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}.

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    <h3 id="back-link"><a href="/#5.3">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $5.3.2.$ 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 $0.18 \text{ nm}$.
    </p>

    <h3>Solution</h3>
    <p>
        We use the formula obtained in <a href="/5.3.1">5.3.1</a> 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
$$\boxed{\lambda = \frac{kT_0}{\sqrt{2}\pi d^2p}\approx60\text{ nm}}\quad(3)$$

    <h4>Answer</h4>
    <p>
        $$\lambda = \frac{kT_0}{\sqrt{2}\pi d^2p}\approx60\text{ nm}$$
    </p>
	<p style="text-align: right; font-style: italic; font-size: 14;">
	  Aliaksandr Melnichenka<br>
	</p>


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