Which of the following complexes show linkage isomerism?

The correct answer is Option (3) → $[Co(NH_3)_5(NO_2)]^{2+}$

$[Co(NH_{3})_{5}(NO_{2})]^{2+}$ shows linkage isomerism.

Reasoning:

Linkage isomerism occurs when a ligand can attach to the central metal atom through two different donor atoms. Such ligands are called ambidentate ligands.

• $NO_{2}^{-}$ (nitrite ion) is an ambidentate ligand. It can bind through:
• Nitrogen atom $\rightarrow$ nitro form ($-NO_{2}$)
• Oxygen atom $\rightarrow$ nitrito form ($-ONO$)

So, $[Co(NH_{3})_{5}(NO_{2})]^{2+}$ can exist in two linkage isomeric forms, hence it shows linkage isomerism.

Option 1: $[Co(H_2O)_5CO]^{3+}$

CO is a monodentate ligand but it binds only through carbon in coordination chemistry. It does not normally form a stable isomer via oxygen bonding in such complexes.

Option 2: $[Co(NH_3)_3Cl_3]$

$NH_3$ and Clare simple monodentate ligands with only one donor atom. They cannot attach through alternate atoms, so linkage is not possible.

Option 4: $[Co(H_2O)_6]^{3+}$

$H_2O$ binds only through oxygen and has no alternative donor atom. Hence, no possibility of linkage isomerism.