The number of air molecules per cm ^ 3 is increased from 3 × 10 ^...

The given data is

${n}_{1} = 3 \times {10}^{19}{n}_{2} = 12 \times {10}^{19}$

The mean time between two collision has the meaning of a period $τ$, since it indicates the repetitive time intervals in which on average collisions take place. The reciprocal of the time $τ$ 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.

$f ∝ \dfrac{1}{τ}$

$⇒ f ∝ n$

$⇒ \dfrac{{f}_{\text{1}}}{{f}_{\text{2}}} = \dfrac{{n}_{1}}{{n}_{2}} = \dfrac{3 \times {10}^{19}}{12 \times {10}^{19}} = 0 . 25$