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

Solution

Chemistry ma’am · 3 steps

Same ligand and same charge everywhere, so only the metal's row decides: 5d beats 4d beats 3d.

1. What is fixed. All four complexes have six H₂O ligands and a metal in the +3 state. Ligand strength and oxidation state are the same, so neither can decide the answer.
2. What changes. The metals come from different transition series. Going from 3d to 4d to 5d, the d orbitals get larger and reach further toward the ligands. They overlap and interact with the ligands more strongly, so Δₒ rises by roughly 30 to 50% at each step down a group.

   Complex	Metal ion	Series	Relative Δₒ
   [Cr(H₂O)₆]³⁺	Cr³⁺, d³	3d	smaller
   [Fe(H₂O)₆]³⁺	Fe³⁺, d⁵	3d	smaller
   [Mo(H₂O)₆]³⁺	Mo³⁺, d³	4d	larger
   [Os(H₂O)₆]³⁺	Os³⁺, d⁵	5d	largest

3. So. Osmium is the only 5d metal here, so [Os(H₂O)₆]³⁺ has the highest Δₒ. The answer is (d).

The idea to keep. When the ligand and the oxidation state are the same, look at the metal's series. Δₒ grows in the order 3d < 4d < 5d, because the bigger d orbitals interact more strongly with the ligands.

Answer from the NTA final answer key. Solution by PrepWiser.