Calculate the value of mean free path
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.

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

1. (1) $58 \mathrm{~nm}$

2. (2) $32 \mathrm{~nm}$

3. (3) $86 \mathrm{~nm}$

4. (4) $102 \mathrm{~nm}$

Correct Option: , 4

Solution:

(4)

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

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