Practice question

**Collision frequency** Z = n σ v_rel, σ = π d² cross-section, v_rel = √2 v_avg, so Z ∝ n, for air at STP n≈2.5×10²⁵ m⁻³ d≈3×10⁻¹⁰ m λ≈68 nm, collision frequency ~10⁹ s⁻¹, illustrating frequent collisions at atmospheric pressure. v_rms = √((3k_B T)/(m)), m = 20.2 × 10⁻³⁶.02 × 10²³ = 3.36 × 10⁻²⁶ kg.620² = 3 × 1.38 × 10⁻²/³ × T3.36 × 10⁻²⁶, T = 3.84 × 10⁵ × 3.36 × 10⁻²⁶/⁴.14 × 10⁻²/³ ≈ 312 K. Substituting values gives 312 K, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P