Assertion `(A)`: The colour of old lead painting can be restored by washing with dilute solution of `H_2O_2`.
Reason `(R)` : Black lead sulphide is oxidised by `H_2O_2` to white lead suphate.

Options

A. If both (A) and (R) are correct and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct.

Explanation

To solve the question, we will analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "the colour of old lead painting can be restored by washing with dilute solution of H2O2." This implies that there is a chemical reaction that can change the color of the lead painting back to its original state.

**Hint:** Consider what happens to lead compounds when they react with hydrogen peroxide.

### Step 2: Analyze the Reason
The reason states that "black lead sulphide is oxidised by H2O2 to white lead sulphate." Here, we need to identify the compounds involved:
- Lead sulphide (PbS) is black in color.
- Lead sulphate (PbSO4) is white in color.

**Hint:** Think about the oxidation states of the elements in these compounds and how they change during the reaction.

### Step 3: Write the Chemical Reaction
The reaction between lead sulphide (PbS) and hydrogen peroxide (H2O2) can be represented as follows:
\[ \text{PbS} + \text{H}_2\text{O}_2 \rightarrow \text{PbSO}_4 + \text{H}_2\text{O} \]

**Hint:** Ensure that you balance the chemical equation properly.

### Step 4: Determine the Color Change
In this reaction, PbS (black) is converted to PbSO4 (white). This confirms that washing with H2O2 can indeed restore the color of the old lead painting.

**Hint:** Visualize the color change from black to white to understand the effect of the reaction.

### Step 5: Evaluate the Oxidation States
In the reaction:
- The oxidation state of sulfur in PbS is -2.
- The oxidation state of sulfur in PbSO4 is +6.

This indicates that sulfur is being oxidized, which means H2O2 is acting as an oxidizing agent.

**Hint:** Remember that an oxidizing agent is a substance that gains electrons and causes another substance to be oxidized.

### Step 6: Conclusion
Both the assertion and the reason are correct, and the reason provides a valid explanation for the assertion. Therefore, the correct answer is that both the assertion and reason are true, and the reason correctly explains the assertion.

**Final Answer:** Both assertion and reason are correct, and the reason is the correct explanation of the assertion.