Write correct order regarding stability of intermediates
(I). `CH_(2)=CH-overset(o+)(C)H_(2)`
(II). `CH_(2)=overset(o+)(C)H`
(III). `CH-=overset(o+)(C)`

Options

A. I=II=III
B. IltIIltIII
C. III=IIgtI
D. IgtIIgtIII

Explanation

To determine the correct order regarding the stability of the given intermediates, we need to analyze each structure based on factors that influence stability, such as hybridization, resonance, and the presence of electron-withdrawing or electron-donating groups.

### Step-by-Step Solution:

1. **Identify the Structures**:
- (I) `CH₂=CH-CH₂^+` (Allylic carbocation)
- (II) `CH₂=CH^+-CH` (Vinyl carbocation)
- (III) `CH^+=C^+` (Carbocation with a positive charge on an sp-hybridized carbon)

2. **Analyze Stability Factors**:
- **Hybridization**:
- sp-hybridized carbons (like in III) are more electronegative and less stable than sp² (like in I and II) and sp³ (like in CH₂).
- **Resonance**:
- (I) has resonance stabilization due to the adjacent double bond. The positive charge can be delocalized.
- (II) has limited resonance stabilization as the positive charge is on a carbon adjacent to a double bond but not directly involved in it.
- (III) has no resonance stabilization as the positive charge is on a carbon that is part of a double bond but does not benefit from adjacent double bond stabilization.

3. **Stability Order**:
- (I) `CH₂=CH-CH₂^+` is the most stable due to resonance stabilization.
- (II) `CH₂=CH^+-CH` is less stable than (I) but more stable than (III) due to limited resonance.
- (III) `CH^+=C^+` is the least stable due to lack of resonance and the instability associated with sp-hybridized carbons.

4. **Final Order**:
- The correct order of stability is: **(I) > (II) > (III)**.