Which of the following compound shows optical isomerism ?

Options

A. `CH_(3) CH_(2)CH_(3)`
B. `CH_(2)OHCHOHCH_(2)OH`
C. `CH_(3)CHOHC_(2)H_(5)`
D. None of these

Explanation

To determine which of the given compounds shows optical isomerism, we need to identify if any of them contain a chiral center. A chiral center is typically a carbon atom bonded to four different groups.

### Step-by-Step Solution:

1. **Identify the Compounds**:
Let's denote the compounds as follows:
- Compound 1: Propane (C3H8)
- Compound 2: A compound with the formula CH2OH-CHOH-CH2OH
- Compound 3: A compound with the structure CH3-CH(OH)-C2H5

2. **Analyze Compound 1 (Propane)**:
- Structure: CH3-CH-CH3
- The middle carbon is attached to two hydrogen atoms and two methyl groups (CH3).
- Since there are two identical groups (methyl), this compound does not have a chiral center.
- **Conclusion**: Propane is optically inactive.

3. **Analyze Compound 2 (CH2OH-CHOH-CH2OH)**:
- Structure: CH2OH-CHOH-CH2OH
- The central carbon (CHOH) is attached to two identical hydroxymethyl groups (CH2OH).
- Since there are two identical groups, this compound also does not have a chiral center.
- **Conclusion**: This compound is optically inactive.

4. **Analyze Compound 3 (CH3-CH(OH)-C2H5)**:
- Structure: CH3-CH(OH)-C2H5
- The central carbon (CH) is attached to four different groups: CH3, OH, C2H5, and H.
- Since all four groups are different, this compound has a chiral center.
- **Conclusion**: This compound is optically active and shows optical isomerism.

5. **Final Answer**:
- The compound that shows optical isomerism is the third compound (CH3-CH(OH)-C2H5).