A : Diphenyl ether is prepared by Williamson synthesis .
R : This reaction generally proceed by `S_(N)1` mechanism .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false , then mark (3)
D. If both Assertion and Reason are false statements , then mark (4)

Answer

To analyze the given assertion and reason, we need to break down the concepts involved in the preparation of diphenyl ether and the mechanisms of the Williamson synthesis.

### Step-by-Step Solution:

1. **Understanding Diphenyl Ether**:
- Diphenyl ether (C12H10O) consists of two phenyl groups (C6H5) connected by an oxygen atom. Its structure can be represented as:
\[ \text{C}_6\text{H}_5\text{-O-C}_6\text{H}_5 \]

2. **Williamson Synthesis Overview**:
- The Williamson ether synthesis is a method for forming ethers from an alkoxide ion (RO⁻) and a primary alkyl halide (R'X). The general reaction can be represented as:
\[ \text{R-O}^- + \text{R'-X} \rightarrow \text{R-O-R'} + \text{X}^- \]

3. **Applying Williamson Synthesis to Diphenyl Ether**:
- To synthesize diphenyl ether, we would ideally use phenoxide ion (C6H5O⁻) and a phenyl halide (C6H5X). However, the phenoxide ion is resonance-stabilized, which makes it less nucleophilic.

4. **Resonance Stabilization**:
- The lone pair on the oxygen in the phenoxide ion can delocalize into the aromatic ring, creating a partial double bond character between the oxygen and the phenyl group. This resonance stabilization reduces the nucleophilicity of the phenoxide ion, making it less likely to attack the electrophile (phenyl halide).

5. **Mechanism of Reaction**:
- The Williamson synthesis typically proceeds via an \( S_N2 \) mechanism, where the nucleophile attacks the electrophile directly. However, in the case of diphenyl ether, the presence of resonance in the phenoxide ion makes \( S_N2 \) less favorable.

6. **Assertion Evaluation**:
- The assertion states that diphenyl ether is prepared by Williamson synthesis. This is incorrect because the resonance stabilization of the phenoxide ion prevents effective nucleophilic attack on the phenyl halide.

7. **Reason Evaluation**:
- The reason states that this reaction generally proceeds by an \( S_N1 \) mechanism. However, the formation of diphenyl ether does not proceed through an \( S_N1 \) mechanism either, as \( S_N1 \) involves the formation of a carbocation, which is not stable in this case.

8. **Conclusion**:
- Both the assertion and the reason are incorrect. Therefore, the correct answer is that neither the assertion nor the reason is true.

### Final Answer:
Both Assertion (A) and Reason (R) are incorrect.