The most stable free radical among the following is

Options

A. `C_(6)H_(5)CH_(2)overset(cdot)CH_(2)`
B. `C_(6)H_(5)overset(cdot)CHCH_(3)`
C. `CH_(3)overset(cdot)CH_(2)`
D. `CH_(3)overset(cdot)CHCH_(3)`

Explanation

To determine the most stable free radical among the given options, we need to analyze the stability factors such as resonance and hyperconjugation. Here’s a step-by-step solution:

### Step 1: Identify the Structures
We have four free radical structures to analyze:
1. **Structure A**: C6H5-CH2• (Benzyl radical)
2. **Structure B**: C6H5-CH•-CH3 (Phenyl ethyl radical)
3. **Structure C**: CH3-CH2• (Ethyl radical)
4. **Structure D**: CH3-CH•-CH3 (Isopropyl radical)

### Step 2: Analyze Each Structure for Stability
- **Structure A (Benzyl radical)**:
- This radical has resonance stabilization because the radical can delocalize into the benzene ring.
- There are also two alpha hydrogens available for hyperconjugation.

- **Structure B (Phenyl ethyl radical)**:
- This radical also has resonance stabilization due to the presence of the phenyl group.
- It has three alpha hydrogens available for hyperconjugation.

- **Structure C (Ethyl radical)**:
- This radical does not have resonance stabilization as it is not connected to any electron-withdrawing or donating groups.
- It has two alpha hydrogens available for hyperconjugation.

- **Structure D (Isopropyl radical)**:
- This radical does not have resonance stabilization either.
- It has six alpha hydrogens available for hyperconjugation, which provides some stability.

### Step 3: Compare Stability
- **Resonance**: The presence of resonance in Structures A and B significantly increases their stability compared to Structures C and D.
- **Hyperconjugation**: While Structure D has more alpha hydrogens, the lack of resonance makes it less stable than Structures A and B.
- **Overall Stability**:
- Structure A (Benzyl radical) benefits from strong resonance stabilization.
- Structure B (Phenyl ethyl radical) has good resonance and hyperconjugation but is slightly less stable than Structure A.
- Structures C and D lack resonance, making them less stable overall.

### Conclusion
The most stable free radical among the given options is **Structure B (C6H5-CH•-CH3)** due to its combination of resonance and hyperconjugation.

### Final Answer
**Option B** is the most stable free radical among the following.

---