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QPages 352-354: Q3: HC Verma: Concepts of Physics - Volume 2 Electric Current through Gases Pages 352-354: Q3 Solution: The mean free path of electrons in a gas in a discharge tube is …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often forget that λ∝1/P, so a change in mean free path is the reciprocal change in pressure. Doubling λ to fill the tube therefore requires halving the pressure, not doubling it. Always invert the ratio before applying the proportionality.

The mean free path of electrons in a gas in a discharge tube is inversely proportional to the pressure inside it. The Crookes dark space occupies half the length of the discharge tube when the pressure is 0.02 mm of mercury. Estimate the pressure at which the dark space will fill the whole tube.

Step-by-Step Verified Solution

**Answer:** The pressure is 0.01 mm of mercury. **Step-by-Step Explanation:** Mean free path λ∝1P\lambda \propto \frac{1}{P}. When the Crookes dark space occupies half the tube length at P=0.02P = 0.02 mm Hg, it will fill the whole tube when the mean free path doubles. Since λ∝1/P\lambda \propto 1/P, doubling λ\lambda means halving the pressure: P′=0.02/2=0.01P' = 0.02/2 = 0.01 mm Hg .

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