4.1 Binding energy per nucleon

1.1 Properties and Application of X-Rays
1.2 Spectra of X-rays

3.1 Atomic Mass Number:

4.1 Binding energy per nucleon
4.2 Variation of Binding energy per nucleon with mass number
4.3 Nuclear stability

6.1 Radioactive equilibrium
6.2 Simultaneous decay modes of radioactive elements

We can define binding energy per nucleon theoretically as the amount of energy needed to remove a nucleon from the nucleus of an atom. It can be given by

$$B{E_N} = \frac{{\Delta m{c^2}}}{A}$$

It is the criterion for comparison of stability among different nucleus.

For example: Let us consider two elements $X$ and $Y$ with mass numbers $A_X$ and $A_Y$ (${A_X} > {A_Y}$) and binding energies $\Delta {E_X}$ and $\Delta {E_Y}$ ($\Delta {E_X} > \Delta {E_Y}$).

We can say that as for the element $X$ having more binding energy than $Y$.

So, the element $X$ has a more stable nucleus.

But if we find the binding energy per nucleon $\left( {B{E_N}} \right)$ of both the elements $X$ and $Y$ such that ${\left( {B{E_N}} \right)_Y} > {\left( {B{E_N}} \right)_X}$.

It implies that to remove a nucleon from element $X$ requires less energy than from element $Y$.

Thus, it is more difficult to remove one nucleon from the nucleus of an element $Y$.

So, the nucleus of $Y$ is more stable than $X$.

Thus, a nucleus having a larger binding energy per nucleon is more stable than one having a smaller binding energy per nucleon.