Nuclear composition and binding energy

The nucleus consists of protons (positive, charge +e) and neutrons (uncharged), the nucleons; it is about 10⁴–10⁵ times smaller than the atom (≈ 10⁻¹⁵–10⁻¹⁴ m) but holds almost all the atom's mass (over 99.9 %). Z is the number of protons (the atomic number), N the number of neutrons, A = Z + N the mass number; a nucleus is written ᴬ_Z X. Nuclei with the same Z but different A are isotopes; nuclei with the same A but different Z are isobars. The nuclear radius is R ≈ R₀·A^(1/3) with R₀ ≈ 1.2·10⁻¹⁵ m, so the density of nuclear matter is nearly the same in all nuclei, about 2·10¹⁷ kg/m³. Protons repel one another yet the nucleus holds, because between nucleons act nuclear forces, strong short-range (≈ 10⁻¹⁵ m) attractive forces that do not depend on charge. The mass of a nucleus is smaller than the sum of the masses of its nucleons: Δm = Z·m_p + (A − Z)·m_n − m_nucleus, the mass defect. The corresponding energy E_bind = Δm·c² is the energy needed to split the nucleus into nucleons; 1 u corresponds to ≈ 931.5 MeV/c². The binding energy per nucleon E_bind/A is greatest for medium-mass nuclei (≈ 8–9 MeV) and ≈ 7.6 MeV for uranium, so both fusion of light nuclei and fission of heavy ones release energy.