The carbocation `CH_(3)overset(+)(C)HCH_(3)` is less stable than

Options

A. `CH_(3)CH_(2)overset(+)(C)H_(2)`
B. `overset(+)(C)H_(2)`
C. `(CH_(3))_(3)overset(+)(C)`
D. `CH_(3)overset(+)(C)H_(2)`

Explanation

To determine the stability of the carbocation \( \text{CH}_3^+(\text{C})\text{HCH}_3 \), we need to analyze its structure and compare it with other carbocations based on the inductive effect provided by alkyl groups.

### Step-by-Step Solution:

1. **Identify the Structure of the Given Carbocation**:
- The carbocation \( \text{CH}_3^+(\text{C})\text{HCH}_3 \) has a positive charge on a carbon atom that is bonded to two methyl groups (CH3) and one hydrogen atom.

2. **Understand Carbocation Stability**:
- Carbocation stability is influenced by the number of alkyl groups attached to the positively charged carbon. Alkyl groups are electron-donating through the +I (inductive) effect, which helps to stabilize the positive charge.

3. **Analyze the Given Carbocation**:
- In this case, the carbocation has two methyl groups providing +I effect. This means it is stabilized to some extent, but we need to compare it with other carbocations.

4. **Compare with Other Carbocations**:
- **Option A**: A carbocation with one alkyl group (e.g., \( \text{CH}_3^+(\text{C})\text{H}_2 \)). It is less stable than the given carbocation because it has only one +I effect.
- **Option B**: A carbocation with no alkyl groups (e.g., \( \text{C}^+(\text{H})_3 \)). This is the least stable as there is no +I effect.
- **Option C**: A carbocation with three alkyl groups (e.g., \( \text{C}^+(\text{CH}_3)_3 \)). This is more stable than the given carbocation due to the maximum +I effect.
- **Option D**: A carbocation with one alkyl group (similar to Option A). It is also less stable than the given carbocation.

5. **Conclusion**:
- The stability order is as follows:
- \( \text{C}^+(\text{CH}_3)_3 \) (most stable) > \( \text{CH}_3^+(\text{C})\text{HCH}_3 \) > \( \text{CH}_3^+(\text{C})\text{H}_2 \) and \( \text{C}^+(\text{H})_3 \) (least stable).
- Therefore, the carbocation \( \text{CH}_3^+(\text{C})\text{HCH}_3 \) is less stable than \( \text{C}^+(\text{CH}_3)_3 \).

### Final Answer:
The carbocation \( \text{CH}_3^+(\text{C})\text{HCH}_3 \) is less stable than \( \text{C}^+(\text{CH}_3)_3 \).