Practice question

**Molecular diameter from mean free path** uses λ =1/(√2 n π d²), solving d = √(1/(√2 n π λ)). At higher pressure n ∝ P, λ ∝1/P, so doubling P halves λ, illustrating pressure dependence of collision distance. v_rms ∝ √(T), (v₂)/(v₁) = √((T₂)/(T₁)).(600)/(300) = √((T₂)/(150)), 2 = √((T₂)/(150)).Square both sides: 4 = (T₂)/(150), T₂ = 600 K. Substituting values gives 600 K, 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.