Mean Free Path
λ = 1/(√2 πd²n) — distance between collisions.
Key Notes
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.
Formulas
Mean free path
d = molecular diameter; n = number density.
Collision frequency
Collisions per molecule per second.
Air at STP (typical values)
Reference values.
Vacuum regimes
Kn < 0.01: continuum flow. Kn > 1: molecular flow.
Important Points
λ inversely proportional to n and d².
λ in atmosphere at sea level ~ 70 nm — very short.
At 100 km altitude: λ ~ meters. In interstellar space: λ ~ light-years.
Diffusion coefficient D ~ λ·⟨v⟩/3 — small λ ⇒ slow diffusion.
Vacuum quality: 'high vacuum' (~10⁻⁸ atm) gives λ ~ km, allowing molecular flow.
λ governs viscosity and thermal conductivity in gases.
Mean Free Path notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.