Question

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

• A. $r^3$
• B. $r^2$
• C. $r$
• D. $\sqrt{r}$

Answer 1

Answer: (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 $d=2r$
$\therefore \lambda =\frac{1}{4\sqrt{2}n\pi r^2}$
or $\lambda \propto \frac{1}{r^2}$