Calculate the value of mean free path

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Question:

Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} \mathrm{C}$ and pressure $1.01 \times 10^{5} \mathrm{~Pa}$. Assume the molecular diameter $0.3 \mathrm{~nm}$ and the gas is ideal. $\left(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)$

$\left(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)$

  1. $58 \mathrm{~nm}$

  2. $32 \mathrm{~nm}$

  3. $86 \mathrm{~nm}$

  4. $102 \mathrm{~nm}$


Correct Option: , 4

Solution:

$\lambda=\frac{\mathrm{RT}}{\sqrt{2} \pi \mathrm{d}^{2} \mathrm{~N}_{\mathrm{A}} \mathrm{P}}$

$\lambda=102 \mathrm{~nm}$

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