Inside the Nucleus

Rutherford showed that an atom’s positive charge and almost all its mass sit in a tiny nucleus. Inside it, protons and neutrons are held together by a force unlike anything in everyday life: enormously strong, but felt only at a distance of about a femtometre.

What a nucleus is made of#

A nucleus contains protons (charge +e, mass about 1840 electron masses) and neutrons (no charge, slightly heavier than a proton). Together they are called nucleons.

Masses as energies

Because mass and energy are equivalent (E = mc²), nuclear physicists often quote masses in energy units: the electron is 0.511 MeV/c², the proton 938.27 MeV/c² and the neutron 939.57 MeV/c². The energy mc² of a particle at rest is its rest-mass energy. Another common unit is the unified atomic mass unit, one twelfth of the mass of a neutral carbon-12 atom:

Protons and neutrons obey the Pauli exclusion principle: no two protons, and no two neutrons, can share a quantum state (a proton and a neutron can).

Naming nuclei

A nucleus has atomic number Z (protons), neutron number N, and mass number A = Z + N. It is written ^A_ZX with X the chemical symbol, e.g. ²³⁵₉₂U has 92 protons and 143 neutrons. Chemistry depends only on Z, because Z fixes the number of electrons.

Which nuclei are stable?#

Over a thousand nuclides are known, but most are unstable: they emit a particle and change. Plotting N against Z, the stable ones lie in a narrow band. Light stable nuclei have N ≈ Z; heavier ones need more and more neutrons, up to N/Z ≈ 1.6. Nuclides to one side of the band have too many neutrons, to the other side too many protons; both are radioactive. The heaviest stable nuclide is ²⁰⁹Bi.

How big is a nucleus?#

A nucleus has no sharp edge (it is described by a wave function), but experiments give an average radius

Nucleons also move in quantum states with orbital angular momentum, and each has spin (m_s = ±½). Their total is the nuclear spin.

The nuclear force#

Protons repel each other electrically, yet nuclei hold together. At separations of about 1 fm a new force acts between nucleons. Its main features:

• Short range: strongest at about 1 fm, negligible beyond about 10 fm.
• Very strong: within its range, roughly 50–60 times stronger than the electric force.
• Charge-independent: the same between p–p, n–n and n–p (the electric force acts on protons as well).
• Not central: it depends on more than distance, e.g. it is stronger when the two spins are parallel.

Because of its short range, each nucleon only feels its nearest neighbours, which is why nuclear density is the same everywhere. In light nuclei, nuclear attraction dominates and pairing favours N ≈ Z. Coulomb repulsion, however, is long-range: every proton repels every other one. In a big nucleus it grows important, so extra neutrons (which add attraction but no repulsion) are needed. Too many neutrons are unfavourable too, and beyond bismuth no N/Z ratio gives a stable nucleus.