Step 1: Ligand Field Strength Determination.
Ligand field strength dictates the extent of d-orbital splitting in transition metal complexes. Strong field ligands induce significant splitting, whereas weak field ligands result in minimal splitting. The order of ligand field strength is as follows:\[\text{CN}^- > \text{CO}_4^{2-} > \text{NH}_3 > \text{OH}^-\]
Step 2: Ligand Classification.
- (A) NH\(_3\) is classified as a weak field ligand.- (B) C\(_2\)O\(_4^{2-}\) (oxalate) is a moderate field ligand.- (C) OH\(^-\) exhibits weaker field strength compared to NH\(_3\).- (D) CN\(^-\) is a strong field ligand, responsible for the most substantial splitting.
Step 3: Final Ordering.
Consequently, the sequence of increasing d-orbital splitting is:\[\text{OH}^- < \text{C}_2\text{O}_4^{2-} < \text{NH}_3 < \text{CN}^-\]The correct option is (4), corresponding to the sequence (C), (B), (A), (D).