Nuclear Physics
The nucleus is a hundred-thousandth the size of its atom yet holds nearly all its mass, bound by a force that overwhelms the electric repulsion of its packed protons. Nuclear physics asks what holds it together, and how it comes apart.
One curve organizes the whole subject: the binding energy per nucleon. It rises steeply through the light elements, crests at iron — the most tightly bound matter there is — and falls away through the heavy ones. Everything downhill of that peak releases energy.
Stability is never guaranteed. An unbalanced nucleus is radioactive: it transmutes toward the valley of stability at a fixed probability per unit time, so a population decays exponentially and each isotope carries its own half-life, from fractions of a second to billions of years.
Decay comes in three modes. Alpha ejects a helium-4 cluster; beta converts a neutron to a proton and emits an electron; gamma sheds pure energy as a photon, dropping the nucleus to a lower state without changing what it is.
Firing particles at nuclei drives reactions — the controlled transmutations that build new isotopes and reveal nuclear structure, each governed by the same conservation laws of energy, momentum, and charge.
Split a heavy nucleus and the fragments are more tightly bound than the whole — fission releases energy, plus spare neutrons that can split more nuclei. When each fission provokes more than one further fission, the chain reaction sustains itself, tamed in a reactor or unleashed in a bomb.
Run the curve uphill from the other end and light nuclei fuse into heavier, more tightly bound ones — the process that powers the stars and forged the elements, if the reactants can first be forced through their mutual repulsion.
From sizes and masses through the nuclear force, the decay laws, reactions, fission, and fusion, the subject is one long reading of a single curve — and of the enormous energies stored in the gap between where a nucleus sits and where it would rather be.