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2 public questions tagged with this topic.

Radioactive Decay, Nuclear Forces and Stability

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

**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

Ref: NCERT > Physics Book > Atoms and Nuclei > Radioactive Decay, Nuclear Forces and Stability

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Nuclear Size, Density and Structure

What is the radius of a nucleus with mass number 200? (Given \( R_0 = 1.2 \times 10^{-15} \, \text{m} \))

**Nuclear size** order 10⁻¹⁵ m femtometer, atomic size 10⁻¹⁰ m, ratio 10⁵, nucleus contains protons and neutrons bound by strong force, density independent of A indicates incompressibility, R₀ determined from electron scattering experiments. R = R₀ A¹/³ . A = 200 , A¹/³ = 200¹/³ ≈ 5.85 . R = 1.2 × 10⁻¹⁵ × 5.85 ≈ 7.0 × 10⁻¹⁵ m . 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 7.0 × 10⁻¹⁵ m, consistent with Bohr model and nuclear binding energy systematics.

Ref: NCERT > Physics Book > Atoms and Nuclei > Nuclear Size, Density and Structure

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