The mean free path of electrons in the 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.

Explanation

Let the mean free path be'L' and pressure
be 'P'
Given L `alpha 1/p for L ` = half on the tube length `
` P = 0.02mm of Hg.`
` As 'P' becomes half, 'L' doubles, that is the
whole tube is filled with Crook's dark
space.
Hence the required pressure
= 0.02 /2 = 0.01 m of Hg .