Practice question

**Kinetic theory mean free path** λ = 1/(√2 π d² n) quantifies collision frequency. With n =1.0×10²⁵ m⁻³, λ=9×10⁻⁷ m, d² =1/(1.414×10²⁵×3.14×9×10⁻⁷)=2.5×10⁻²⁰ m², d≈1.58×10⁻¹⁰ m, typical molecular size ~10⁻¹⁰ m, consistent with gas kinetic theory. v_rms ∝ (1)/(√(m)), v_Nev_Ar = √(m_Ar)m_Ne.v_Ne430 = √((39.9)/(20.2)) ≈ √(1.975) ≈ 1.405.v_Ne = 430 × 1.405 ≈ 604 m/s. Substituting values gives 604 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.