Step 1: Definition:
Ambidentate ligands are monodentate ligands that contain more than one different donor atoms but coordinate through only one atom at a time. This leads to linkage isomerism.
Step 2: Evaluating Options:
- (A) \( \text{CN}^- \): Can bond through Carbon (Cyano) or Nitrogen (Isocyano). Ambidentate.
- (B) \( \text{SCN}^- \): Can bond through Sulfur (Thiocyanato) or Nitrogen (Isothiocyanato). Ambidentate.
- (D) \( \text{NO}_2^- \): Can bond through Nitrogen (Nitro) or Oxygen (Nitrito). Ambidentate.
- (C) \( \text{SO}_4^{2-} \): The sulfate ion coordinates through Oxygen atoms. Although it has multiple oxygen atoms and can act as a monodentate, bidentate, or bridging ligand, it does not have two *chemically different* types of donor atoms (like C vs N, or S vs N) to be classified as ambidentate in the classical sense.
Step 3: Final Answer:
\( \text{SO}_4^{2-} \) is not an ambidentate ligand.