Nuclear Binding Energy

The sum of the masses of the individual components of a nucleus that contains Z protons and (A − Z) neutrons is larger than the actual mass of the nucleus. This difference in mass is called the mass defect (Δm), and its energy equivalent Δm² is called the total binding energy E_B of the nucleus. The total binding energy can be defined as the energy liberated when Z protons and (A − Z) neutrons are brought together to form the nucleus.

Formula for Binding Energy

The total binding energy E_B of a nucleus is given by:

E_B = Δm * c²

Binding Energy Per Nucleon

The binding energy per nucleon (E_B/A) in a nucleus (i.e., the total binding energy of a nucleus divided by the number of nucleons in the given nucleus) varies with the number of nucleons A. It is typically of the order of 8 MeV/nucleon.

A plot of the binding energy per nucleon (E_B/A) against the atomic mass number A shows:

• A rapid rise in (E_B/A) for small atomic mass numbers (A).
• A broad maximum of about 8.7 MeV/nucleon around A ≈ 60, corresponding to elements like iron, cobalt, and nickel.
• A gradual decrease in (E_B/A) for larger A, especially for heavy nuclei.

Stability of Nuclei

The larger the binding energy per nucleon (E_B/A) of an atom, the greater the stability of the atom. Thus, the most stable nuclei in nature are those with A ≈ 60 (such as iron, cobalt, nickel). Nuclei of light elements (small A) are generally less stable than those with A ≈ 60, and the heaviest nuclei (large A) are also less stable.

General Trends

The general trend of binding energy per nucleon (E_B/A) as a function of the atomic mass number A is:

• A rapid rise for small A.
• A broad maximum around A ≈ 60.
• A gradual decrease for large A.