Which of the following has three different stereoisomers?

Options

A. `2,4`-hexadiene
B. `1,3`-butadiene
C. `2,5`-hexadiene
D. `2,4`-heptadiene

Explanation

To determine which of the given compounds has three different stereoisomers, we will analyze the structures of the compounds mentioned in the question.

### Step-by-Step Solution:

1. **Identify the Compounds**: The question mentions several compounds, including 2,4-hexadiene, 1,3-butadiene, 2,5-hexadiene, and 2,4-heptadiene.

2. **Draw the Structure of 2,4-Hexadiene**:
- The structure of 2,4-hexadiene can be represented as:
```
CH3-CH=CH-CH=CH-CH3
```
- Here, the double bonds are located at the 2nd and 4th carbon atoms.

3. **Analyze Stereoisomerism**:
- For 2,4-hexadiene, we can have cis and trans configurations around each double bond.
- The first double bond (C2=C3) can be either cis (both substituents on the same side) or trans (substituents on opposite sides).
- The second double bond (C4=C5) can also be either cis or trans.

4. **Count the Stereoisomers**:
- For the first double bond (C2=C3), we have two possibilities: cis and trans.
- For the second double bond (C4=C5), we again have two possibilities: cis and trans.
- However, due to symmetry, some combinations will lead to identical structures.
- The combinations yield three unique stereoisomers:
1. **Cis-Cis** (both double bonds in the cis configuration)
2. **Cis-Trans** (first double bond cis, second trans)
3. **Trans-Trans** (both double bonds in the trans configuration)

5. **Evaluate Other Compounds**:
- **1,3-Butadiene**: This compound can only form two stereoisomers (cis and trans) due to the presence of only one double bond.
- **2,5-Hexadiene**: This compound has no stereoisomers because it does not have any double bonds that can exhibit stereochemistry.
- **2,4-Heptadiene**: Similar to 2,4-hexadiene, it can only form two stereoisomers.

6. **Conclusion**:
- The only compound that can form three different stereoisomers is **2,4-hexadiene**.

### Final Answer:
**The compound that has three different stereoisomers is 2,4-hexadiene.**