Binding Energy Per Nucleon | Binding Energy Curve

 

Binding Energy Per Nucleon | Binding Energy Curve :- The stability of a nucleus is not measured by it’s binding energy, but it is measured by “binding energy per nucleon”. If B.E./nucleon of a nucleus is less, the nucleus is less stable whereas the nucleus is more stable if its B.E./nucleon is higher.

Definition of Binding Energy Per Nucleon

 

“Binding Energy Per Nucleon is the average energy we have to spend to remove a nucleon from the nucleus to infinite distance.”

It is given by total binding energy divided by the mass number of the nucleus, i.e.,

 

Binding Energy Curve

“The variation of average binding energy per nucleon with mass number A is known as binding energy curve.”

The variation of B.E./nucleon with mass number (A) is shown in figure below :-

From the graph, we note that :-

1. For small nuclei like ₁H¹, ₁H², ₁H³, average B.E./nucleon is small.
2. In the range, 2 < A < 20, there are some nuclei like ₂He⁴, ₆C¹², ₈O¹⁶ for which B.E./nucleon is more than their neighbours (indicated by sharp peaks). So these nuclei are more stable than their neighbours.
3. For A > 30, B.E./nucleon increases gradually till it attains a maximum value of 8.8 MeV/nucleon corresponding to Iron ₂₆Fe⁵⁶ nucleus. Thus, iron is a stable element. For 30 < A < 120, average B.E./nucleon is 8.5 MeV.
4. As the mass number increases, B.E./nucleon decreases. This is because as the mass number increases, the number of protons in the nucleus increases and hence Coulomb repulsion also increases. This makes the heavy nuclei unstable. For ₉₂U²³⁸ B.E./nucleon is 7.6 MeV.

From above observations we can draw following conclusions :-

1. Binding energy per nucleon is lower for both light nuclei (A<30) and heavy nuclei (A>170).
2. The intermediate nuclei have large value of B.E./nucleon, so they are more stable.
3. When we move from lighter nuclei to heavier nuclei, we find that there is an increase in B.E. This indicates that energy can be released when two or more lighter nuclei fuse to form a heavy nucleus and the final system will be more tightly bound than the initial system. This process is called Nuclear Fusion which is the energy source of the Sun.
4. When we move from the heavy nuclei region to the middle region of the curve, we notice that there is an increase in B.E. This indicates that energy can be released when a heavy nucleus breaks into two lighter nuclei. These new nearly equal fragments will have more tightly packed nucleons. This process is called Nuclear Fission.