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 results in a racemic mixture, we need to analyze the mechanisms of SN1 and SN2 reactions, particularly focusing on the formation of carbocations and the stereochemistry involved.

### Step-by-Step Solution:

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

2. **Identifying SN1 and SN2 Mechanisms**:
- **SN1 Mechanism**: This mechanism occurs in two steps:
1. Formation of a carbocation by the departure of the leaving group (halogen).
2. Nucleophilic attack on the planar carbocation.
- **SN2 Mechanism**: This mechanism occurs in one step where the nucleophile attacks the substrate simultaneously as the leaving group departs.

3. **Formation of Racemic Mixture**:
- In an SN1 reaction, the formation of a planar carbocation allows the nucleophile to attack from either side of the carbocation.
- This leads to the formation of two enantiomers (optical isomers) in equal amounts, resulting in a racemic mixture.

4. **Carbocation Stability**:
- The stability of the carbocation is crucial for determining the reaction pathway.
- Tertiary carbocations are more stable than secondary or primary carbocations and are more likely to form in SN1 reactions.

5. **Analyzing the Given Options**:
- We need to identify which alkyl halide leads to the formation of a tertiary carbocation upon the departure of the halogen.
- If the alkyl halide is tertiary, the resulting carbocation will be planar, allowing for the nucleophile to attack from both sides, creating a racemic mixture.

6. **Conclusion**:
- The correct option will be the one that leads to a tertiary carbocation and thus results in a racemic mixture upon nucleophilic substitution.