Question:
If the volume of a gas is reduced to half then the change in its mean free path is
If the volume of a gas is reduced to half then the change in its mean free path is
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Mean free path is inversely proportional to number density of molecules.
Updated On: Jun 20, 2026
- Becomes half
- Unchanged
- Doubles
- Depends on temperature
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The Correct Option is A
Solution and Explanation
Step 1: Mean free path formula.
\[ \lambda = \frac{1}{\sqrt{2}\pi n d^2} \] where \(n = \frac{N}{V}\).
Step 2: Effect of volume change.
If volume is halved: \[ n \rightarrow 2n \]
Step 3: Substitute in formula.
\[ \lambda \propto \frac{1}{n} \] So: \[ \lambda' = \frac{\lambda}{2} \]
Step 4: Physical interpretation.
Higher density means more frequent collisions, reducing mean free path.
Step 5: Final conclusion.
\[ \boxed{\text{Becomes half}} \]
\[ \lambda = \frac{1}{\sqrt{2}\pi n d^2} \] where \(n = \frac{N}{V}\).
Step 2: Effect of volume change.
If volume is halved: \[ n \rightarrow 2n \]
Step 3: Substitute in formula.
\[ \lambda \propto \frac{1}{n} \] So: \[ \lambda' = \frac{\lambda}{2} \]
Step 4: Physical interpretation.
Higher density means more frequent collisions, reducing mean free path.
Step 5: Final conclusion.
\[ \boxed{\text{Becomes half}} \]
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