For the given reaction,
`R-underset(R_(2))underset(|)overset(R_(1))overset(|)(C )-x overset(HOH)(rarr) R-underset(R_(2))underset(|)overset(R_(1))overset(|)(C )-OH`
Which substrate will give maximum racemisation?

Options

A. `H_(5)C_(6)- underset(C_(2)H_(5))underset(|)overset(CH_(3))overset(|)C-Br`
B. `CH_(2)-CH- underset(C_(2)H_(5))underset(|)overset(CH_(3))overset(|)C-Br`
C.
D.

Explanation

To determine which substrate will give maximum racemization in the given reaction, we need to analyze the stability of the carbocation formed during the reaction mechanism, specifically under the SN1 mechanism.

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
The reaction is a nucleophilic substitution reaction (SN1). In this mechanism, the leaving group (X) is replaced by a nucleophile (OH).

**Hint**: Recognize that SN1 reactions involve the formation of a carbocation intermediate.

2. **Formation of Carbocation**:
In the first step of the SN1 mechanism, the leaving group (X) departs, forming a carbocation. The stability of this carbocation is crucial for the rate of the reaction.

**Hint**: The more stable the carbocation, the faster the reaction will proceed.

3. **Evaluate Carbocation Stability**:
The stability of carbocations increases in the following order:
- Methyl < Primary < Secondary < Tertiary < Benzylic < Allylic (due to resonance stabilization).

**Hint**: Look for resonance stabilization from adjacent groups (like benzene rings) that can stabilize the positive charge on the carbocation.

4. **Analyze Each Option**:
- **Option A**: Contains a benzylic carbocation which is resonance stabilized. This is a strong candidate for maximum racemization.
- **Option B**: Contains a tertiary carbocation, which is stable but not as stable as a benzylic carbocation.
- **Option C**: Contains two benzene rings with electron-donating groups, providing significant resonance stabilization.
- **Option D**: Contains three benzene rings, but with one of the rings having a deactivating group, which destabilizes the carbocation.

**Hint**: Compare the resonance effects of the substituents on the carbocation for each option.

5. **Determine Maximum Racemization**:
Since racemization occurs when a chiral center is converted to a planar carbocation, the substrate that forms the most stable carbocation will lead to the highest degree of racemization.
- **Option C** has the most resonance stabilization due to the presence of electron-donating groups on the benzene rings, making it the most favorable for maximum racemization.

**Hint**: The presence of electron-donating groups enhances the stability of the carbocation, leading to more efficient racemization.

### Conclusion:
The substrate that will give maximum racemization is **Option C**, which contains two benzene rings with electron-donating substituents.