Question

Mean free path for molecules of a gas is $\lambda$. If diameter of molecules is kept constant and the number density is increased to two times of its initial value, then new mean free path will be

• A. $\lambda$
• B. $\frac{\lambda }{2}$
• C. $4\lambda$
• D. $\frac{\lambda }{4}$

Answer 1

The correct option is B $\frac{\lambda }{2}$

Mean free path of ideal gas molecules is given by

$\lambda =\frac{1}{\sqrt{2}\pi n{d}^2}$, where $n$ is number density.

Since $n$ becomes double, the mean free path $\left({\lambda }^{{}^{\prime }}\right)$ becomes $\frac{\lambda }{2}$