Assertion : Mean free path of a gas molecule varies inversely as density of the gas.
Reason : Mean free path varies inversely as pressure of the gas.

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 solve the question, we need to analyze both the assertion and the reason provided regarding the mean free path of gas molecules.

### Step 1: Understand the Mean Free Path
The mean free path (λ) is defined as the average distance a gas molecule travels between successive collisions. It is an important concept in kinetic theory.

### Step 2: Analyze the Assertion
The assertion states that the mean free path of a gas molecule varies inversely as the density of the gas.
- The mean free path can be expressed as:
\[ \lambda = \frac{m}{\sqrt{2} \pi \sigma^2 d} \]
where \( m \) is the mass of the gas molecule, \( \sigma \) is the effective collision cross-section, and \( d \) is the density of the gas.
- From this equation, we can see that as the density \( d \) increases, the mean free path \( \lambda \) decreases.
- Therefore, the assertion is **true**.

### Step 3: Analyze the Reason
The reason states that the mean free path varies inversely as the pressure of the gas.
- The mean free path can also be expressed as:
\[ \lambda = \frac{kT}{\sqrt{2} \pi \sigma^2 p} \]
where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( p \) is the pressure.
- From this equation, we can see that as the pressure \( p \) increases, the mean free path \( \lambda \) decreases.
- Therefore, the reason is also **true**.

### Step 4: Determine the Relationship Between Assertion and Reason
While both the assertion and the reason are true, we need to determine if the reason correctly explains the assertion.
- The assertion refers to density, while the reason refers to pressure. Although both are inversely related to mean free path, the reason does not directly explain why the assertion is true.
- Thus, the reason is not the correct explanation of the assertion.

### Conclusion
Both the assertion and the reason are true, but the reason is not the correct explanation of the assertion. Therefore, the correct answer is:
- **Option B**: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.

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