Practice question

**Maxwell-Boltzmann distribution** gives distribution of speeds, v_rms = √(3kT/m), most probable v_mp = √(2kT/m), average v_avg = √(8kT/πm), all ∝ √T, ratio v_rms:v_avg:v_mp =1.732:1.596:1.414, temperature raises all speeds proportionally. Mean free path l = (1)/(√(2) n π d²), where n ∝ P at constant T.If P doubles, n doubles, so l halves.New l = 2 × 10⁻⁷/2 = 1 × 10⁻⁷ m . Substituting values gives 1 × 10⁻⁷ m, 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.