$5.3.2.$ Estimate the mean free path of a nitrogen molecule in air under normal conditions. The radius of nitrogen and oxygen molecules is assumed to be $0.18 \text{ nm}$.
We use the formula obtained in 5.3.1 for the mean free path $$ \lambda = \frac{1}{\pi d^2n}\quad(1) $$ The concentration of particles can be expressed through the Ideal Gas Law $$ p=nkT_0\Rightarrow n=\frac{p}{kT_0}\quad(2) $$ Substituting $(2)$ into $(1)$, we get $$ \boxed{\lambda = \frac{kT_0}{\sqrt{2}\pi d^2p}\approx60\text{ nm}}\quad(3) $$
$$\lambda = \frac{kT_0}{\sqrt{2}\pi d^2p}\approx60\text{ nm}$$