Binding Energy
Earlier, I was telling Alex about the mass defect: the mass of any nucleus is less than the sum of the separate masses of
its protons and neutrons. In other words, sticking protons and neutrons
together somehow causes some of their mass to vanish into thin air.
I bet this has something to do with Einstein's equation E=mc^{2}...
Very good! Einstein showed that mass and energy are really two different
forms of the same thing; the "vanishing" mass of the protons and neutrons
is simply converted to energy.
So you can produce energy by building nuclei.
Exactly right; that's the idea behind fusion. The "binding energy"
of a particular isotope is the amount of energy released at its creation;
you can calculate it by finding the amount of mass that "disappears" and
using Einstein's equation. The binding energy is also the amount of energy
you'd need to add to a nucleus to break it up into protons and
neutrons again; the larger the binding energy, the more difficult that
would be.

