Binding energy is the energy required to separate a bound state into specified free constituents. For an Electron bound in a chemical atom, neglecting this cost is an assumption of the free-Electron Compton scattering model.
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Binding energy is the energy required to disassemble a system of particles into its individual components. In the context of nuclear physics, it specifically refers to the energy needed to separate a nucleus into its individual protons and neutrons. When these nucleons are bound together within the nucleus, they exhibit a lower total energy compared to when they are free and unbound.