Given below are two statements:
Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II: For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.
Choose the correct answer.
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Maximum nuclear stability occurs near iron due to peak binding energy per nucleon.
The question presents two statements regarding the binding energy per nucleon in atomic nuclei. Let's analyze each statement:
Statement I: "For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon."
The binding energy per nucleon is a measure of how strongly the nucleons (protons and neutrons) are held together in a nucleus. Generally, as we move from lighter nuclei to heavier nuclei, the binding energy per nucleon initially increases, reaching a peak around the region of iron and nickel isotopes (such as \(^{56}\text{Fe}\) and \(^{62}\text{Ni}\)), and then begins to decrease for nuclei heavier than these.
This pattern is due to the balance between the attractive nuclear force and the repulsive Coulomb force. However, for the very heavy nuclei, such as uranium, the binding energy per nucleon is actually lower than for lighter (but still relatively heavy) elements like iron.
Thus, the statement "greater the mass of the nucleus, greater is the binding energy per nucleon" is not true for all elements, particularly for very heavy elements where the binding energy per nucleon decreases. Therefore, Statement I is false.
Statement II: "For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon."
This statement relates to nuclear reactions, such as fusion and fission. In fusion, lighter nuclei combine to form a heavier nucleus with higher binding energy per nucleon, releasing energy. In fission, a heavy nucleus splits into lighter nuclei, again increasing the binding energy per nucleon and releasing energy.
While it is generally true that nuclear transformations occur towards configurations with greater binding energy per nucleon, this is not always the path for all nuclei. Some nuclear decays do not result in an increase in binding energy per nucleon; rather, they aim at increasing nuclear stability by other means (e.g., alpha decay in heavy elements where the daughter nucleus does not have a significantly larger binding energy per nucleon).
Therefore, the notion that all nuclear transformations result in a transformation from less to more binding energy is not universally valid. Thus, Statement II is false.
Conclusion: After analyzing both statements, we determine the correct answer is: Both Statement I and Statement II are false.
