Question

Assertion (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Formation of a stable nucleus always releases energy. \[ \text{Mass defect} \Longleftrightarrow \text{Binding Energy} \] A larger binding energy means a more stable nucleus.

Answer 1

The Correct Option is C

Concept: The mass of a nucleus is always less than the sum of the masses of its constituent protons and neutrons. The difference in mass is called the mass defect. \[ \Delta m=Zm_p+Nm_n-M_{\text{nucleus}} \] The mass defect is converted into binding energy according to Einstein's relation \[ E=\Delta mc^2. \] When a nucleus is formed, energy is released, not absorbed.

Step 1: Examine the Assertion (A).
Since some mass is converted into binding energy, \[ M_{\text{nucleus}} < Zm_p+Nm_n. \] Thus, the Assertion is true.

Step 2: Examine the Reason (R).
The statement says that energy is absorbed during nucleus formation. This is incorrect. Actually, energy is released when nucleons combine to form a stable nucleus. Therefore, the Reason is false. Hence, \[ \boxed{\text{Assertion is true but Reason is false.}} \]