The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7}…

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$ respectively. Find the frequency of its collisions.
  1. $2 \times 10^{10} / \mathrm{s}$
  2. $9 \times 10^5 / \mathrm{s}$
  3. $2 \times 10^9 / \mathrm{s}$
  4. $5 \times 10^8 / \mathrm{s}$

Solution

$\begin{aligned} & \text { Frequency }=\frac{1}{T}=\frac{V_{\text {avg }}}{\lambda} \\ & =\frac{600}{3 \times 157}=2 \times 10^9 \mathrm{sec}^{-1}\end{aligned}$

Asked in: JEE Main 2025 (04 Apr Shift 1)

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