C-C bond length would be minimum in

Options

A. `-=C-underset(|)overset(|)(C)-`
B. `=overset(|)(C)-underset(|)overset(|)(C)-`
C. `=underset(|)(C)-underset(|)(C)=`
D. `-=C-C=`

Answer

To determine where the C-C bond length would be minimum among the given options, we need to analyze the hybridization of the carbon atoms in each compound and how it affects the bond length.

### Step-by-Step Solution:

1. **Understanding Bond Length**:
- The bond length is defined as the average distance between the nuclei of two bonded atoms. It is influenced by the type of hybridization of the orbitals involved in the bond.

2. **Identify Hybridization**:
- The bond length is affected by the hybridization of the carbon atoms:
- **sp hybridization**: 50% s character, shorter bond length.
- **sp2 hybridization**: 33.33% s character, intermediate bond length.
- **sp3 hybridization**: 25% s character, longer bond length.

3. **Analyze Each Option**:
- **Option A**: Contains a carbon-carbon bond with one carbon in sp hybridization and the other in sp3 hybridization.
- **Option B**: Contains a carbon-carbon bond with both carbons in sp2 hybridization.
- **Option C**: Contains a carbon-carbon bond with one carbon in sp2 and the other in sp3 hybridization.
- **Option D**: Contains a carbon-carbon bond with one carbon in sp hybridization and the other in sp2 hybridization.

4. **Determine S Character**:
- For each hybridization:
- sp: 50% s character
- sp2: 33.33% s character
- sp3: 25% s character

5. **Compare S Character**:
- The bond length decreases as the s character increases. Therefore:
- In **Option D**, the carbon with sp hybridization has the highest s character (50%) compared to the other options.

6. **Conclusion**:
- Since the bond length is inversely related to the s character, the C-C bond length would be minimum in **Option D**, where one carbon is sp hybridized and the other is sp2 hybridized.

### Final Answer:
The C-C bond length would be minimum in **Option D**.