Which of the following is the correct order of stability of free radicals ?

Options

A. benzyl `gt` allyl `gt 2^(underset(-)o) gt 1^(underset(-)o)`
B. allyl `gt` benzyl `gt 2^(underset(-)o) gt 1^(underset(-)o)`
C. allyl `gt 2^(underset(-)o) gt 1^(underset(-)o)` benzyl
D. benzyl `gt 2^(underset(-)o) gt 1^(underset(-)o)` allyl

Answer

To determine the correct order of stability of free radicals, we need to analyze the stability of the following radicals: benzyl, allyl, secondary, and primary.

### Step-by-Step Solution:

1. **Identify the Structure of Each Radical:**
- **Benzyl Radical:** This can be represented as \( \text{C}_6\text{H}_5\text{CH}_2^{\cdot} \) (where the radical is on the \( \text{CH}_2 \) group attached to a benzene ring).
- **Allyl Radical:** This can be represented as \( \text{CH}_2=CH-\text{CH}_2^{\cdot} \) (where the radical is on the terminal \( \text{CH}_2 \) group).
- **Secondary Radical:** This can be represented as \( \text{CH}_3-\text{CH}^{\cdot}-\text{CH}_3 \) (where the radical is on a carbon attached to two other carbons).
- **Primary Radical:** This can be represented as \( \text{CH}_3-\text{CH}_2^{\cdot} \) (where the radical is on a carbon attached to only one other carbon).

2. **Analyze the Stability Factors:**
- **Benzyl Radical:** The benzyl radical is highly stabilized by resonance. The radical can delocalize over the aromatic system, making it very stable.
- **Allyl Radical:** The allyl radical is also stabilized by resonance, but to a lesser extent than the benzyl radical. The radical can delocalize between the two terminal carbons.
- **Secondary Radical:** The secondary radical is stabilized by hyperconjugation and inductive effects from the adjacent carbon atoms, but it does not have resonance stabilization.
- **Primary Radical:** The primary radical is the least stable as it has no resonance stabilization and minimal hyperconjugation.

3. **Rank the Stability:**
- Based on the above analysis, we can rank the stability of the radicals:
- **Most Stable:** Benzyl Radical (due to resonance)
- **Next Stable:** Allyl Radical (due to resonance)
- **Next Stable:** Secondary Radical (due to hyperconjugation)
- **Least Stable:** Primary Radical (no resonance and minimal hyperconjugation)

4. **Final Order of Stability:**
- The correct order of stability is:
\[ \text{Benzyl} > \text{Allyl} > \text{Secondary} > \text{Primary} \]

5. **Check the Options:**
- The correct option matches the derived order: Benzyl > Allyl > Secondary > Primary.

### Conclusion:
The correct order of stability of free radicals is **Benzyl > Allyl > Secondary > Primary**.