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Question

What is the radius of a nucleus with mass number 16? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m}
\))

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Explanation

**Nuclear force** strong, short-range ~1 fm, attractive, charge independent, saturated in large nuclei because each nucleon interacts only with neighbors, not all others, so BE/A saturates ~8 MeV, primary factor limiting stable nuclei size is Coulomb repulsion between protons growing as Z² vs strong force saturating, beyond Z≈83 no stable nuclei, competition between Coulomb and strong. The radius of a nucleus is given by R = R₀ A¹/³ , where A = 16 . A¹/³ = 16¹/³ = (2⁴)¹/³ = 2⁴/³ ≈ 2.52 . R = 1.2 × 10⁻¹⁵ × 2.52 ≈ 3.0 × 10⁻¹⁵ m . Using E_n = -13.6/n² eV, r_n = n²

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