Practice question

**Nuclear density** nearly constant because R ∝ A^{1/3} so volume ∝ A, mass ∝ A, ratio constant, ~10¹⁷ kg/m³, 10¹⁴ times water density, shows nucleus compact, nuclear force short-range saturated, mass number 16 radius ~3×10⁻¹⁵ m, mass number from radius R=5.4×10⁻¹⁵ m => A=(R/R₀)³=(4.5)³=91. Radius ratio = (R₁/R₂) = ( (A₁/A₂) )¹/³ . A₁ = 125 , A₂ = 27 . (125/27) ≈ 4.63 , (4.63)¹/³ ≈ 1.67 . 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 1.67, consistent with Bohr model and nuclear binding energy systematics.