The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 × 10⁻⁷ m and 600 m / s, respectively. Find the frequency of its collisions.

Solution

Physics sir · 3 steps

Each collision happens after one mean free path, so divide the speed by the path length.

1. What frequency means. Between two collisions a molecule travels, on average, one mean free path λ. In one second it covers a distance v_(avg), so it makes v_(avg)/λ collisions per second.

   f = v_(avg)/λ

2. Put in numbers. f = 600/(3 × 10⁻⁷) = (6 × 10²)/(3 × 10⁻⁷) = 2 × 10²⁺⁷ = 2 × 10⁹ s⁻¹.
3. So. An oxygen molecule collides about 2 × 10⁹ times every second, which is option (d).

The idea to keep. Collision frequency is just speed divided by mean free path. Its inverse, λ/v, is the average time between collisions.

Answer from the NTA final answer key. Solution by PrepWiser.