Question

A container contains $1\text{mol}$ of nitrogen gas at temperature ${17}^{\circ }C$ and pressure 2 atmospheres. If the radius of nitrogen molecule is $1A^{\circ }$, the mean free path of nitrogen molecules will be

• A. $1.1\times {10}^{-7}\text{m}$
• B. $2.2\times {10}^{-7}\text{m}$
• C. $3.3\times {10}^{-7}\text{m}$
• D. $4.4\times {10}^{-7}\text{m}$

Answer 1

The correct option is A $1.1\times {10}^{-7}\text{m}$

Mean free path of a molecule is $\lambda =\frac{kT}{\sqrt{2}\pi P{d}^2}$

Here, $T=17+273=290\text{K}$

$P=2\text{atm}=2\times 1.013\times {10}^5\text{Pa}$

diameter of the molecule $=d=2\times {10}^{-10}\text{m}$

Boltzman Constant, $k=1.38\times {10}^{-23}$

Substituting all the values,

$\lambda =\frac{1.38\times {10}^{-23}\times 290}{\sqrt{2}\times 3.14\times 2\times 1.013\times {10}^5\times 4\times {10}^{-20}}$

$\lambda =1.1\times {10}^{-7}\text{m}$