Nuclear Binding Energy

The energy equivalent to that of mass defect, i.e., the energy required for holding the nucleons together in a nucleus, is called the Binding Energy of the nucleus.

The ratio of the binding energy \[E_n\]_​ of a nucleus to the number of nucleons A in that nucleus is called Binding Energy Per Nucleon.

The definite amount of energies associated with the electrons in different orbits of an atom are called the Energy Levels (of that atom).

The energy required to take an electron from the ground state to an excited state is called the Excitation Energy of the electron in that state.

The minimum energy required to make an electron free from the nucleus is called the Binding Energy of an electron.

The minimum amount of energy required to be given to an electron in the ground state of an atom to set the electron free is called the Ionization Energy of that atom.

E_b = ΔM ⋅ c²

E_b ​= [(Zm_p​ + (A − Z)m_n​) − M] × c²

In a graph plotting binding energy per nucleon (Bₙ) against mass number (A) for all known nuclei, the resulting curve is called binding energy curve.

BE per nucleon ​= \[\frac {E.E.}{A}\]

Binding Energy = \[(\Delta m)\cdot c^2=(\text{Mass defect})\cdot c^2\]

\[\text{Binding Energy per Nucleon}=\frac{\text{Binding Energy}}{\text{Nucleon Number}}\]

• The greater the binding energy per nucleon, the more stable the nucleus.
• Iron-56 (Fe⁵⁶) and Nickel-62 are among the most stable nuclei, lying at the peak of the binding energy curve.
• Light nuclei (A < 20): Binding energy per nucleon increases rapidly with mass number.
• Intermediate nuclei (A ≈ 20–60): Highest binding energy per nucleon — most stable region.
• Heavy nuclei (A > 60): Binding energy per nucleon gradually decreases — less tightly bound.
• Very heavy nuclei can become unstable and may undergo fission, splitting into smaller, more stable nuclei, releasing energy.
• If nucleons are separated, the energy required to separate them gets converted into mass.