Question

The mean free path for a gas, with molecular diameter $d$ and number density $n$ can be expressed as:

• A. $\frac{1}{\sqrt{2}{n}^2{d}^2\pi }$
• B. $\frac{1}{\sqrt{2}{n}^2{d}^2{\pi }^2}$
  
• C. $\frac{1}{\sqrt{2}nd\pi }$
• D. $\frac{1}{\sqrt{2}n{d}^2\pi }$

Answer 1

The correct option is D $\frac{1}{\sqrt{2}n{d}^2\pi }$

Mean free path displays linear proportionality to the temperature and inverse proportionality to the pressure and molecular diameter.
Mathematically, it is expressed as:

Mean free path, $\lambda =\frac{1}{\sqrt{2}n{d}^2\pi }$

Therefore, mean free path $\propto$ $\frac{1}{\sqrt{2}n{d}^2\pi }$.