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

The binding energy per nucleon in a nucleus is a measure of how strongly the nucleons (protons and neutrons) are bound together. This energy is dependent on the mass number \( A \) of the nucleus, and its trend as a function of \( A \) shows an interesting pattern.

Trend of Binding Energy per Nucleon:

As a function of mass number \( A \), the binding energy per nucleon increases with \( A \) up to iron (\( A \approx 56 \)) and then decreases as \( A \) increases further. This is because:

• Nuclei with mass number around \( A = 56 \) (like iron) have the highest binding energy per nucleon, meaning they are the most stable nuclei.
• For lighter nuclei (with smaller \( A \)), the binding energy per nucleon increases as nucleons come together and form more stable configurations.
• For heavier nuclei (with larger \( A \)), the binding energy per nucleon decreases. This is because, as the nucleus becomes larger, the nuclear forces are less effective at binding the nucleons at the edges of the nucleus, and the overall energy required to hold the nucleus together becomes less efficient.

Conclusion:

The correct graph representing this behavior is one that shows a peak at \( A = 56 \) (for iron) with the binding energy per nucleon increasing initially as \( A \) increases and then decreasing for heavier nuclei.