Nuclear Binding Energy & Mass Defect Calculator

Nuclear Binding Energy Guide

What do I need to know about 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.

What should I know about 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 energy input rather than releasing it, which is why iron marks the practical end point of energy-producing fusion inside a star.

What should I know about 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 extracted from seawater and tritium bred from lithium — is abundant enough to supply energy needs for many thousands of years if commercial fusion power ever becomes practical.

What do I need to know about 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 decay chains often involve several successive decays of different types before reaching a stable isotope, sometimes taking many steps to get there.