Atomic Nucleus
The atomic nucleus is the tiny, dense center of an atom that contains its protons and neutrons and almost all of its mass.
Definition
The nucleus is the small, heavy center of an atom that holds the protons and neutrons (together called nucleons), with the electrons moving around outside it. It carries the atom's positive charge and more than $99.9\%$ of its mass, yet its diameter is about $100{,}000$ times smaller than the whole atom. Protons repel each other electrostatically, but the strong nuclear force binds them together with the neutrons at distances of a few femtometers; nuclear radii scale roughly as $r \approx 1.2\text{ fm} \times A^{1/3}$, where $A$ is the mass number. Whether a nucleus is stable depends on its neutron-to-proton ratio, and unstable nuclei undergo radioactive decay.
Example
A helium nucleus is $2$ protons and $2$ neutrons packed together, with $2$ electrons outside. A carbon-12 nucleus has $6$ protons and $6$ neutrons, a charge of $+6$, and a mass number of $12$, balanced by $6$ electrons. Uranium-238 has $92$ protons and $146$ neutrons, a radius near $7.4\text{ fm}$, and is unstable, emitting a helium-4 nucleus in alpha decay to become thorium-234.
Key Insight
Rutherford discovered the nucleus when most alpha particles passed straight through gold foil but a few bounced almost straight back, which only made sense if the positive charge was concentrated in a tiny core. The mass of a nucleus is slightly less than the sum of its separate nucleons; that missing mass, the mass defect, is the binding energy released when the nucleus formed, given by $E = mc^2$.