Atoms are made of electrons, neutrons and protons. Protons have the same electrical charge, so they naturally want to repel each other. To keep them together as atoms there is something called the strong nuclear force binding the protons and neutrons together in the nucleus.
Einstein said that mass and energy are the same thing in different forms, and described that by the famous equation of E=MC^2. A little bit of mass times the speed of light squared is equal to a lot of energy.
That binding energy of the strong nuclear force thus adds to the mass of the atom. Very large atoms, such as uranium, have a lot of binding energy since they are made of lots of protons and neutrons.
If you send a fast neutron into the center of a uranium atom, it’s going to knock the nucleus apart like a cue ball hitting a rack of pool balls. In doing so, new, smaller atoms are formed using the same amount of protons and neutrons, as well as a few extra free neutrons that will break open more uranium atoms before they decay into a proton and an electron themselves.
However, the total binding energy for those three new atoms is going to be less than the binding energy needed for the original uranium atom, so there is some excess energy left over. As more and more uranium atoms break apart, more and more free binding energy is released. That’s the power of the nuclear reaction.
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