Which of the following has an optical isomer?

A coordination complex exhibits optical isomerism if its structure is chiral, meaning it lacks an improper axis of rotation (most commonly checked as lacking a plane of symmetry, $$\sigma$$, and a center of inversion, $$i$$). This allows it to exist as non-superimposable mirror images (enantiomers).

• Monodentate ligands alone in symmetric arrangements (like square planar or octahedral complexes with high symmetry) rarely form chiral centers unless configured asymmetric mixed-ligand types.
• Bidentate chelating ligands like ethylenediamine ($$\text{en}$$) form stable rings that constrain the geometry. In octahedral complexes, having two or more bidentate ligands frequently creates a helical skew, eliminating planes of symmetry and producing optically active cis isomers.

Analysis of the Complexes:

• Option A: $$[\text{Co(NH}_3)_3\text{Cl}]^+$$

  This formula represents a coordination number of 4. Assuming a standard tetrahedral or square planar geometry, the distribution of three identical ligands and one distinct ligand creates a highly symmetric layout with multiple planes of symmetry. It is optically inactive.




• Option B: $$[\text{Co(en)(NH}_3)_2]^{2+}$$

  This complex also possesses a lower coordination number environment where the single bidentate ligand along with two ammine groups coordinates symmetrically, yielding a configuration that contains an internal plane of symmetry. It is optically inactive.




• Option C: $$[\text{Co(H}_2\text{O})_4\text{en}]^{3+}$$

  This is an octahedral complex of the general formula $$[\text{M(AA)B}_4]$$. The single ethylenediamine ring lies entirely within one plane, and a plane of symmetry can easily be drawn that cuts directly through the ethylenediamine ring and bisects the pairs of aquo ($$\text{H}_2\text{O}$$) ligands. Because it possesses a plane of symmetry, it cannot exhibit optical isomerism.




• Option D: $$[\text{Co(en)}_2\text{NH}_3)_2]^{3+}$$

  This is an octahedral complex of the general formula $$[\text{M(AA)}_2\text{B}_2]$$. It can exist as two distinct geometric isomers:

  1. trans-isomer: The two monodenate $$\text{NH}_3$$ ligands are positioned at $$180^\circ$$ to each other. This form has a center of inversion and planes of symmetry, making it optically inactive.
  2. cis-isomer: The two mono-dentate $$\text{NH}_3$$ ligands are located adjacent ($$90^\circ$$) to each other. This forces the two chelating $$\text{en}$$ rings into a non-planar, propeller-like skew layout. The cis-form lacks any plane of symmetry or center of inversion, separating into a pair of non-superimposable dextro ($$d$$) and levo ($$l$$) enantiomers.

  Because its cis geometric variant is chiral, this complex exhibits optical isomerism.

Conclusion:

Only the complex containing two bidentate ethylenediamine ligands, $$[\text{Co(en)}_2\text{NH}_3)_2]^{3+}$$, can form a non-superimposable mirror image geometry via its cis-isomer config.

Answer: Option D — $$[\text{Co(en)}_2\text{NH}_3)_2]^{3+}$$