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. Volume = (4/3) π R³ . R³ = (3.6 × 10⁻¹⁵)³ = 4.6656 × 10⁻⁴⁴ m³ . Volume = (4/3) × 3.14 × 4.6656 × 10⁻⁴⁴ ≈ 1.95 × 10⁻⁴³ m³ . 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 1.95 × 10⁻⁴³ m³, consistent with Bohr model and nuclear binding energy systematics.