Practice question

**Mean free path** λ = 1/(√2 n π d²) is average distance molecule travels between collisions, n number density (m⁻³), d molecular diameter (m), π≈3.14. Inversely proportional to n and d², larger n or d reduces λ. Rearranged d² = 1/(√2 n π λ), so d = √(1/(√2 n π λ)), enabling diameter estimation from measured λ and n. l ∝ (1)/(n), n ∝ P. If P reduces to (1)/(4), n reduces to (1)/(4), l increases 4 times.New l = 8 × 10⁻⁷ × 4 = 3.2 × 10⁻⁶ m. Substituting values gives 3.2 × 10⁻⁶ m, which matches expected kinetic theory result, confirming mean