The number of hyperconjugating structures shown by the carbocations are given below. Which one is not correctly matched?

Options

A. `CH_(3)-underset(CH_(3))underset("| ")overset(+)"C "-CH_(3)`, 9 hyperconjugating
B. `CH_(3)-overset(+)C-CH_(3)`, 8 hyperconjugating structures
C. `CH_(3)-overset(+)CH_(2)`, 3 hyperconjugating structures
D. `overset(+)CH_(3)`, No hyperconjugating structures

Answer

To solve the question regarding the number of hyperconjugating structures shown by the carbocations, we will analyze each option provided and determine which one is not correctly matched.

### Step-by-Step Solution:

1. **Understanding Hyperconjugation**:
- Hyperconjugation involves the interaction of the electrons in a sigma bond (C-H or C-C) with an adjacent empty or partially filled p-orbital or π-orbital.
- The number of hyperconjugating structures is equal to the number of alpha hydrogens (hydrogens attached to the carbon adjacent to the positively charged carbon).

2. **Analyzing Each Option**:
- **Option 1**:
- Given: 9 alpha hydrogens.
- Calculation: Since there are 9 alpha hydrogens, the number of hyperconjugating structures = 9.
- Conclusion: This option is correctly matched.

- **Option 2**:
- Given: 6 alpha hydrogens but matched with 8 hyperconjugating structures.
- Calculation: There are 6 alpha hydrogens, so the number of hyperconjugating structures should be 6, not 8.
- Conclusion: This option is **not correctly matched**.

- **Option 3**:
- Given: 3 alpha hydrogens.
- Calculation: Since there are 3 alpha hydrogens, the number of hyperconjugating structures = 3.
- Conclusion: This option is correctly matched.

- **Option 4**:
- Given: 0 alpha hydrogens.
- Calculation: Since there are no alpha hydrogens, the number of hyperconjugating structures = 0.
- Conclusion: This option is correctly matched.

3. **Final Conclusion**:
- The only option that is not correctly matched is **Option 2**, where it states there are 8 hyperconjugating structures instead of the correct 6.

### Answer:
**Option 2 is not correctly matched.**

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