Question Analysis: Assertion-Reasoning type question.
Step 1 (Governing Principle): [0.5 Mark]
The mass of a nucleus $M_N$ is related to the mass of its constituent nucleons (protons $Z$ and neutrons $N$) by the concept of Mass Defect ($\Delta m$). According to Einstein’s mass-energy equivalence principle, the binding energy $BE$ is given by:
$$BE = \Delta m \cdot c^2 = [Z m_p + (A - Z) m_n - M_N] c^2$$Where $\Delta m$ is the mass defect, $c$ is the speed of light, $m_p$ is the mass of a proton, and $m_n$ is the mass of a neutron.
Step 2 (Step-by-Step Logical Deduction): [0.25 Mark]
- Assertion (A): Since the nucleus is a stable bound system, the binding energy is positive ($BE > 0$). This implies $\Delta m > 0$, meaning $Z m_p + (A - Z) m_n > M_N$. Thus, the mass of the nucleus is indeed less than the sum of the masses of its constituents. (Assertion is True).
- Reason (R): When nucleons are bound together to form a nucleus, the system moves to a lower energy state. Therefore, energy is released (as binding energy) rather than absorbed. (Reason is False).
Step 3 (Final Concluded Answer): [0.25 Mark]
Conclusion: Assertion (A) is true, but Reason (R) is false.
💡 EL10 Concept Insight: Think of a nucleus like a group of friends who are happier (more stable) together; when they join up, they "let go" of some extra energy, which makes the whole group weigh slightly less than they did when they were standing apart!