Assertion : `PbI_(4)` doesn't exist and converts into `PbI_(2) and I_(2)` spontaneously at room temperature but `PbCl_(4)` needs heatin to convert into `PbCl_(2) and Cl_(2)`.
Reason : `Pb^(2+)` is more stable than `Pb^(4+)`due to inert pair effect.

Options

A. If assertion is true but the reason is false
B. If assertion is false but reason is true
C. If both assertion and reason are true and the reason is the correct explanation of assertion
D. If both assertion and reason are true and the reason is not the correct explanation of assertion

Explanation

To analyze the assertion and reason provided in the question, we will break down the information step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that \( \text{PbI}_4 \) does not exist and spontaneously converts into \( \text{PbI}_2 \) and \( \text{I}_2 \) at room temperature.
- It also states that \( \text{PbCl}_4 \) requires heating to convert into \( \text{PbCl}_2 \) and \( \text{Cl}_2 \).

2. **Analyzing \( \text{PbI}_4 \)**:
- \( \text{PbI}_4 \) is a compound where lead is in the +4 oxidation state. However, iodine is a strong reducing agent and can reduce \( \text{Pb}^{4+} \) to \( \text{Pb}^{2+} \) while itself being oxidized to \( \text{I}_2 \).
- The reaction can be represented as:
\[ \text{PbI}_4 \rightarrow \text{PbI}_2 + \text{I}_2 \]
- This reaction occurs spontaneously at room temperature due to the strong reducing nature of iodine.

3. **Analyzing \( \text{PbCl}_4 \)**:
- In contrast, \( \text{PbCl}_4 \) also has lead in the +4 oxidation state, but chlorine is a much weaker reducing agent compared to iodine.
- Therefore, \( \text{PbCl}_4 \) does not spontaneously reduce to \( \text{PbCl}_2 \) and \( \text{Cl}_2 \) at room temperature. Instead, it requires heating to facilitate this reaction:
\[ \text{PbCl}_4 \xrightarrow{\text{heat}} \text{PbCl}_2 + \text{Cl}_2 \]

4. **Conclusion on Assertion**:
- The assertion is correct: \( \text{PbI}_4 \) does not exist at room temperature and converts to \( \text{PbI}_2 \) and \( \text{I}_2 \) spontaneously, while \( \text{PbCl}_4 \) requires heating to convert to \( \text{PbCl}_2 \) and \( \text{Cl}_2 \).

5. **Understanding the Reason**:
- The reason states that \( \text{Pb}^{2+} \) is more stable than \( \text{Pb}^{4+} \) due to the inert pair effect.
- The inert pair effect refers to the tendency of the s-electrons (in this case, the 6s electrons of lead) to remain non-bonding in heavier elements, leading to greater stability in the lower oxidation state (+2) compared to the higher oxidation state (+4).

6. **Conclusion on Reason**:
- The reason is also correct: \( \text{Pb}^{2+} \) is indeed more stable than \( \text{Pb}^{4+} \) due to the inert pair effect. However, while this is a true statement, it does not directly explain why \( \text{PbI}_4 \) decomposes spontaneously while \( \text{PbCl}_4 \) does not.

7. **Final Evaluation**:
- The assertion is true, and the reason is true, but the reason does not adequately explain the assertion. Therefore, the assertion is correct, and the reason is correct but not a valid explanation for the assertion.