Transition metal complex with highest value of crystal field splitting (Δ₀) will be:

🧠 Same Ligand, Same OS — Compare Metals Across Periods

All four complexes are $[\mathrm{M(H_2O)_6}]^{3+}$ — same ligand, same OS. The variable is the metal.

🗺️ Δ Trend Down a Group: 3d < 4d < 5d

$\Delta_o$ increases by ~50% from 3d → 4d, and another ~25% from 4d → 5d. Reasons: larger d-orbitals → better overlap with ligand orbitals → stronger crystal-field interaction.

| Metal | Period | Relative $\Delta_o$ | |---|---|---| | Cr | 3d | low | | Fe | 3d | low | | Mo | 4d | mid-high | | Os | 5d | highest ✓ |

So $[\mathrm{Os(H_2O)_6}]^{3+}$ has the largest $\Delta_o$.

⚡ 3d→4d→5d Δ Boost Is Why 4d/5d Are Always LS

Because $\Delta_o$ scales up sharply with $n$, second- and third-row transition metals (Pd, Pt, Rh, Ir, Os, Ru, etc.) are almost always low-spin, regardless of ligand field strength. F⁻ on Os(III)? Still low-spin. Cl⁻ on Pt(II)? Still square planar diamagnetic. The 3d HS/LS dichotomy largely disappears in 4d/5d.

⚠️ Period Matters More Than Ligand Sometimes

Going from $[\mathrm{Cr(H_2O)_6}]^{3+}$ (3d) to $[\mathrm{Os(H_2O)_6}]^{3+}$ (5d) raises $\Delta_o$ by a factor of ~2 — a much bigger effect than swapping a moderate ligand for a slightly stronger one within the same period.

$\boxed{\text{Answer: (3) } [\mathrm{Os(H_2O)_6}]^{3+}}$