Question

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.

Answer 1

ANSWER:

Let the mean free path be L and pressure be P

Given,

L∝ 1/P

where L = half of the tube length and P = 0.02 mm of Hg

∴ When P becomes half, L doubles, i.e. the whole tube is filled with Crook’s dark space.

Hence the required pressure

= 0.02/2 = 0.01 m of Hg