Question Analysis: Assertion-Reason type question.
Step 1 (Foundational Law & Definition): [0.25 Mark]
The mass defect ($\Delta m$) is defined as the difference between the sum of the masses of individual nucleons and the actual mass of the nucleus ($M$). According to Einstein’s mass-energy equivalence principle, the binding energy ($BE$) is given by:
$$BE = \Delta m \cdot c^2$$where $c$ is the speed of light in vacuum.
Step 2 (Step-by-Step Logical Evaluation): [0.50 Mark]
- Assertion (A): The mass defect represents the energy released when nucleons bind together to form a nucleus. This energy is indeed the source of the binding energy. Thus, Assertion (A) is True.
- Reason (R): The binding energy per nucleon ($BE/A$) curve shows that it increases for light nuclei, reaches a maximum for intermediate nuclei (like $^{56}_{26}\text{Fe}$), and then decreases for heavy nuclei (like $^{238}_{92}\text{U}$). Thus, Reason (R) is False.
Step 3 (Final Concluded Answer): [0.25 Mark]
Since the Assertion is true but the Reason is false, the correct option is: Assertion (A) is true, but Reason (R) is false.
💡 EL10 Concept Insight: Think of the nucleus like a group of friends holding hands; the "mass defect" is the tiny bit of energy they lose to hold on tight, while the "binding energy per nucleon" is just a measure of how strong that grip is—and it doesn't just keep getting stronger forever as you add more friends!