binding energy

Binding energy is the amount of energy required to separate two objects that are bound together by some force. The concept and term are used in respect to nuclear reactions, ionization, chemical reactions, but also applies to items bound together by gravity. Given that it refers to energy required, it is generally expressed as a negative number, and when the opposite is done, i.e., the two unbound objects are bound together, binding energy is released, and this is expressed as a positive number. Examples:

• For a rock sitting on the Earth, their binding energy (specifically, gravitational binding energy) is the energy to lift the rock until it is virtually independent of Earth's gravity, which is the same as the kinetic energy of the rock moving at escape velocity.
• For a neutral atom, e.g., hydrogen, its ionization potential, the energy required to totally remove the electron from orbiting the nucleus is a binding energy.
• For a nucleus, e.g., deuterium, the binding energy between the nucleons (the proton and the neutron) is the energy required to separate them into a lone proton and a lone neutron.

In the nuclear case (nuclear binding energy), transformations that release binding energy (e.g., fusion) are of detailed interest due to their role in powering stars and some transients. In fact, a major step in developing current models of stellar structure was the conceptualization of fusion reactions that could be plausibly triggered by the Sun's internal temperature and pressure and that would release significant binding energy, i.e., sufficient energy to power the Sun for its billions of years. The power associated with the release of binding energy due to gravity can be as significant as that of fusion, e.g., during star formation, or when it involves a compact object.