First slide

Mean free path formulae

Question

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

Easy

A

$r^{3}$
B

$r^{2}$
C

r
D

$\sqrt{r}$

Solution

$Mean free path, λ = \frac{1}{\sqrt{2} n π d^{2}}$
where n is the number density and d is the diameter of the molecule.
As d = 2r
$∴ λ = \frac{1}{4 \sqrt{2} n π r^{2}} or λ \propto \frac{1}{r^{2}}$

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