Mean free path formulae

Question

The mean free path of molecules of a gas, (radius r) is inversely proportional to

Easy

Solution

$\text{Mean free path,}\lambda =\frac{1}{\sqrt{2}n\pi {d}^{2}}$

where n is the number density and d is the diameter of the molecule.

As d = 2r

$\therefore \lambda =\frac{1}{4\sqrt{2}n\pi {r}^{2}}\text{or}\lambda \propto \frac{1}{{r}^{2}}$

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