Alkyl halides undergo nucleophilic substitution reactions in which halogen atom is replaced by other atom.
`RX + Nu:^(-) to Nu-R + X^(-)`
These reactions follow `S_(N)1` and `S_(N)2` type mechanism, in which `S_(N)1` takes place in two steps while `S_(N)2` takes place in single step. Due to their tendency to undergo substitution by a large number of nucleophiles, they form a variety of products.
In which of the following nucleophilic substitution reaction, the product formed is racemic mixture ?

Options

A. `(CH_(3))_(3)CBr`
B. `CH_(3)CH_(2)Br`
C. `(CH_(3)CH_(2))_(2)CHBr`
D. `C_(6)H_(5)CH_(2)Br`

Answer

To determine which nucleophilic substitution reaction produces a racemic mixture, we need to analyze the mechanisms of SN1 and SN2 reactions and how they relate to the structure of the alkyl halide involved.

### Step-by-Step Solution:

1. **Understanding Nucleophilic Substitution Reactions**:
- Nucleophilic substitution reactions involve the replacement of a leaving group (like a halogen) in an alkyl halide (RX) with a nucleophile (Nu^-).
- The general reaction can be represented as:
\[ RX + Nu^- \rightarrow Nu-R + X^- \]

2. **Identifying Mechanisms**:
- There are two primary mechanisms for nucleophilic substitution: SN1 and SN2.
- **SN1 Mechanism**:
- This is a two-step process where the first step involves the formation of a carbocation after the leaving group departs.
- The nucleophile can then attack the carbocation from either side, leading to the formation of a racemic mixture if the carbon is chiral.
- **SN2 Mechanism**:
- This is a one-step process where the nucleophile attacks the carbon from the opposite side of the leaving group, resulting in inversion of configuration.
- This does not produce a racemic mixture.

3. **Analyzing the Given Alkyl Halides**:
- We need to evaluate the structure of the alkyl halides provided and determine whether they will undergo SN1 or SN2 reactions.
- **3° Alkyl Halide**:
- A tertiary alkyl halide (like (CH3)3CBr) will undergo SN1 due to the stability of the carbocation formed.
- This will lead to a racemic mixture since the nucleophile can attack from both sides of the planar carbocation.
- **1° Alkyl Halide**:
- A primary alkyl halide (like CH3CH2Br) typically undergoes SN2, leading to inversion and not a racemic mixture.
- **2° Alkyl Halide**:
- A secondary alkyl halide (like CH3CHBrCH2CH3) can undergo both SN1 and SN2, but it will not necessarily lead to a racemic mixture unless the reaction conditions favor SN1.
- **Benzyl Halide**:
- A benzyl halide (like C6H5CH2Br) is also likely to undergo SN1 due to the stability of the carbocation formed, leading to a racemic mixture.

4. **Conclusion**:
- The alkyl halide that will produce a racemic mixture is the one that undergoes the SN1 mechanism, which is typically a tertiary alkyl halide or a benzyl halide.
- Therefore, the correct answer is the alkyl halide that is a tertiary halide or a benzyl halide.

### Final Answer:
The product formed is a racemic mixture in the nucleophilic substitution reaction involving a **tertiary alkyl halide** or a **benzyl halide**.