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#radius ratio

3 public questions tagged with this topic.

Nuclear Size, Density and Structure

What is the ratio of nuclear radii of two nuclei with mass numbers 27 and 125?

**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. Radius ratio = (R₁/R₂) = (R₀ A₁¹/³/R₀ A₂¹/³) = ( (A₁/A₂) )¹/³ . A₁ = 27 , A₂ = 125 . (27/125) = 0.216 , (0.216)¹/³ ≈ 0.6 . 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 0.6, 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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Nuclear Size, Density and Structure

What is the ratio of nuclear radii of nuclei with mass numbers 125 and 27?

**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.

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

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Nuclear Size, Density and Structure

What is the ratio of nuclear radii of two nuclei with mass numbers 64 and 8?

**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. Radius ratio = (R₁/R₂) = ( (A₁/A₂) )¹/³ . A₁ = 64 , A₂ = 8 . (64/8) = 8 , (8)¹/³ = 2 . 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 2.0, 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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