The order of reactivity of halides towards `S_(N)` 1 mechanism is

Options

A. `"benzy"1gt"ally"1^(@)gt2^(@)gt3^(@)gt"Me"`
B. `"Me"gt1^(@)gt2^(@)gt3^(@)gt"ally"1gt"benzy"1`
C. `3^(@)gt2^(@)gt1^(@)gt"Me"gt"ally"1gt"benzy"1`
D. `"benzy"1gt"ally"1gt3^(@)gt2^(@)gt1^(@)gt"Me"`

Answer

To determine the order of reactivity of halides towards the \( S_N1 \) mechanism, we need to analyze the stability of the carbocations formed during the reaction. The \( S_N1 \) mechanism involves the formation of a carbocation intermediate, and the more stable the carbocation, the more reactive the halide will be.

### Step-by-Step Solution:

1. **Understand the \( S_N1 \) Mechanism**:
- The \( S_N1 \) mechanism involves two steps:
1. Formation of a carbocation after the leaving group departs.
2. Nucleophilic attack on the carbocation.
- The rate-determining step is the formation of the carbocation.

2. **Identify the Types of Carbocations**:
- The stability of carbocations can be classified as:
- **Tertiary (3°) carbocations**: Three alkyl groups attached to the positively charged carbon.
- **Secondary (2°) carbocations**: Two alkyl groups attached.
- **Primary (1°) carbocations**: One alkyl group attached.
- **Methyl carbocations**: No alkyl groups attached.

3. **Evaluate Carbocation Stability**:
- The stability order of carbocations is influenced by two main factors:
- **Hyperconjugation**: More alkyl groups provide more hyperconjugation, stabilizing the carbocation.
- **Inductive Effect**: Alkyl groups can donate electron density, stabilizing the positive charge.
- The general stability order is:
- Benzyl > Allyl > Tertiary > Secondary > Primary > Methyl.

4. **Consider Resonance Effects**:
- **Benzyl Carbocation**: The benzyl carbocation is highly stabilized due to resonance with the benzene ring.
- **Allyl Carbocation**: The allyl carbocation is also resonance-stabilized, but not as effectively as the benzyl carbocation.

5. **Final Order of Reactivity**:
- Based on the stability of the carbocations formed, the order of reactivity of halides towards \( S_N1 \) mechanism is:
- **Benzyl > Allyl > 3° > 2° > 1° > Methyl**.

### Conclusion:
The correct order of reactivity of halides towards \( S_N1 \) mechanism is:
**Benzyl > Allyl > 3° > 2° > 1° > Methyl**.