Mass Defect, Binding Energy and Binding Energy per nucleon

Binding Energy:

The difference between the total mass of individual nucleons (i.e. total number of proton and neutron) and actual mass of nucleus of that energy is called binding energy.

$\Delta m = \left (P \times m_{P} + N \times m_{N} \right) - m_{actual} \qquad (1)$

Where
$\Delta m \rightarrow$ Mass Defect
$P \rightarrow$ Number of Proton
$N \rightarrow$ Number of Neutron
$m_{actual} \rightarrow$ Actual mass of nucleus
$m_{P} \rightarrow$ Mass of a Proton
$m_{N} \rightarrow$ Mass of a Neutron

We know that

$Z=P=e \\ N=A-Z \qquad (2)$

Where
$Z \rightarrow $ Atomic Number
$A \rightarrow $ Atomic Mass Number
$ e \rightarrow $ Number of Electrons

From above two equation $(1)$ and equation $(2)$

$\Delta m = \left [ Z \times m_{P} + \left ( A-Z \right) \times m_{N} \right] - m_{actual} \qquad (1)$

Binding Energy:

The energy require to form or break a nucleous is called the binding energy of nucleous.

$B.E= \Delta m \times c^{2} Joule$

Where $B.E.\rightarrow$ Binding Energy

$B.E= \Delta m (in \: a.m.u.) \times 931.5 \: MeV$

Where $1 \: a.m.u. = 1.67377 \times 10^{-27} kilograms$

Binding energy per nucleon:

The energy require to emit one nucleon from the nucleous is called binding energy per nucleon.

$B.E. \: per \: nucleon = \frac{B.E.}{ Total \: No. \: of \: Nucleons}$

Where $B.E.\rightarrow$ Binding Energy

Note: Higher binding energy per nucleon shows higher stability of the nucleus.