The most stable radical among the following is :

Options

A. `{:(CH_(2)-CH_(2)^(*)),(|),(NO_(2)):}`
B. `{:(CH_(2)-CH_(2)^(*)),(|),(COO^(-)):}`
C. `{:(C_(2)-CH_(2)^(*)),(|),(CH_(3)):}`
D. `{:(CH_(2)-CH_(2)^(*)),(|),(O^(-)):}`

Answer

To determine the most stable radical among the given options, we need to analyze the electron-donating or electron-withdrawing nature of the substituents attached to the radicals.

### Step-by-Step Solution:

1. **Understand the Nature of Radicals**:
- Radicals are species with unpaired electrons and are electron-deficient. To stabilize these radicals, we need electron-donating groups.

**Hint**: Remember that electron-donating groups help stabilize radicals, while electron-withdrawing groups destabilize them.

2. **Identify the Groups**:
- We are given several radicals with different substituents. We need to identify whether these substituents are electron-donating or electron-withdrawing.

**Hint**: Familiarize yourself with common electron-donating groups (like alkyl groups) and electron-withdrawing groups (like nitro groups).

3. **Analyze Each Group**:
- **NO2 (Nitro Group)**: This is an electron-withdrawing group. It will destabilize the radical.
- **COO⁻ (Carboxylate Group)**: This is also an electron-withdrawing group, which will not stabilize the radical.
- **CH3 (Methyl Group)**: This is an electron-donating group (through +I effect), which can stabilize the radical.
- **O⁻ (Oxy Group)**: This also has a negative charge and can donate electrons, making it a strong electron-donating group.

**Hint**: Compare the stability of radicals based on the strength of the electron-donating ability of the groups attached.

4. **Compare the Electron-Donating Ability**:
- Between CH3 and O⁻, the O⁻ group has a negative charge, which allows it to donate electrons more effectively than the CH3 group.
- Therefore, the radical with the O⁻ group will be more stabilized than the one with the CH3 group.

**Hint**: Consider the extent of electron donation; groups with negative charges often have a stronger electron-donating effect.

5. **Conclusion**:
- Since the radicals with NO2 and COO⁻ are destabilized, and the radical with O⁻ is more stabilized than the one with CH3, the radical with the O⁻ group is the most stable among the options provided.

**Final Answer**: The most stable radical is the one with the O⁻ group.