The complex that can show optical activity is:

🧠 Look for Lack of Mirror Symmetry

A complex is optically active if it has no mirror plane, no centre of inversion, no improper axis. cis-bisbidentate octahedrals with two extra ligands are the classic chiral motif.

🗺️ Evaluate Each

| Complex | Symmetry | Optical activity | |---|---|---| | trans-$[\mathrm{CrCl_2(ox)_2}]^{3-}$ | Has $\sigma_h$ plane | ✗ achiral | | trans-$[\mathrm{Fe(NH_3)_2(CN)_4}]^-$ | Has $\sigma$ planes ($D_{4h}$) | ✗ achiral | | cis-$[\mathrm{Fe(NH_3)_2(CN)_4}]^-$ | Has $\sigma$ plane through CN ligands | ✗ achiral | | cis-$[\mathrm{CrCl_2(ox)_2}]^{3-}$ | $C_2$ only, no mirror plane | ✓ chiral (Δ/Λ) |

🗺️ Why cis-$[M(AA)_2 X_2]$ is Chiral

Two cis Cl⁻ ligands occupy adjacent positions; the two oxalate ligands wrap diagonally around the metal. The resulting structure has only a $C_2$ axis (passing through the midpoints of Cl-Cl and one oxalate). No mirror planes → chiral.

🗺️ Why trans Isomer is Achiral

In trans-$[\mathrm{CrCl_2(ox)_2}]^{3-}$, the two Cl⁻ are at axial positions (180° apart). The two oxalates lie in the equatorial plane and are related by a $\sigma_h$ mirror plane. → achiral.

⚡ Cis-Trans Chirality Quick Test

| Geometry | Chiral? | |---|---| | cis-$[M(AA)_2 X_2]$ | ✓ (Δ/Λ) | | trans-$[M(AA)_2 X_2]$ | ✗ | | cis-$[M A_2 B_4]$ (mono only) | ✗ | | $[M(AA)_3]$ | ✓ |

⚠️ Identical Mono-Ligands ≠ Chiral

$[\mathrm{Fe(NH_3)_2(CN)_4}]^-$ has only mono-ligands. Cis or trans, mirror symmetry exists in both — neither is chiral.

$\boxed{\text{Answer: (4) cis-}[\mathrm{CrCl_2(ox)_2}]^{3-}}$