Practice question

**Angular momentum** L_n = n h/2π, h=6.6×10⁻³⁴ J·s, L₂=2×6.6×10⁻³⁴/2π=2.11×10⁻³⁴ J·s, speed v_n = e²/(2 ε₀ h) ×1/n ≈2.2×10⁶/n m/s, kinetic energy ½ m v² =13.6/n² eV, illustrating Bohr model predictions for hydrogen-like atoms. E = m c² . m = 1.67262 × 10⁻²⁷ kg , c² = (3 × 10⁸)² = 9 × 10¹⁶ m²/s² . E = 1.67262 × 10⁻²⁷ × 9 × 10¹⁶ ≈ 1.505 × 10⁻¹⁰ J . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation yields 1.505 × 10⁻¹⁰ J, consistent