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 that energy is released in fission and fusion because the products are more tightly bound than the reactants. The reason related to binding energy per nucleon is true but doesn't fully explain this energy release process.

Answer 1

The Correct Option is B

Let's break down the two parts of this question: ### Assertion (A): Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. This statement is true and aligns with our understanding of nuclear reactions: - In nuclear fission, a heavy nucleus (such as uranium) splits into two smaller nuclei, releasing a significant amount of energy. This occurs because the mass of the products is less than the mass of the original nucleus, and the difference in mass is converted into energy, according to Einstein's mass-energy equivalence (\( E = \Delta m c^2 \)). - In nuclear fusion, light nuclei (such as hydrogen) combine to form a heavier nucleus, also releasing energy. Fusion of light nuclei occurs in stars (including the sun), where hydrogen nuclei fuse to form helium, releasing energy. Thus, the assertion is correct: energy is indeed released in both fission and fusion processes. ### Reason (R): For heavy nuclei, binding energy per nucleon increases with increasing \( Z \) while for light nuclei, it decreases with increasing \( Z \). This statement is also true, but let's explain it more clearly: - **Binding energy per nucleon** refers to the energy required to disassemble a nucleus into its individual protons and neutrons. It is a measure of the stability of the nucleus. - For **heavy nuclei** (e.g., uranium, thorium), the binding energy per nucleon increases as the atomic number \( Z \) increases, up to a certain point. This means that as you go from lighter to heavier elements (but still within the range of stable nuclei), the nucleus becomes more tightly bound and stable. However, this increase in binding energy per nucleon is not indefinite—after a certain mass number, the binding energy begins to decrease. - For **light nuclei** (e.g., hydrogen, helium), the binding energy per nucleon decreases with increasing \( Z \). For example, the binding energy per nucleon for hydrogen (1 proton) is very low, and it increases for helium (with 2 protons), but for nuclei with a higher \( Z \) in the light element range, the binding energy decreases as you increase \( Z \). This is one of the reasons why lighter elements tend to undergo fusion (because they gain more binding energy per nucleon in the process), while heavier elements undergo fission. ### Why the Reason (R) does not fully explain Assertion (A): While Reason (R) is true, it does not fully explain why energy is released in both fission and fusion. The reason involves the fact that energy is released when the final products are more tightly bound (more stable) than the initial reactants. However, the assertion itself refers more to the general process of energy release during both fission (splitting heavy nuclei) and fusion (combining light nuclei), and the reason provides only part of the context related to binding energy per nucleon. Therefore, while the reason is correct, it does not directly explain the assertion. ### Conclusion: Both Assertion (A) and Reason (R) are true, but the reason does not provide the correct explanation for the assertion. The correct answer is thus (B). Final Answer: (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).