Consider the following octahedral coordination complexes: [ Fe(CN) ₆ ]⁴⁻ , [ Co(NH ₃ ) ₆ ]³⁺ , [ Cr(NH ₃ ) ₆ ]³⁺ , [ V(H ₂ O) ₆ ]³⁺ , [ CoF ₆ ]³⁻ , and [ Ni(NH ₃ ) ₆ ]²⁺ Let x be the number of diamagnetic complexes and y be the number of inner orbital complexes among the given species. The value of (x + y) is

Step-by-step solution

Let us evaluate the magnetic behavior and hybridization of each complex: 1. [ Fe(CN) ₆ ]⁴⁻ : Fe ²⁺ ( 3 d ^6 ). CN ^- is a strong field ligand. Electrons pair up ( t _ 2 g ^6 e _ g ^0 ). Diamagnetic. Uses 3 d orbitals for d ^2 sp ^3 hybridization (inner orbital). 2. [ Co(NH ₃ ) ₆ ]³⁺ : Co ³⁺ ( 3 d ^6 ). NH ₃ acts as a strong field ligand for Co ³⁺ . Electrons pair up. Diamagnetic. Uses 3 d orbitals for d ^2 sp ^3 hybridization (inner orbital). 3. [ Cr(NH ₃ ) ₆ ]³⁺ : Cr ³⁺ ( 3 d ^3 ). Has 3 unpaired electrons. Parama