The Nucleus: Within the nucleus are positively-charged protons and uncharged
neutrons. However, like charges repel each other, so it would seem that protons wouldn't
want to hang around near each other. Of course they do, so the question becomes why
they do. The answer is that there is another force present that keeps them together. This
force is known as the Strong Nuclear Force and is responsible for the binding together of
nuclei. Observations of this force would indicate that it would be very strong over very
short distances (say, about the size of a nucleus) but would decrease to virtually nothing
over larger distances. Observations would also indicate that both protons and neutrons
experience the strong nuclear force.
The presence and behavior of both the strong nuclear force and the electromagnetic force
within the nucleus lead us to a better understanding of why large nuclei decay. These
nuclei are subject to a balancing act. They are so large that protons and neutrons on one
side of the nucleus aren't feeling the effect of the strong nuclear force relative to the
protons and neutrons on the other side of the nucleus. However, the protons on one side
are definitely experiencing electromagnetic repulsion from the protons on the other side
of the nucleus. Thus, adding protons to the nucleus increases the desire of the nucleus to
break apart without increasing its desire to stay together. This is also why large nuclei
have more neutrons than protons--adding neutrons can add binding nuclear forces
without adding disruptive electromagnetic forces.
The radioactive decay of smaller nuclei is due to the presence of yet another force, the
weak nuclear force. Bare neutrons don't last forever--in a relatively short period of time
(15 minutes to half an hour), most will decay into a proton and an electron (and a
neutrino) through this force. This decay is behind beta decay. In nuclei with too many
neutrons, one or more will ultimately desire to undergo this decay.
Mass-Energy Relationship: In 1905, Albert Einstein published his first studies on
relativity. In it, he showed that mass was another means by which energy could be
stored. In fact, the amount of energy stored in mass was E = mc2. In fact, it is the
conversion of mass into energy that allows a nucleus to stay together--a small part of the
mass of each of the particles in a nucleus is converted into binding energy. Thus, a
nucleus has less mass than if the nucleus was broken apart into its constituent particles. It
turns out that the nucleus most proficient at converting mass into energy is iron; it has the
highest value of binding energy/nucleon (proton or neutron). Thus, in building up to iron
the addition of more nucleons increases the overall binding energy of the nucleus.
However, in getting higher than iron, the addition of more protons increases the repulsive
aspect of the electrostatic force, decreasing the binding energy/nucleon in the nucleus.