Question

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.

• A. $2 \times 10^{10} / \mathrm{s}$
• B. $9 \times 10^{9} / \mathrm{s}$
• C. $2 \times 10^{9} / \mathrm{s}$
• D. $5 \times 10^{8} / \mathrm{s}$

Hint:

The frequency of collisions is given by the average speed divided by the mean free path.

Answer 1

The Correct Option is C

1. Given: - Mean free path, $\lambda = 3 \times 10^{-7} \mathrm{~m}$ - Average speed, $v_{\text{avg}} = 600 \mathrm{~m/s}$
2. Frequency of collisions: \[ \text{Frequency} = \frac{v_{\text{avg}}}{\lambda} = \frac{600}{3 \times 10^{-7}} = 2 \times 10^{9} \mathrm{~s^{-1}} \] Therefore, the correct answer is (3) $2 \times 10^{9} / \mathrm{s}$.