Question

Show the variation of binding energy per nucleon with mass number. Write the significance of the binding energy curve.

Hint:

The binding energy per nucleon increases up to iron, indicating that fusion of lighter nuclei and fission of heavier nuclei both release energy.

Answer 1

Variation of Binding Energy per Nucleon with Mass Number: The binding energy per nucleon is the energy required to remove a nucleon from a nucleus. It generally increases with mass number up to iron (Fe), after which it begins to decrease. This is because larger nuclei become less tightly bound as their size increases, while smaller nuclei (like hydrogen and helium) are more tightly bound. The binding energy curve has a peak around \( A = 56 \) (the mass number of iron), after which it decreases. The curve is roughly shaped like a bell, with the highest point at iron, indicating that nuclei around this mass number are the most stable.

Significance of the Binding Energy Curve:
The curve shows that nuclei with mass numbers near 56 (such as iron) are the most stable, meaning they require the most energy to break apart.
Nuclei with mass numbers greater than 56 can release energy by fission (splitting), as splitting them into smaller nuclei releases energy.
Nuclei with mass numbers less than 56 can release energy by fusion, as fusing them to form heavier nuclei also releases energy.