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

Step 1 (Governing Principle): [0.25 Mark]

The binding energy per nucleon, denoted as $BE/A$, is defined as the total binding energy of a nucleus divided by its mass number $A$. The stability of a nucleus is directly proportional to its $BE/A$ value. According to the NCERT physics curriculum, the curve is plotted with $BE/A$ on the y-axis and mass number $A$ on the x-axis.

Step 2 (Step-by-Step Analysis of the Curve): [0.5 Mark]

• For light nuclei (e.g., $^2_1H$), the $BE/A$ is low.
• The curve rises sharply and reaches a broad maximum in the region of intermediate mass numbers ($30 < A < 170$), where the value is approximately $8.0 \text{ MeV}$ per nucleon.
• The maximum value of $BE/A$ is observed for $^{56}_{26}Fe$, which is approximately $8.75 \text{ MeV}$.
• For heavy nuclei ($A > 170$), the curve gradually decreases as the Coulombic repulsion between protons increases, making them less stable.

Step 3 (Final Concluded Answer): [0.25 Mark]

The correct figure is the one that shows a steep rise for low $A$, a broad plateau/peak around $A \approx 56$, and a gradual decline for high $A$. Any graph depicting this specific "hump" shape is the correct representation of the binding energy per nucleon curve.

💡 EL10 Concept Insight: Think of the binding energy per nucleon like a "stability score" for atoms; medium-sized atoms are the most stable (like a perfectly sized team), while very small atoms want to fuse together and very large atoms want to break apart to reach that stable middle ground.