Consider the following carbocation-
(a). `CH_(3)-overset(o+)(C)H_(2)`
(b). `CH_(2)=overset(o+)(C)H`
(c). `CH_(2)=CH-overset(o+)(C)H_(2)`
(d). `C_(6)H_(5)-Coverset(o+)(H)_(2)`

Options

A. `dgtcgtagtb`
B. `dgtcgtbgta`
C. `cgtdgtbgta`
D. `cgtdgtagtb`

Answer

To determine the stability of the given carbocations, we will analyze each one based on the principles of carbocation stability, which include the effects of hyperconjugation, resonance, and the degree of substitution.

### Step-by-Step Solution:

1. **Identify the Type of Each Carbocation:**
- (a) `CH₃-CH₂^+` (Primary carbocation)
- (b) `CH₂=CH^+` (Vinylic carbocation)
- (c) `CH₂=CH-CH₂^+` (Secondary carbocation with conjugation)
- (d) `C₆H₅-CH₂^+` (Benzyl carbocation with resonance)

2. **Analyze Stability:**
- **(a) `CH₃-CH₂^+`:** This is a primary carbocation. Primary carbocations are generally less stable due to the lack of hyperconjugation and inductive effects from neighboring alkyl groups.
- **(b) `CH₂=CH^+`:** This is a vinylic carbocation. Vinylic carbocations are unstable because they involve sp-hybridized carbon, which does not stabilize the positive charge effectively.
- **(c) `CH₂=CH-CH₂^+`:** This is a secondary carbocation. It has some stability due to hyperconjugation from the adjacent alkyl group. Additionally, it has conjugation with the double bond, which provides some resonance stabilization.
- **(d) `C₆H₅-CH₂^+`:** This is a benzyl carbocation. Benzyl carbocations are highly stable due to resonance stabilization from the aromatic ring, which can delocalize the positive charge.

3. **Rank the Carbocations by Stability:**
- **Most Stable:** (d) `C₆H₅-CH₂^+` (Benzyl carbocation with resonance)
- **Next Stable:** (c) `CH₂=CH-CH₂^+` (Secondary carbocation with conjugation)
- **Less Stable:** (a) `CH₃-CH₂^+` (Primary carbocation)
- **Least Stable:** (b) `CH₂=CH^+` (Vinylic carbocation)

4. **Final Order of Stability:**
- The order of stability from most stable to least stable is: **(d) > (c) > (a) > (b)**.