Calculate the mean free path of air molecules at STP. The diameter of $N_2$ and $O_2$ is about $3\times10^{-10}$ m

Calculate the mean free path of air molecules at STP. The diameter of N₂ and O₂ is about 3×10⁻¹⁰ m

IV. Numerical Problems · Q7

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Step 1. STP: $T=273$ K, $P=1.013\times10^5$ Pa, $k=1.38\times10^{-23}\ \text{J K}^{-1}$ , $d=3\times10^{-10}$ m.

Step 2. Number density: $n=\dfrac{P}{kT}=\dfrac{1.013\times10^5}{1.38\times10^{-23}\times273}\approx2.69\times10^{25}\ \text{m}^{-3}$ .

Step 3. $\pi d^2=\pi\times(3\times10^{-10})^2=\pi\times9\times10^{-20}\approx2.827\times10^{-19}\ \text{m}^2$ . …