Which of the following cyclopentane derivative is optically inactive ?

Options

A.
B.
C.
D.

Explanation

To determine which cyclopentane derivative is optically inactive, we need to analyze the structures of the given derivatives and check for symmetry. Here's a step-by-step solution:

### Step 1: Understand Optical Activity
Optical activity refers to the ability of a compound to rotate plane-polarized light. A compound is optically active if it lacks any symmetry elements, such as a plane of symmetry (POS) or a center of symmetry (COS). If a compound has either of these symmetries, it is considered optically inactive.

### Step 2: Analyze the Given Cyclopentane Derivatives
We have four derivatives of cyclopentane. We need to examine each one for symmetry.

1. **Derivative 1**: Analyze its structure for symmetry.
2. **Derivative 2**: Analyze its structure for symmetry.
3. **Derivative 3**: Analyze its structure for symmetry.
4. **Derivative 4**: Analyze its structure for symmetry.

### Step 3: Identify Symmetries
- **Derivative 1**: No plane or center of symmetry → Optically active.
- **Derivative 2**: No plane or center of symmetry → Optically active.
- **Derivative 3**: Has a plane of symmetry → Optically inactive.
- **Derivative 4**: No plane or center of symmetry → Optically active.

### Step 4: Conclusion
Based on the analysis, only **Derivative 3** has a plane of symmetry, making it optically inactive. Therefore, the correct answer is:

**Answer: Derivative 3 is optically inactive.**

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