Optically active tert alkyl halide given below on hydrolysis gives recemic mixture. Soparation of (d) and (l) form from the recemic mixture is known as resultuion.
`C_(6)H_(5)-overset(C_(6)H_(13)) overset(|)underset(CH_(3))underset(|)(c)overset overset(HOH)toC_(6)H_(5)C-overset(C_(6)H_(13)) overset(|)underset((X))underset(CH_(3))underset(|)C-OH+HO-overset(C_(6)H_(13)) overset(|) underset((Y))underset(CH_(3)) underset(|)C-C_(6)H_(5)`
The given reaction is :

Options

A. `SN1`
B. `SN2`
C. `SNi`
D. None of the above

Answer

To solve the problem, we need to analyze the hydrolysis of the given optically active tert-alkyl halide and understand why it results in a racemic mixture.

### Step-by-Step Solution:

1. **Identify the Structure of the Tert-Alkyl Halide**:
The given structure is a tert-alkyl halide, which means it has a tertiary carbon atom bonded to a halogen. The general structure can be represented as:
\[ R_3C-X \]
where \( R \) represents alkyl groups and \( X \) is the halogen.

2. **Understand the Hydrolysis Reaction**:
When a tert-alkyl halide undergoes hydrolysis, it reacts with water to form an alcohol and a halide ion. The reaction can be represented as:
\[ R_3C-X + H_2O \rightarrow R_3C-OH + HX \]
This reaction typically proceeds via an SN1 mechanism.

3. **Mechanism of SN1 Reaction**:
In the SN1 mechanism, the first step is the formation of a carbocation intermediate after the halogen leaves. This carbocation is planar, allowing for nucleophilic attack from either side:
\[ R_3C^+ \text{ (carbocation)} \]
The nucleophile (water in this case) can attack from the top or bottom of the planar carbocation, leading to two different stereoisomers.

4. **Formation of Racemic Mixture**:
The attack from the top leads to one stereoisomer (R), and the attack from the bottom leads to the other stereoisomer (S). Since both products are formed in equal amounts, the result is a racemic mixture (equal amounts of R and S):
\[ \text{R} + \text{S} \rightarrow \text{Racemic Mixture} \]

5. **Conclusion**:
The hydrolysis of the optically active tert-alkyl halide results in a racemic mixture due to the formation of a planar carbocation that allows for nucleophilic attack from both sides. This is characteristic of SN1 reactions.

### Final Answer:
The hydrolysis of the optically active tert-alkyl halide gives a racemic mixture due to the formation of a planar carbocation intermediate, allowing for nucleophilic attack from both sides.