing (high spin): the fourth and fifth electrons go to e_g, and the sixth and seventh pair up in t_2g.

(A) d⁴ — This matches (r) −0.6Δ_o. Configuration t_2g³e_g¹.

    \( \displaystyle \text{CFSE}=3(-0.4)+1(0.6)=-1.2+0.6=-0.6\,\Delta_o \)

(B) d⁵ — This matches (p) 0. Configuration t_2g³e_g², one electron in each d orbital.

    \( \displaystyle \text{CFSE}=3(-0.4)+2(0.6)=-1.2+1.2=0 \)

(C) d⁶ — This matches (q) −0.4Δ_o. Configuration t_2g⁴e_g².

    \( \displaystyle \text{CFSE}=4(-0.4)+2(0.6)=-1.6+1.2=-0.4\,\Delta_o \)

(D) d⁷ — This matches (s) −0.8Δ_o. Configuration t_2g⁵e_g².

    \( \displaystyle \text{CFSE}=5(-0.4)+2(0.6)=-2.0+1.2=-0.8\,\Delta_o \)

NCERT (2026-27 edition):
5.5.4 Crystal Field Theory – “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. … Thus, the energy of the two e_g orbitals will increase by (3/5) Δ_o and that of the three t_2g will decrease by (2/5)Δ_o.”

“(i) If Δ_o < P, the fourth electron enters one of the e_g orbitals giving the configuration t_2g³ e_g¹. Ligands for which Δ_o < P are known as weak field ligands and form high spin complexes.”

Fig. 5.8: d orbital splitting in an octahedral crystal field