Nuclear binding energy

From mass defect to binding energy

If tabulated atomic masses are used instead of bare nuclear masses, electron masses must be handled consistently so that the same constituents are compared on both sides.

Binding energy per nucleon compares different sizes

Total binding energy naturally tends to grow with A, so B/A is more useful for broad comparisons. It rises quickly among light nuclei, reaches a broad maximum in the iron–nickel region, then decreases gradually for very heavy nuclei.

Why the curve has this shape

The strong nuclear interaction is short-ranged and approximately saturating: a nucleon interacts most strongly with nearby nucleons rather than equally with every nucleon in the nucleus. Proton–proton Coulomb repulsion is longer-ranged and becomes increasingly important as Z grows. Surface effects, neutron–proton balance, pairing and shell structure add finer features.

High B/A does not guarantee stability

A nuclide can be relatively tightly bound and still have an energetically allowed radioactive transition. Stability depends on whether a lower-energy state is accessible and on the quantum probability for the transition. Alpha decay can be extremely slow even when energetically allowed because of tunnelling through a Coulomb barrier.

Use B/A for trends, B for an actual separation. The binding energy per nucleon is an average that helps compare nuclei of different size; it is not the energy needed to remove one particular proton or neutron. Separation energies depend on the detailed initial and final nuclei and can differ substantially from B/A, especially near shell closures or close to the limits of nuclear stability.

Worked examples

1. Total binding energy

2. Mass defect

3. Energy direction