Question

Assertion : 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:

Remember the binding energy curve:

Fusion releases energy for light nuclei
Fission releases energy for heavy nuclei
Maximum stability near iron

Answer 1

The Correct Option is C

The question examines our understanding of nuclear reactions, particularly fission and fusion, and their relation to binding energy. Let's analyze the assertion and reason to determine their validity.

<h3>Step-by-Step Analysis:</h3>

1. Understanding the Assertion (A):

   The assertion states that energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. This is true because:

   • Nuclear Fission: Heavy nuclei (like Uranium-235) split into lighter nuclei, with a net release of energy, due to the conversion of some mass into energy, as per E=mc^2.
   • Nuclear Fusion: Light nuclei (like Hydrogen isotopes) combine to form heavier nuclei, releasing energy in the process as they reach a more stable state.
   • The energy released in both processes is due to the increase in binding energy per nucleon, moving towards maximum stability.
2. Understanding the Reason (R):

   The reason states that for heavy nuclei, the binding energy per nucleon increases with increasing Z, while for light nuclei, it decreases with increasing Z. This is incorrect because:

   • For Heavy Nuclei: Binding energy per nucleon actually decreases with increasing atomic number (or Z) after reaching a peak (around Iron).
   • For Light Nuclei: Binding energy per nucleon increases with increasing atomic number up to Iron, after which it decreases.

   Therefore, Reason (R) is false as it inaccurately describes the behavior of binding energy across the nuclear chart.

3. Conclusion:

   The assertion is true as energy release is accurately explained by fission and fusion processes. However, the reason provided, due to its incorrect explanation of trends in binding energy per nucleon, is false. Hence, the correct answer is:

   Assertion (A) is true, but Reason (R) is false.

As additional information, students can refer to the curve of binding energy per nucleon versus mass number, which helps visualize why fusion happens at low atomic numbers and fission at high atomic numbers for energy release.

Answer 2

Let's reason through this using the shape of the binding-energy-per-nucleon curve rather than treating the assertion and reason as two separate claims to check one after another.

Picture the standard binding-energy-per-nucleon versus mass-number graph: it climbs steeply for the lightest nuclei, peaks around iron (mass number near 56), and then falls slowly for heavier nuclei.

Two consequences follow directly from this shape:
Light nuclei sit on the rising part of the curve, so combining them through fusion moves them further up the curve toward higher binding energy per nucleon, releasing energy in the process.
Heavy nuclei sit on the falling part of the curve, so splitting them through fission moves the fragments back up toward the peak, again releasing energy.
This confirms the assertion: both processes release energy because both move nuclei closer to the maximum-stability point at iron.

Now check the reason against the same curve. It claims binding energy per nucleon increases with increasing \( Z \) for heavy nuclei and decreases with increasing \( Z \) for light nuclei, but the curve shows precisely the reverse: it increases while nuclei are still light, up to iron, and decreases once nuclei get heavier than iron. So the reason inverts the true relationship and does not correctly describe why energy is released.

Since the assertion aligns with the graph but the reason contradicts it, the assertion stands true while the reason stands false.

Therefore, the correct answer is Assertion (A) is true, but Reason (R) is false.