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. v_rms ∝ (1)/(√(m)), v_Arv_He = √(m_He)m_Ar.v_Ar1370 = √((4)/(39.9)) ≈ √(0.1) ≈ 0.316.v_Ar = 1370 × 0.316 ≈ 433 m/s. Substituting values gives 433 m/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.