The complex that can show optical activity is :

Options

A. `cis-[CrCl_(2)(o x)_(2)]^(3-)" (ox = oxalate)"`
B. `trans - [Fe(NH_(3))_(2)(CN)_(4)]^(-)`
C. `trans - [Cr(Cl_(2))(o x)_(2)]^(3-)`
D. `cis - [Fe(NH_(3))_(2)(CN)_(4)]^(-)`

Explanation

To determine which complex can show optical activity, we need to analyze the given options based on the criteria for optical activity. A complex is optically active if it has a non-superimposable mirror image and lacks any type of symmetry (like a plane of symmetry or a center of symmetry).

Let's analyze each option step by step:

### Step 1: Analyze the first option - **Cis-chromium chloride oxalate**
- Structure: This is an octahedral complex with two oxalate ligands and two chloride ligands in the cis position.
- Symmetry: When we draw the structure, we see that there is no plane of symmetry. The two oxalate ligands and two chloride ligands are arranged such that if we place a mirror behind it, the image will not superimpose on the original structure.
- Conclusion: This complex is optically active.

### Step 2: Analyze the second option - **Trans-NH3 twice CN4**
- Structure: This complex has four cyanide ligands in a horizontal plane and two ammine ligands in a vertical position.
- Symmetry: The horizontal plane acts as a plane of symmetry, making the upper and lower parts identical.
- Conclusion: This complex is optically inactive.

### Step 3: Analyze the third option - **Trans-chromium oxalate**
- Structure: Similar to the previous one, this complex has two oxalate ligands and two chloride ligands in a trans position.
- Symmetry: The horizontal plane again serves as a plane of symmetry, making the upper and lower parts identical.
- Conclusion: This complex is optically inactive.

### Step 4: Analyze the fourth option - **Cis-iron NH3 twice CN4**
- Structure: The two ammine ligands are positioned side by side, while the cyanide ligands are arranged in a way that could potentially allow for symmetry.
- Symmetry: A plane can be drawn through the vertical axis that divides the complex into two identical halves.
- Conclusion: This complex is optically inactive.

### Final Conclusion:
After analyzing all the options, we find that the only complex that can show optical activity is **Cis-chromium chloride oxalate**.

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