To determine where the C-H bond length is minimum, we need to analyze the hybridization states of carbon in different types of hydrocarbons and how they affect the bond length.
### Step-by-Step Solution:
1. **Identify the Hybridization States**:
- In hydrocarbons, carbon can be in different hybridization states:
- **SP3** hybridization (single bonds, e.g., alkanes like CH4)
- **SP2** hybridization (double bonds, e.g., alkenes like C2H4)
- **SP** hybridization (triple bonds, e.g., alkynes like C2H2)
2. **Understand the Relationship Between Hybridization and Bond Length**:
- The bond length is influenced by the percentage of s-character in the hybrid orbitals.
- SP3 hybridization has 25% s-character, SP2 has 33% s-character, and SP has 50% s-character.
- As the s-character increases, the bond length decreases.
3. **Analyze the C-H Bonds in Different Hydrocarbons**:
- In **SP3 hybridization** (e.g., CH4), the C-H bond is longer due to lower s-character.
- In **SP2 hybridization** (e.g., C2H4), the C-H bond is shorter than in SP3 due to increased s-character.
- In **SP hybridization** (e.g., C2H2), the C-H bond is the shortest because it has the highest s-character.
4. **Conclusion**:
- Therefore, the C-H bond length is minimum in the bond formed by carbon in the **SP hybridization** state, which occurs in alkynes (e.g., C2H2).
### Final Answer:
The C-H bond length is minimum in the bond formed by carbon in **SP hybridization** (as in alkynes like C2H2).
