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_N₂ = √(m_N)₂m_Ar.v_Ar516 = √((28)/(39.9)) ≈ √(0.7017) ≈ 0.8375.v_Ar = 516 × 0.8375 ≈ 432 m/s. Substituting values gives 432 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.