The nucleus, binding energy, and E = mc^2
An atomic nucleus is made of protons and neutrons packed very closely together. The positively charged protons repel each other, so a stronger force must hold the nucleus together: the strong nuclear force, which attracts protons and neutrons to each other but acts only over very short distances, about the width of a nucleus. A nucleus has slightly less mass than its protons and neutrons would have if they were separated. This missing mass, called the mass defect, corresponds to the nucleus's binding energy, the energy needed to pull it apart, through Einstein's equation E = mc^2, where c is the speed of light. Because c^2 is enormous, a tiny amount of mass corresponds to a huge amount of energy. The binding energy per proton or neutron is highest for nuclei near iron. So splitting a very heavy nucleus like uranium-235 (fission), or joining very light nuclei such as hydrogen isotopes into helium (fusion), makes products that are more tightly bound, and the difference in mass is released as energy. That is why nuclear fuel, in a power plant or in the Sun, releases millions of times more energy per kilogram than burning coal or gasoline.
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