The mean free path of molecules ofa gas, (radius $r$) is inversely proportional to
A${r^3}$
B$\;{r^2}$
C$r$
D$\sqrt r $
AIPMT 2014, Easy
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B$\;{r^2}$
b 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 $d=2 r$
$\therefore \quad \lambda=\frac{1}{4 \sqrt{2} n \pi r^{2}} \quad$ or $\quad \lambda \propto \frac{1}{r^{2}}$
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