Which of the following alkyl halides is hydrolysis by `S_(N^(2))` mechanism?

Options

A. `H_(2)C=CHCH_(2)Br`
B. `(CH_(3))_(3) CBr`
C. `CH_(3)Br`
D. None of these

Answer

To determine which alkyl halide undergoes hydrolysis by the \( S_N2 \) mechanism, we need to analyze the stability of the carbocations formed during the reaction. The \( S_N2 \) mechanism involves a nucleophilic substitution that is bimolecular, meaning it depends on both the substrate (alkyl halide) and the nucleophile.

### Step-by-Step Solution:

1. **Understand the \( S_N2 \) Mechanism**:
- The \( S_N2 \) mechanism involves a nucleophile attacking the carbon atom bonded to the halide from the opposite side, leading to a transition state where both the nucleophile and the leaving group (halide) are partially bonded to the carbon. This results in the inversion of configuration at the carbon center.

2. **Identify the Alkyl Halides**:
- We have three alkyl halides to consider:
1. \( CH_2=CH-CH_2Br \) (Allyl bromide)
2. \( (CH_3)_3CBr \) (Tert-butyl bromide)
3. \( CH_3Br \) (Methyl bromide)

3. **Analyze Each Alkyl Halide**:
- **Option 1: \( CH_2=CH-CH_2Br \)** (Allyl bromide)
- Removing the bromine forms an allyl carbocation, which can be stabilized by resonance. However, this stabilization makes it less favorable for \( S_N2 \) because \( S_N2 \) prefers less stable carbocations.

- **Option 2: \( (CH_3)_3CBr \)** (Tert-butyl bromide)
- Removing the bromine forms a tertiary carbocation, which is highly stable. However, tertiary carbocations do not favor \( S_N2 \) reactions due to steric hindrance. Thus, this option is also not favorable for \( S_N2 \).

- **Option 3: \( CH_3Br \)** (Methyl bromide)
- Removing the bromine forms a methyl carbocation, which is the least stable but is not hindered sterically. This makes it highly favorable for \( S_N2 \) reactions.

4. **Conclusion**:
- Based on the analysis, the only alkyl halide that undergoes hydrolysis by the \( S_N2 \) mechanism is **Option 3: \( CH_3Br \)** (Methyl bromide).

### Final Answer:
The alkyl halide that is hydrolyzed by the \( S_N2 \) mechanism is **\( CH_3Br \)**.