The stablest radical among the following is
(a) `C_6 H_5 CH_2 - overset(*) CH_2`
(b) `CH_3 Coverset(*) H_2`
(c) `C_6 H_5 - overset(*) CH -CH_3`
(d) `CH_3 - overset(*) CH- CH_3`
(e) `CH_3 - CH_2 - Coverset(*)H_2`

Answer

To determine the most stable radical among the given options, we will analyze the stability of each radical based on the number of alpha hydrogens and the effects of resonance and hyperconjugation.

### Step-by-Step Solution:

1. **Identify the radicals**:
- (a) `C6H5CH2•`
- (b) `CH3•`
- (c) `C6H5•CH-CH3`
- (d) `CH3-CH•-CH3`
- (e) `CH3-CH2•`

2. **Count the alpha hydrogens**:
- **Radical (a)**: `C6H5CH2•` has 2 alpha hydrogens (from the `CH2` group).
- **Radical (b)**: `CH3•` has 0 alpha hydrogens.
- **Radical (c)**: `C6H5•CH-CH3` has 3 alpha hydrogens (from the `CH` and `CH3` groups).
- **Radical (d)**: `CH3-CH•-CH3` has 6 alpha hydrogens (3 from each `CH3` group).
- **Radical (e)**: `CH3-CH2•` has 2 alpha hydrogens (from the `CH2` group).

3. **Evaluate resonance and hyperconjugation effects**:
- **Radical (a)**: The phenyl group can stabilize the radical through resonance, but it has only 2 alpha hydrogens.
- **Radical (b)**: No alpha hydrogens, hence very unstable.
- **Radical (c)**: The phenyl group can stabilize the radical through resonance. It has 3 alpha hydrogens.
- **Radical (d)**: It has 6 alpha hydrogens, but no resonance stabilization.
- **Radical (e)**: It has 2 alpha hydrogens and no resonance stabilization.

4. **Compare the stability**:
- Radicals with resonance (like (a) and (c)) are generally more stable than those without.
- Radical (c) benefits from both resonance stabilization from the phenyl group and has 3 alpha hydrogens.
- Radical (d) has the most alpha hydrogens (6) but lacks resonance stabilization.

5. **Conclusion**:
- Comparing all the radicals, radical (c) `C6H5•CH-CH3` is the most stable due to the combination of resonance stabilization from the phenyl ring and a reasonable number of alpha hydrogens (3).

### Final Answer:
The stablest radical among the given options is **(c) `C6H5•CH-CH3`**.