Which of the following will have maximum stabilization due to crystal field?

🧠 CFSE Magnitude in Real Energy = (Coefficient) × $\Delta_o$

Maximum CFSE requires (a) a large CFSE-coefficient and (b) a large $\Delta_o$.

| Complex | Metal/OS | d-count | Spin | Coef | $\Delta_o$ | |---|---|---|---|---|---| | $[\mathrm{Ti(H_2O)_6}]^{3+}$ | Ti(III) d¹ | — | $-0.4$ | small (H₂O, d¹) | | $[\mathrm{Co(H_2O)_6}]^{2+}$ | Co(II) d⁷ HS | weak | $-0.8$ | small (H₂O, +2) | | $[\mathrm{Co(CN)_6}]^{3-}$ | Co(III) d⁶ LS | — | $-2.4$ | largest (CN⁻ + +3) ✓ | | $[\mathrm{Cu(NH_3)_4}]^{2+}$ | Cu(II) d⁹ sq pl | — | various | mid (NH₃, sq pl) |

For $[\mathrm{Co(CN)_6}]^{3-}$: both factors are maximal — coefficient $-2.4$ (LS d⁶) and $\Delta_o$ (Co(III) + CN⁻ ≈ 33,500 cm⁻¹).

🗺️ Two Factors Combined

$|\mathrm{CFSE}_{\mathrm{Co(CN)_6}^{3-}}| = 2.4 \times 33{,}500 \approx 80{,}400$ cm⁻¹ ≈ 962 kJ/mol — the largest crystal-field stabilisation among standard JEE complexes.

⚡ Maximum-CFSE Recipe

To maximise CFSE, combine:

• Strong-field ligand (CN⁻ ≫ NH₃ > H₂O).
• High OS metal (+3 ≫ +2).
• Octahedral geometry ($\Delta_o > \Delta_t$).
• d-count that maximises coefficient (d⁶ LS gives $-2.4$, the biggest).

$[\mathrm{Co(CN)_6}]^{3-}$ ticks every box.

⚠️ Don't Just Pick the Strongest Ligand

A complex with strong CN⁻ but a low CFSE coefficient (e.g. d¹ → $-0.4$) wouldn't beat a d⁶ LS complex despite the strong ligand. Always check both coefficient and ligand together.

$\boxed{\text{Answer: (3) } [\mathrm{Co(CN)_6}]^{3-}}$