Zigzor

Meet Zigzor, a gas molecule who zigzags from bump to bump.

In a gas, molecules fly in straight lines until they hit one another. The mean free path is the average distance a molecule travels between collisions. Rudolf Clausius introduced the idea in the 1850s to explain why gases mix slowly even though their molecules move fast. Treating molecules as hard spheres of diameter d at number density n gives λ = 1/(√2 π d² n).

For air at 20 °C and normal pressure, n = p/(kT) ≈ 2.5 × 10²⁵ molecules per cubic metre. With d ≈ 3.7 × 10⁻¹⁰ m, λ = 1/(1.414 × 3.14 × (3.7 × 10⁻¹⁰)² × 2.5 × 10²⁵) ≈ 6.6 × 10⁻⁸ m, about 66 nm. Halve the pressure and n halves, so λ doubles to about 130 nm.

The mean free path matters in vacuum systems, where it must be long so beams of electrons or atoms can travel without being scattered, and it helps explain how well a gas conducts heat.

The hard-sphere model is a simplification, because real molecules are not solid balls, so d is an effective size and the result is an estimate.