Where among the following metal complexes the one which exhiibits optical activity is: (AA=bidentate ligand, A, X=monodentate ligand)

Options

A. cis-`[MA_(4)X_(2)]`
B. trans-`[MA_(4)X_(2)]`
C. cis-`[M(A A)_(2)X_(2)]`
D. trans-`[M(A A)_(2)X_(2)]`

Answer

To determine which metal complex exhibits optical activity, we need to analyze the given complexes based on their structural characteristics and the nature of their ligands.

### Step-by-Step Solution:

1. **Understanding Optical Activity**:
Optical activity is exhibited by compounds that have non-superimposable mirror images, meaning they lack an internal plane of symmetry. This is often the case with chiral molecules.

2. **Identifying Ligands**:
- **Bidentate Ligand (AA)**: A ligand that can attach to the metal at two points. An example is ethylene diamine (en).
- **Monodentate Ligand (X)**: A ligand that can attach to the metal at only one point.

3. **Analyzing Each Complex**:
- **Option A: cis MA4X2**:
- In this complex, there are four monodentate ligands (A) and two monodentate ligands (X). The arrangement is symmetrical, and upon drawing the mirror image, it can be shown that the two structures are superimposable. Hence, this complex does not exhibit optical activity.

- **Option B: trans MA4X2**:
- Similar to option A, this structure is also symmetrical. The mirror image will also be superimposable, indicating that it does not exhibit optical activity.

- **Option C: cis MA2X2**:
- Here, we have two bidentate ligands (AA) and two monodentate ligands (X). The arrangement can lead to a chiral structure, as the two bidentate ligands can create a non-superimposable mirror image. Therefore, this complex exhibits optical activity.

- **Option D: trans MA2X2**:
- This arrangement is also symmetrical. The mirror image will be superimposable, indicating that it does not exhibit optical activity.

4. **Conclusion**:
Based on the analysis, the complex that exhibits optical activity is **Option C: cis MA2X2**.

### Final Answer:
The metal complex that exhibits optical activity is **Option C: cis MA2X2**.