The electrostatic energy of Z protons uniformly distributed in a spherical nucleus of radius R is E = 3Z(Z-1)e²/(20πε₀R). The measured masses are mₙ=1.008665 u, m(¹H)=1.007825 u, m(¹⁵₇N)=15.00010⁹ u and m(¹⁵₈O)=15.003065 u. Assuming the binding-energy difference between ¹⁵N and ¹⁵O is purely electrostatic, find the common nuclear radius. Use e²/(4πε₀)=1.44 MeV·fm.
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Question

The electrostatic energy of Z protons uniformly distributed in a spherical nucleus of radius R is E = 3Z(Z-1)e²/(20πε₀R). The measured masses are mₙ=1.008665 u, m(¹H)=1.007825 u, m(¹⁵₇N)=15.00010⁹ u and m(¹⁵₈O)=15.003065 u. Assuming the binding-energy difference between ¹⁵N and ¹⁵O is purely electrostatic, find the common nuclear radius. Use e²/(4πε₀)=1.44 MeV·fm.

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G1 Physics · Accepted Answer

Step 1: Use conservation of mass number and charge, together with Q = (m₁−m₂)c². Step 2: For fission/fusion compare total binding energies; for β decay the mass number stays unchanged. Final: C: 3.42 fm.