So far we have treated the nucleus as a positive point charge and focused the electrons to understand the atom. To explain radioactivity and nuclear reactions we'll do the opposite, focus on the nucleus and ignore the electrons.

A nucleus consists of a bunch of protons and neutrons; these are known as nucleons. Each nucleus can be characterized by two numbers: A, the atomic mass number, which is the total number of nucleons; and Z, the atomic number, representing the number of protons. The number of neutrons is given by N, so A = N + Z.

Any nucleus can be written in a form like this:

The general case is shown on the left, with the X standing for the chemical symbol. On the right we're specifying a particular isotope of aluminum, aluminum-27. Isotopes of an element have the same Z, but a different number of neutrons.

How big is a nucleus? We know that atoms are a few angstroms, but most of the atom is empty space. The nucleus is much smaller than the atom, and is typically a few femtometers. 1 fm = 1 x 10^-15 m, and is also known as a fermi. The nucleus can be thought of as a bunch of balls (the protons and neutrons) packed into a sphere, with the radius of the sphere being approximately:

r = 1.2 x 10^-15 A^1/3

The implication here is that all nuclei have essentially the same density.