Binding Energy of a Nucleus

Binding Energy

When free nucleons combined together to form a nucleus, then decrease in mass (according to Einstein mass energy relation), is released as equivalent energy. This energy equivalent to mass defect is used in binding the nucleons inside the nucleus and is called binding energy of the nucleus. An equal amount of work has to be done to completely separate the nucleons from each other.

Definition

Thus binding energy of a nucleus may be defined as energy equivalent to mass defect.

Mathematically

If mass defect is Δm then binding energy of the nucleus according to Einstein mass energy relation is given as:

Binding Energy of the nucleus = Δm c²

If Δm is in kg and c in m/s, then B.E. will be in joules.

In case mass defect is measured in a.m.u. then

Binding energy of the nucleus = Δm × 931.5 (in MeV)      

The binding energy of the nucleus with mass number A and atomic number Z is given by

B.E. = [Zm_p + (A - Z) m_n - M] c² using eq. from mass defect

or

B.E. = [Zm_p + (A - Z) m_n - M] in a.m.u.