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 \( Z \).
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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.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Both Assertion (A) and Reason (R) are false.
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The Correct Option isB
Solution and Explanation
The assertion states that energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. This is indeed true. In nuclear reactions, both fission and fusion result in the conversion of a small amount of nuclear mass into energy, as described by Einstein's mass-energy equivalence principle E = mc^2. In fission, a heavy nucleus splits into smaller nuclei, and in fusion, light nuclei combine to form a heavier nucleus.
To understand why energy is released, we need to consider binding energy per nucleon, which is a measure of the stability of a nucleus. For heavy nuclei, the binding energy per nucleon tends to increase when they split, thus releasing energy. For light nuclei, combining them into a heavier one also increases the binding energy per nucleon, releasing energy in the process.
The reason (R) states that for heavy nuclei, binding energy per nucleon increases with increasing atomic number \( Z \), while for light nuclei, it decreases with increasing \( Z \). While binding energy per nucleon generally increases for heavy nuclei as they split, and increases for light nuclei as they fuse, the reasoning linked to the increase or decrease with atomic number \( Z \) is not entirely correct in explaining the energy release during fission or fusion. The actual reason is related to the position of nuclei in the binding energy curve.
The binding energy curve shows that very light nuclei and very heavy nuclei both have higher potential gains in stability (higher binding energy per nucleon), which makes them prone to undergo fusion and fission, respectively, to reach a more stable state with higher binding energy per nucleon.
Therefore, both the assertion and reason are true independently, but the reason does not correctly explain the assertion. The correct relationship between binding energy and these nuclear reactions is more accurately related to the binding energy curve rather than simply changes in \( Z \).
The correct answer is: Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).