Mean Free Path

Mean free path λ: average distance a molecule travels between successive collisions.

λ = 1/(√2·π·d²·n), where d = molecular diameter, n = number density.

At 1 atm and 25°C (n ~ 2.5 × 10²⁵ /m³, d ~ 3.7 Å): λ ~ 70 nm in air. Very short.

λ inversely proportional to n and to d². Lower density (higher altitude) ⇒ longer λ.

λ in space (interstellar medium, n ~ 10⁵/m³): kilometers to light-years.

Collision frequency f = ⟨v⟩/λ ~ 10¹⁰ collisions/second in atmosphere.

Vacuum quality determined by λ: 'molecular flow' regime when λ exceeds container size.

Important for diffusion, viscosity, thermal conductivity calculations.