Question

Which of the following figures correctly represent the shape of the curve of binding energy per nucleon as a function of mass number?

• A.
• B.
• C.
• D.

Hint:

Nuclei with mass number around \( A = 56 \) have the highest binding energy per nucleon. This explains the characteristic curve that peaks at \( A = 56 \).

Answer 1

The Correct Option is B

Binding Energy per Nucleon vs. Mass Number

Binding energy per nucleon quantifies the force holding protons and neutrons (nucleons) within a nucleus. This quantity varies with the nucleus's mass number \( A \) and exhibits a notable trend.

Trend of Binding Energy per Nucleon:

The binding energy per nucleon rises with mass number \( A \) up to iron (\( A \approx 56 \)), after which it declines as \( A \) increases. This behavior is explained by:

• Nuclei near \( A = 56 \) (e.g., iron) possess the highest binding energy per nucleon, indicating maximum stability.
• In lighter nuclei (\( A \) small), binding energy per nucleon increases as nucleons assemble into more stable arrangements.
• In heavier nuclei (\( A \) large), binding energy per nucleon decreases. This occurs because larger nuclei experience diminished effectiveness of nuclear forces at their edges, reducing the overall efficiency of binding nucleons.

Conclusion:

The appropriate graph illustrating this phenomenon will display a maximum at \( A = 56 \) (corresponding to iron), showing an initial ascent in binding energy per nucleon with increasing \( A \) followed by a descent for more massive nuclei.