Isotopes of the same element share the same proton count Z (so the same
chemistry) but differ in neutron count N, changing the mass number and nuclear
stability. The semi-empirical mass formula estimates binding energy per nucleon;
nuclei far from the stability valley are radioactive and decay.
A = Z + N
BE/A ≈ a_v − a_s·A^(−1/3) − a_c·Z²/A^(4/3) − a_a·(N−Z)²/A²
stable when N/Z ≈ 1 (light) to ≈ 1.5 (heavy)
- Protons (Z) — determines which element this is; changing it changes the element label.
- Neutrons (N) — determines which isotope of that element; too few or too many destabilises the nucleus.
- Binding energy per nucleon — energy needed to pull the nucleus apart, divided by nucleon count; peaks near iron-56.
- Trigger decay — for an unstable N:Z ratio, emits a beta particle to nudge the nucleus toward the stability line.