The mean free path of molecules of a gas, (radius ) is inversely proportional to [2014]

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Solution

Q.
The mean free path of molecules of a gas, (radius $r$ ) is inversely proportional to [2014]

1 $r^{3}$

2 $r^{2}$

3 $r$

4 $\sqrt{r}$

Ans.
(2)

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 $d = 2 r,$ $∴$ $λ = \frac{1}{4 \sqrt{2} n π r^{2}} or λ \propto \frac{1}{r^{2}}$

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