massadefect

Mass defect is the difference between the total rest masses of the individual protons and neutrons that compose a nucleus and the actual mass of the nucleus itself. It reflects the energy released when the nucleus forms from its constituent nucleons, in accordance with Einstein’s equation E = mc^2. The mass defect is a direct measure of the nuclear binding energy, which holds the nucleus together.

The mass defect Δm can be calculated from the numbers of protons (Z) and neutrons (N) in a nucleus (A = Z + N) using the masses of the constituents and the nuclear mass: Δm = Z m_p + N m_n − M_nucleus, where m_p and m_n are the rest masses of the proton and neutron. If atomic masses are used instead of nuclear masses, the relation becomes Δm = Z m_p + N m_n + Z m_e − M_atom, with m_e the electron mass and M_atom the atomic mass of the neutral atom. The resulting Δm, in atomic mass units, can be converted to energy in MeV by multiplying by 931.5 MeV/u. Binding energy is then B = Δm c^2.

As an example, helium-4 has a mass defect of about 0.030 u, corresponding to roughly 28 MeV of binding energy. In general, the mass defect decreases per nucleon for very heavy nuclei and reaches a maximum near iron-56, illustrating why energy can be released when light nuclei fuse and heavy nuclei fission.

Mass defect is a fundamental concept in nuclear physics, underpinning nuclear stability, reactions, and energy production in stars and reactors.