A graph is plotted for different nuclei between the binding energy per nucleon and the atomic mass number. This graph gives a curve which is called " binding energy curve".
Binding Energy Curve
Binding Energy Curve :
There are following discussion point obtained from the binding energy curve :
1.) For Nuclei with $A=50$ TO $A=80$:
For nuclei with atomic mass number $A = 50 - 80$ , the B.E./ nucleon (i.e. binding energy per nucleon) is approximately $8.5 MeV$.
The curve is almost flat in this and indicate the highly stability of the nucleus.
2.) For Nuclei with $A \geq 80$:
For heavier nuclei with $A \gt 80$, the B.E. /nucleon ( i.e. binding energy per nucleon) decreases slowly and reaching about $7.6 MeV$ for uranium ($U \: A = 238$).
The lower value of binding energy per nucleon fails to counteract the Coulombian repulsion among protons in nuclei having large number of protons resulting instability
Consequently, the nuclei of heavier atoms beyond $_{83}Bi^{209}$ are radioactive.
3.) For Nuclei with $A \leq 50$:
For nuclei with atomic mass number below $50$ , the B.E./ nucleon decreases, with a sharp drop below $A=20$.
For example: Heavy hydrogen (i.e $_{1}H^{2}$), it is only about $1.1 MeV$. it indicates that lower stability for nuclear with mass number below $20$.
4.) Subsidiary Peak for $A \lt 50$:
Below $A = 50$, the curve does not fall continuously, but the subsidiary peaks at $_{8}O^{16}, _{6}C^{12},_{2}He^{4}$.
These peak indicate that such even-even nuclear are more stable compared to the immediate neighbours .
5.) Nuclear fusion and Nuclear fission process release energy:
From curve, it shows that drops down in curve at both high and low mass number and lower binding energy per nucleon.
For example:
A very high amount of energy is released in the process of nuclear fission and fusion because of Lo binding energy causes instability of the nucleus.
