JEE Main 2023 — Kinetic Theory of Gases Question with Solution

The given data is 

$$\begin{gathered} n_1=3\times {10}^{19} \\ {n}_2=12\times {10}^{19} \end{gathered}$$

The mean time between two collision has the meaning of a period $\tau$, since it indicates the repetitive time intervals in which on average collisions take place. The reciprocal of the time $\tau$ can be understood as the collision frequency$f$, which indicates the number of collisions per unit time.The collision frequency is also directly proportional to the number molecules per unit volume.

$f\propto \frac{1}{\tau }$

$\Rightarrow f\propto n$

$\Rightarrow \frac{f_{\text{1 }}}{f_{\text{2 }}}=\frac{n_1}{n_2}=\frac{3\times {10}^{19}}{12\times {10}^{19}}=0.25$