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. l ∝ (1)/(n), n ∝ P. If P increases by 4 times (0.1 to 0.4), n increases 4 times, l reduces to (1)/(4).New l = 2.0 × 10⁻⁶/4 = 5.0 × 10⁻⁷ m. Substituting values gives 5.0 × 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.