Nuclear size, shape and charge distribution
Nuclear physics · Physics
Study notes
Worked example: Estimate the radius and density of the iron-56 nucleus (A = 56). Step 1: R = 1.2 × A^{1/3} fm = 1.2 × 56^{1/3} = 1.2 × 3.83 = 4.6 fm. Step 2: Volume = (4/3)πR³ = 4.19 × (4.6×10⁻¹⁵)³ = 4.07×10⁻⁴³ m³. Step 3: Mass = 56 u = 56 × 1.661×10⁻²⁷ = 9.30×10⁻²⁶ kg. Step 4: Density = 9.30×10⁻²⁶/4.07×10⁻⁴³ ≈ 2.3×10¹⁷ kg/m³. Step 5: Compare with water (10³ kg/m³): nuclear matter is ~2×10¹⁴ times denser — a teaspoon would weigh ~a billion tonnes (like neutron-star matter). Conclusion: R ∝ A^{1/3} gives every nucleus the same incredible density — nuclei are droplets of one universal nuclear fluid.