Nuclear Binding Energy & Mass Defect Calculator
Calculate mass defect, binding energy, and binding energy per nucleon for any nucleus using E=mc².
Nuclear Binding Energy Guide
Mass Defect and E=mc²
The mass of a nucleus is always LESS than the total mass of its constituent protons and neutrons. This difference is the mass defect Δm. E = Δm × c². c = 3×10⁸ m/s. 1 atomic mass unit (u) = 1.66054×10⁻²⁷ kg = 931.5 MeV/c². Proton mass: 1.00728 u. Neutron mass: 1.00866 u. Example: Helium-4 nucleus (α particle). Expected mass: 2×1.00728 + 2×1.00866 = 4.03188 u. Actual mass: 4.00260 u. Mass defect: 4.03188 - 4.00260 = 0.02928 u. Binding energy: 0.02928 × 931.5 = 27.27 MeV.
Binding Energy Per Nucleon
The binding energy per nucleon is the key measure of nuclear stability. Peaks at iron-56 (approximately 8.79 MeV/nucleon) — the most stable nucleus. Below iron: fusing lighter nuclei releases energy (nuclear fusion). Above iron: splitting heavier nuclei releases energy (nuclear fission). This explains the energy source of stars: main sequence stars fuse hydrogen to helium (releasing energy). Late-stage stars fuse up to iron (less energy per reaction). Beyond iron: nuclear reactions require energ
Fission and Fusion Energy
Nuclear fission (e.g. U-235): a heavy nucleus splits into two medium nuclei closer to iron on the binding energy curve. Energy released per fission event: approximately 200 MeV. 1 gram of U-235: 2.56×10²¹ atoms × 200 MeV = 5.1×10²³ MeV = 8.2×10¹⁰ J = 82 GJ. Compare with: 1 gram of coal: approximately 30 kJ. Nuclear fission is about 2.7 million times more energy-dense than coal. Nuclear fusion (D-T reaction): deuterium + tritium → helium-4 + neutron + 17.6 MeV. Fusion fuel (deuterium from seawate
Radioactivity and Stability
Stable nuclei: balance of strong nuclear force (attractive, short range) and electromagnetic repulsion between protons. Light nuclei: most stable at N≈Z (equal neutrons and protons). Heavy nuclei: need excess neutrons to dilute proton repulsion. Above Z=83 (bismuth): no stable nuclei exist. Alpha decay: common in heavy nuclei. Reduces A by 4, Z by 2. Beta decay: converts neutron to proton (β⁻) or proton to neutron (β⁺). Gamma radiation: nucleus releases energy without changing Z or A. Nuclear de
Recommended for this calculator