The number of unbranched isomers (including stereoisomers) of `C_(6)H_(12)` are

Answer

To find the number of unbranched isomers (including stereoisomers) of \( C_6H_{12} \), we need to consider the structural possibilities for hexene, which is the alkene formed from hexane by introducing a double bond.

### Step-by-Step Solution:

1. **Identify the Molecular Formula**:
The molecular formula \( C_6H_{12} \) indicates that we are dealing with an alkene (since it has one double bond).

2. **Determine the Structure**:
The simplest structure for \( C_6H_{12} \) is hexene, which can be represented as follows:
- Straight-chain structure: \( CH_3-CH_2-CH_2-CH_2-CH=CH_2 \)

3. **Identify Possible Positions for the Double Bond**:
For hexene, the double bond can be located at different positions:
- 1-hexene: \( CH_3-CH_2-CH_2-CH_2-CH=CH_2 \)
- 2-hexene: \( CH_3-CH_2-CH=CH-CH_2-CH_3 \)
- 3-hexene: \( CH_3-CH=CH-CH_2-CH_2-CH_3 \)

4. **Consider Stereoisomers**:
- **2-hexene** can exhibit geometric (cis/trans) isomerism because the double bond is between two different groups:
- **Cis-2-hexene**: Both methyl groups on the same side.
- **Trans-2-hexene**: Methyl groups on opposite sides.
- **1-hexene** and **3-hexene** do not have stereoisomers since they do not have two different groups attached to the carbons involved in the double bond.

5. **Count the Isomers**:
- 1-hexene: 1 isomer
- 2-hexene: 2 isomers (cis and trans)
- 3-hexene: 1 isomer
- Total = 1 (from 1-hexene) + 2 (from 2-hexene) + 1 (from 3-hexene) = 4 isomers.

### Final Answer:
The total number of unbranched isomers (including stereoisomers) of \( C_6H_{12} \) is **4**.