What is the time between collisions for a gas molecule with a mean free path of 1.5 × 10⁻⁷ m and average speed of 450 m/
**Mean free path variation** λ ∝1/n ∝1/P at constant T, λ ∝ T/P, temperature increase increases λ because n decreases at constant P, but also v increases, overall λ ∝ T/P, for gas at 2 atm λ=4×10⁻⁷ m, at 4 atm λ=2×10⁻⁷ m halves when pressure doubles, as n doubles. tau = (l)/() = 1.5 × 10⁻⁷/4⁵⁰ = 3.33 × 10⁻¹⁰ s. Substituting values gives 3.33 × 10⁻¹⁰ s, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Collision Frequency and Mean Free Path Variation