Question

In a dilute gas at pressure $P$ and temperature $T,$ the mean time between successive collisions of a molecule varies with $T$ is :

• A. $T$
• B. $\frac{1}{\sqrt{T}}$
• C. $\frac{1}{T}$
• D. $\sqrt{T}$

Answer 1

The correct option is B $\frac{1}{\sqrt{T}}$

We know that, $v_{rms}=\sqrt{\frac{3kT}{R}}$
Mean free path, $\lambda =\frac{1}{\sqrt{2}\pi n{d}^2}$
where, $d=$ diameter of the molecule
$n=$ number of molecules per unit volume

So, mean time of collision, $\tau =\frac{\lambda }{v_{rms}}$


$\tau =\frac{\lambda }{\sqrt{\frac{3kT}{m}}}$

$\Rightarrow \tau \propto \frac{1}{\sqrt{T}}$

Hence, option $\left(\text{B}\right)$ is correct.