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: Binding energy per nucleon, the energy to extract a nucleon, generally rises with mass number until iron (Fe), then declines. This is due to larger nuclei being less tightly bound as size increases, while smaller nuclei (e.g., hydrogen, helium) are more tightly bound. The binding energy curve peaks around \( A = 56 \) (iron's mass number), subsequently decreasing. The curve, resembling a bell, attains its highest point at iron, signifying maximal nuclear stability around this mass number.

Significance of the Binding Energy Curve:
The curve indicates that nuclei with mass numbers near 56 (like iron) are the most stable, requiring the highest energy for disintegration.
Nuclei with mass numbers exceeding 56 can generate energy through fission (splitting), releasing energy when divided into smaller nuclei.
Nuclei with mass numbers below 56 can generate energy through fusion, releasing energy when combined into heavier nuclei.