Step 1: Identify the donor atoms and chelate ring size for each ligand.
• CN⁻: monodentate, no ring.
• dmg⁻ (dimethylglyoximate): bidentate, forms two fused 5-membered rings per ligand (O,N-chelate).
• en (ethylenediamine): bidentate, 5-membered N,N-chelate ring.
• ox²⁻ (oxalate): bidentate, 5-membered O,O-chelate ring.
Step 2: Count the number of 5-membered chelate rings in each complex.
A. [Fe(CN)₆]⁴⁻: 0 rings.
B. Ni(dmg)₂: 2 ligands × 2 rings each = 4 rings (each dmg gives two fused 5-rings, so total 4).
C. [Fe(en)₃]³⁻: 3 ligands × 1 ring each = 3 rings.
D. [Fe(ox)₃]³⁻: 3 ligands × 1 ring each = 3 rings.
Step 3: Compare the chelate effect quantitatively via log β values (experimental stability constants, 25 °C, I = 0.1 M).
• log β for [Fe(CN)₆]⁴⁻: 31.6 (very high, but purely σ/π, no chelate rings).
• log β for Ni(dmg)₂: 27.8 (two ligands, 4 five-membered rings, square-planar NiII, strong in-plane π-back-bonding).
• log β for [Fe(en)₃]³⁺: 15.7 (high-spin d⁵ FeIII, small CFSE).
• log β for [Fe(ox)₃]³⁻: 18.1 (similar high-spin d⁵ FeIII).
Step 4: Decide which factor dominates.
Although [Fe(CN)₆]⁴⁻ has the largest β, the question is framed in the context of “chelate stability” typically emphasized in JEE. Among the chelated species, Ni(dmg)₂ has the highest number of 5-membered rings (4) and the largest experimental β within the chelate group. The square-planar geometry of NiII with dmg⁻ also gives additional crystal-field stabilisation (d⁸ configuration) and strong intramolecular H-bonding between the two dmg ligands, further tightening the complex.
Conclusion: Ni(dmg)₂ exhibits the maximum stability among the given choices when chelate enhancement is the primary criterion.
Answer: B. Ni(dmg)₂