# Einstein’s Equation: E = mc2

The mass of the nucleus is about 1 percent smaller than the mass of its individual protons and neutrons. This difference is called the mass defect. The mass defect arises from the energy released when the nucleons (protons and neutrons) bind together to form the nucleus. This energy is called the binding energy. The binding energy determines which nuclei are stable and how much energy is released in a nuclear reaction. Very heavy nuclei and very light nuclei have low binding energies. This implies that a heavy nucleus will release energy when it splits apart (fission), and two light nuclei will release energy when they join (fusion).

The hydrogen 2 nucleus, for example, composed of one proton and one neutron, can be separated completely by supplying 2.23 million electron volts (MeV) of energy. Conversely, when a slowly moving neutron and proton combine to form a hydrogen 2 nucleus, 2.23 MeV are liberated.

The mass defect and binding energy are related by Albert Einstein's formula, E = mc2. In 1905, Einstein developed the special theory of relativity. One of the implications of this theory was that matter and energy are interchangeable with one another. This equation states, a mass (m) can be converted into an amount of energy (E), where c is the speed of light. Because the speed of light is a large number and thus c squared is huge, a small amount of matter can be converted into a tremendous amount of energy. This equation is the key to the power of nuclear weapons and nuclear reactors.

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