Size of nucleus and nuclear density
Nuclear structure · Physics
Bohr atom
Interactive 3DElectrons orbit the nucleus in shells — switch element to see H, He and Li fill their shells.
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Study notes
(a) Estimate the radius of a uranium-238 nucleus. (b) Estimate nuclear density using R₀ = 1.2 fm. (c) What would be the mass of 1 cm³ of nuclear matter? Solution: (a) R = 1.2 × A¹ᐟ³ fm = 1.2 × 238¹ᐟ³ = 1.2 × 6.20 ≈ 7.44 fm = 7.44×10⁻¹⁵ m. (b) Volume per nucleon = (4/3)πR₀³ = 4.19 × (1.2×10⁻¹⁵)³ ≈ 7.24×10⁻⁴⁵ m³. ρ = 1.67×10⁻²⁷/7.24×10⁻⁴⁵ ≈ 2.3×10¹⁷ kg/m³. (c) 1 cm³ = 10⁻⁶ m³ → mass = 2.3×10¹⁷ × 10⁻⁶ = 2.3×10¹¹ kg ≈ 230 million tonnes!