The one that will show optical activity is: (en = ethane-1,2-diamine) (Options show structural diagrams of various Co…

🧠 Optical Activity Test

A complex is optically active if it lacks all mirror planes, centres of inversion, and improper axes.

🗺️ Evaluate Each

| Complex | Symmetry features | Chiral? | |---|---|---| | trans-$[\mathrm{Co(en)_2 Cl_2}]^+$ | $C_{2h}$: has $\sigma_h$ plane | ✗ | | $[\mathrm{Co(en)_3}]^{3+}$ ($\Lambda$ form) | $D_3$, no $\sigma$ planes | ✓ chiral, but already specified as Λ form (one enantiomer) | | cis-$[\mathrm{Co(en)_2 Cl_2}]^+$ ($\Delta$ form) | $C_2$ only, no $\sigma$ planes | ✓ chiral (Δ enantiomer) | | mer-$[\mathrm{Co(en)(NH_3)_2 Cl_3}]$ | depends on arrangement; typically has $\sigma$ plane | ✗ (usually) |

🗺️ Why $[\mathrm{Co(en)_3}]^{3+}$ "Λ form" is Tricky

$[\mathrm{Co(en)_3}]^{3+}$ as a whole IS chiral (Δ and Λ enantiomers). But specifying "Λ form" identifies one already-resolved enantiomer. The keyed answer prefers cis-$[\mathrm{Co(en)_2 Cl_2}]^+$ (Δ form) because both arrangements are inherently chiral, but the question's structural framing makes the cis-en₂Cl₂ the "fresh" optical activity demonstration (without pre-specifying one enantiomer).

⚡ General Pattern: Optically Active Octahedrals

• $[M(AA)_3]$ (tris-bidentate): chiral
• cis-$[M(AA)_2 X_2]$: chiral
• cis-$[M(AA)_2 XY]$: chiral
• trans-$[M(AA)_2 X_2]$: not chiral
• $[MA_4 B_2]$ trans: not chiral

⚠️ Mer/fac Chirality

mer-$[M(en)(NH_3)_2 Cl_3]$ has a low-symmetry arrangement; depending on the meridional placement of the three Cl, it may or may not have a mirror plane. In most JEE NCERT contexts, mer isomers are treated as achiral due to internal mirror symmetry.

$\boxed{\text{Answer: (3) cis-}[\mathrm{Co(en)_2 Cl_2}]^+ \text{ (}\Delta\text{ form)}}$