What is the number of optically active isomers of compound having molecular formula `C_(5)H_(9)Cl`.

Explanation

To determine the number of optically active isomers for the compound with the molecular formula C₅H₉Cl, we need to analyze the possible structures and identify chiral centers. Here’s a step-by-step solution:

### Step 1: Identify the Structure
The molecular formula C₅H₉Cl suggests that the compound is likely an alkene due to the degree of unsaturation (since a saturated alkane with 5 carbons would have the formula C₅H₁₂). The presence of chlorine also indicates that it could be a haloalkene.

### Step 2: Draw Possible Structures
1. **Position of the Double Bond**: The double bond can be located in different positions. For five carbons, the double bond can be:
- Between C1 and C2
- Between C2 and C3
- Between C3 and C4
- Between C4 and C5

2. **Chlorine Placement**: For each double bond position, chlorine can be placed on different carbon atoms.

### Step 3: Identify Chiral Centers
A chiral center is a carbon atom that has four different substituents. We need to analyze each structure to find chiral centers:
- For structures where the double bond is between C1 and C2, and C2 has a chlorine and two different groups, it can be chiral.
- Similarly, for other positions of the double bond, we check if any carbon has four different substituents.

### Step 4: Count Optically Active Isomers
1. **Isomers with Double Bond at C1-C2**:
- Structure 1: Chiral (two configurations possible)
- Structure 2: Chiral (two configurations possible)

2. **Isomers with Double Bond at C2-C3**:
- Structure 3: Chiral (two configurations possible)
- Structure 4: Not chiral (due to symmetry)

3. **Isomers with Double Bond at C3-C4**:
- Structure 5: Not chiral (due to symmetry)
- Structure 6: Chiral (two configurations possible)

4. **Isomers with Double Bond at C4-C5**:
- Structure 7: Not chiral (due to symmetry)

### Step 5: Total Count
After analyzing all possible structures, we find:
- From double bond at C1-C2: 2 optically active isomers
- From double bond at C2-C3: 2 optically active isomers
- From double bond at C3-C4: 1 optically active isomer
- From double bond at C4-C5: 0 optically active isomers

Adding these gives us a total of **4 optically active isomers**.

### Final Answer
The number of optically active isomers of the compound with the molecular formula C₅H₉Cl is **4**.

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