Practice question

**Degrees of freedom** f counts independent motions, monatomic 3 translational, diatomic 3 translational +2 rotational =5 at room T, vibrational adds at high T, molar specific heat at constant volume C_v = f/2 R, at constant pressure C_p = C_v + R, ratio γ = C_p/C_v = (f+2)/f, monatomic γ=5/3≈1.67, diatomic γ=7/5=1.4. l = (1)/(√(2) n π d²), d² = (1)/(√(2) n π l).d² = (1)/(1.414 × 2 × 10²⁵) × 3.14 × 5 × 10⁻⁷ = (1)/(4.44 × 10⁻¹⁹) ≈ 2.25 × 10⁻²⁰.d = √(2.25 × 10⁻²⁰) ≈ 1.5 × 10⁻¹⁰ m. Substituting values gives 1.5 × 10⁻¹⁰ m, which matches expected kinetic theory