Question

Assertion (A) : Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. Reason (R) : For heavy nuclei, binding energy per nucleon increases with increasing \(Z\) while for light nuclei, it decreases with increasing \(Z\).

• 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:

Energy is released whenever the final nuclei have a higher binding energy per nucleon than the initial nuclei. \[ \text{Light nuclei} \Rightarrow \text{Fusion} \] \[ \text{Heavy nuclei} \Rightarrow \text{Fission} \]

Answer 1

The Correct Option is C

Concept: The binding energy per nucleon curve rises rapidly for light nuclei, reaches a maximum around iron (\(A \approx 56\)), and then slowly decreases for heavier nuclei. A nuclear reaction releases energy whenever the products have a higher binding energy per nucleon than the reactants.

Step 1: Examine the Assertion. For light nuclei: \[ \text{Fusion} \Rightarrow \text{Higher binding energy per nucleon} \] therefore energy is released. For heavy nuclei: \[ \text{Fission} \Rightarrow \text{Higher binding energy per nucleon} \] therefore energy is released. Hence, the Assertion is true.

Step 2: Examine the Reason. The reason states:
• For heavy nuclei, binding energy per nucleon increases with increasing \(Z\).
• For light nuclei, binding energy per nucleon decreases with increasing \(Z\). This is opposite to the actual binding energy curve. For light nuclei, binding energy per nucleon generally increases with increasing mass number. For heavy nuclei, binding energy per nucleon decreases. Therefore, the Reason is false.

Step 3: Final conclusion. \[ \boxed{\text{Assertion is true}} \] \[ \boxed{\text{Reason is false}}. \] Hence, \[ \boxed{\text{(C)}}. \]