A hundred-thousand times smaller than the atom
An atom is almost entirely empty space. Rutherford's 1911 gold-foil experiment fired alpha particles at a thin sheet and found that a few bounced almost straight back — impossible unless nearly all the atom's mass and all its positive charge sat in a tiny, dense core. That core is the atomic nucleus. If the atom were a sports stadium, the nucleus would be a grain of rice at the centre.
Nuclei are built from protons and neutrons — collectively nucleons. Their radius follows a strikingly simple empirical rule: pack A nucleons into a nearly incompressible ball and the radius grows as the cube root of the number, so nuclear matter has a nearly constant density.
The nuclear radius. A femtometre (fm) is 100,000 times smaller than an atom.
What holds it together against itself
Here is the puzzle. Protons all carry positive charge, so by Coulomb's law they repel one another ferociously at femtometre range — the electrostatic energy of two protons 2 fm apart is nearly a million times a typical chemical bond. Yet nuclei not only survive, they are among the most tightly bound systems known. Something far stronger than electricity must be at work: the strong nuclear force.
The nuclear force is attractive, short-ranged (its pull dies past about 2–3 fm), charge-independent (proton–proton, proton–neutron and neutron–neutron feel it nearly alike), and it saturates — a nucleon bonds only to its immediate neighbours, not to the whole nucleus. Saturation is why binding energy grows in proportion to volume, the seed of everything in the next guide.
Isotopes and the chart of nuclides
A nucleus is labelled by two integers: the proton number Z (which fixes the chemical element) and the neutron number N, with mass number A = Z + N. Fix Z and vary N and you get the isotopes of one element — carbon-12 and carbon-14 are the same element, chemically identical, but nuclear worlds apart (one stable, one radioactive).
Plot every known nuclide on a grid of N (across) versus Z (up) and the stable ones trace a narrow diagonal band — the valley of stability. Light stable nuclei hug the line N \approx Z; heavy ones bend toward a neutron excess (N > Z), because extra neutrons dilute the proton–proton repulsion without adding charge. Off the valley walls, nuclei are radioactive and decay back toward it — the subject of guide 4.
Mass is energy — the master idea
Weigh a helium-4 nucleus and compare it to two free protons plus two free neutrons: the nucleus is lighter than its own ingredients. That missing mass, the mass defect, did not vanish — via $E=mc^2$ it was released as energy when the nucleus formed. To pull the nucleus apart again you must pay that energy back. That is exactly the nuclear binding energy.
The unit conversion every nuclear physicist memorises: one atomic mass unit is worth 931.5 MeV.
Why fusion AND fission both release energy
Here is the single picture the whole field hangs on. Divide each nucleus's binding energy by its number of nucleons, B/A, and plot it against mass number A. The curve rises steeply from hydrogen, reaches a broad maximum of about 8.8 MeV per nucleon near A \approx 56–62 (the iron–nickel region), then declines gently toward uranium.
A nucleus is more tightly bound — and therefore lighter, more stable, lower in energy — the higher it sits on this curve. So there are two ways downhill. Take two light nuclei on the steep left slope and fuse them into one heavier nucleus higher on the curve: energy comes out. Take one very heavy nucleus on the gentle right slope and split it into two mid-weight fragments higher on the curve: energy comes out too. Fusion of the light and fission of the heavy both march toward the iron peak.