For a molecule of an ideal gas, the number density is $2 \sqrt{2} imes 10^8 \mathrm{~cm}^{-3}$ and the mean free path is $\frac{10^{-2}}{\pi} \mathrm{cm}$. The diameter of the gas molecule is

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For a molecule of an ideal gas, the number density is $2 \sqrt{2} 	imes 10^8 \mathrm{~cm}^{-3}$ and the mean free path is $\frac{10^{-2}}{\pi} \mathrm{cm}$. The diameter of the gas molecule is

Aicharya · Accepted Answer

Mean free path, $ \begin{aligned} \lambda & =\frac{1}{\sqrt{2} \pi n d^2} \ \Rightarrow \quad d^2 & =\frac{1}{\sqrt{2} \pi n \lambda}=\frac{1 	imes \pi}{\sqrt{2} 	imes \pi 	imes 2 \sqrt{2} 	imes 10^8 	imes 10^{-2}} \ \Rightarrow \quad d^2 & =\frac{1}{4 	imes 10^6} \ \Rightarrow \quad d & =\frac{1}{2} 	imes 10^{-3} \mathrm{~cm} \ \Rightarrow \quad d & =5 	imes 10^{-4} \mathrm{~cm} \end{aligned} $

For a molecule of an ideal gas, the number density is $2 \sqrt{2} \times 10^8 \mathrm{~cm}^{-3}$ and the…

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