All the carbon-carbon bond lengths are equal in

Options

A. `CH_(2)=CH-CH_(2)-CH_(3)`
B.
C. `CH_(3)-CH=CH-CH_(3)`
D. `CH_(2)=CH-CH=CH_(2)`

Answer

To determine which molecule has equal carbon-carbon bond lengths, we need to analyze the hybridization of the carbon atoms in the given options. Here’s a step-by-step solution:

### Step 1: Understand Hybridization and Bond Lengths
The bond length between carbon atoms is influenced by their hybridization:
- **sp hybridization**: Involves a triple bond (short bond length).
- **sp² hybridization**: Involves a double bond (intermediate bond length).
- **sp³ hybridization**: Involves single bonds (longer bond length).

### Step 2: Identify the Hybridization in Each Option
We need to check the hybridization of carbon atoms in each of the given options:
1. **Option 1**: Contains both sp² and sp³ hybridized carbons.
2. **Option 2**: Benzene ring, where all six carbon atoms are sp² hybridized.
3. **Option 3**: Contains a mix of sp² and sp³ hybridized carbons.
4. **Option 4**: Contains sp² and sp³ hybridized carbons, with at least one carbon-carbon single bond.

### Step 3: Analyze Each Option
- **Option 1**: Since there are both sp² and sp³ hybridized carbons, the bond lengths will differ. **(Discard)**
- **Option 2**: All carbon atoms in benzene are sp² hybridized, leading to equal bond lengths. **(Keep)**
- **Option 3**: Contains a mix of sp² and sp³ hybridized carbons, leading to different bond lengths. **(Discard)**
- **Option 4**: Contains sp² and sp³ hybridized carbons, and a single bond, leading to different bond lengths. **(Discard)**

### Step 4: Conclusion
The only molecule where all carbon-carbon bond lengths are equal is **Option 2**, which is benzene.

### Final Answer
All the carbon-carbon bond lengths are equal in **benzene**.

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