Step 1: Understanding coordination isomerism.
Coordination isomerism occurs when there is a possibility of swapping ligands between the metal centers of a coordination compound. This happens when there are two or more metal centers and ligands are distributed in different ways between them, leading to isomers with different structures but the same molecular formula.
Step 2: Analyzing the compounds.
- (A) \( [\text{Fe(NH}_3)_6] [\text{Co(CN)}_6] \): This compound contains two metal centers, \( \text{Fe} \) and \( \text{Co} \), and can show coordination isomerism by exchanging ligands between them.
- (B) \( [\text{Cr(NH}_3)_6] [\text{Co(CN)}_6] \): Similarly, this compound contains two metal centers, \( \text{Cr} \) and \( \text{Co} \), and can also show coordination isomerism.
- (C) \( [\text{Co(NH}_3)_6] [\text{Co(CN)}_6] \): This compound contains the same metal center \( \text{Co} \), but it can still show coordination isomerism by the exchange of ligands between the two coordination spheres.
- (D) \( [\text{Ag(NH}_3)_2] [\text{Ag(CN)}_2] \): This compound contains the same metal center \( \text{Ag} \), but since there is no possibility of exchanging ligands between two different metal centers, it cannot show coordination isomerism.
- (E) \( [\text{Fe(NH}_3)_6] [\text{Cr(CN)}_6] \): This compound contains two different metal centers \( \text{Fe} \) and \( \text{Cr} \), and can show coordination isomerism by exchanging ligands between them.
Step 3: Conclusion.
The compounds that can show coordination isomerism are A, B, C, and E.
Final Answer: (C) A, B, C & E only