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.
Statement I is true but Statement II is false
Both Statement I and Statement II are false
Statement I is false but Statement II is true
Both Statement I and Statement II are true
Correct answer:C
Standard Method
Given: Two statements about binding energy per nucleon and nuclear stability.
Find: Which statement is true.
Step 1: Analyse Statement I. Binding energy per nucleon does not keep increasing as nuclear mass increases. It reaches a maximum near iron and then decreases for heavier nuclei. Therefore, Statement I is false.
Step 2: Analyse Statement II. Nuclei tend to transform in ways that increase binding energy per nucleon, because that leads to greater stability. This is why fusion of light nuclei and fission of very heavy nuclei release energy. Therefore, Statement II is true.
Step 3: Conclude. So the correct choice is: Statement I is false but Statement II is true. Therefore, the correct option is C.
Note: The solution states "corresponding to option (1)" after concluding I is false and II is true. This conflicts with the listed options. Based on the statement analysis, the defensible correct option is C.
Binding Energy Trend
Given: Nuclear stability depends on binding energy per nucleon.
Find: The truth value of both statements.
The graph of binding energy per nucleon versus mass number rises for light nuclei, reaches a peak near nucleons around iron, and then slowly falls for heavier nuclei. Hence a larger nuclear mass does not always mean greater binding energy per nucleon.
So Statement I is false.
Also, spontaneous or induced nuclear processes generally move nuclei toward greater stability, which corresponds to higher binding energy per nucleon. Thus light nuclei undergo fusion and very heavy nuclei undergo fission to move toward more stable configurations.
So Statement II is true.
Therefore, the correct option is C.
Assuming binding energy per nucleon always increases with mass number. This is wrong because it peaks near iron and then decreases for heavier nuclei. Always recall the peak stability curve instead of using a monotonic trend.
Confusing total binding energy with binding energy per nucleon. A heavier nucleus may have larger total binding energy, but not necessarily larger binding energy per nucleon. Compare the correct quantity before judging stability.
Trusting the answer key label without checking the statement logic. Here the solution text concludes Statement I is false and Statement II is true, which matches option C, not option A. Always map the conclusion back to the listed options carefully.
Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.
