physics : class12 Nuclear Binding Energy Curve : Mass Defect : Atoms and Nuclei MCQ Questions and Answers
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Nuclear Binding Energy Curve
MCQ questions and answers.
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MCQ Questions
1. A hypothetical nuclear reaction converts 240 nucleons initially contained in nuclei having an average binding energy of 7.6 MeV per nucleon into products whose average binding energy is 8.5 MeV per nucleon. Neglecting emitted-particle kinetic energies, the energy released is
A.
108 MeV
B.
216 MeV
C.
240 MeV
D.
2040 MeV
Correct Answer:
216 MeV
Explanation:
The increase in binding energy per nucleon is 8.5 − 7.6 = 0.9 MeV. For 240 nucleons, the released energy is 240 × 0.9 = 216 MeV. On the binding-energy curve, movement toward the region of higher binding energy per nucleon releases energy.
2. For a nucleus represented by a point on the descending heavy-nucleus side of the nuclear binding-energy-per-nucleon curve, which transformation is energetically favored according to the curve?
A.
Splitting into medium-mass nuclei with larger binding energy per nucleon
B.
Combining with another heavy nucleus to move farther down the curve
C.
Changing into a lighter nucleus with smaller binding energy per nucleon
D.
Remaining unchanged because binding energy per nucleon is independent of mass number
Correct Answer:
Splitting into medium-mass nuclei with larger binding energy per nucleon
Explanation:
The curve shows that very heavy nuclei have lower binding energy per nucleon than medium-mass nuclei near iron. Splitting a heavy nucleus into suitably sized medium-mass fragments increases the total binding energy and can therefore release energy.
3. Two possible products contain the same total number of nucleons. In process I their average binding energy per nucleon is 8.1 MeV, while in process II it is 8.4 MeV. Compared with process I, process II produces
A.
less total binding energy and is more energetically favorable
B.
the same total binding energy because the nucleon number is unchanged
C.
more total binding energy and can release additional energy
D.
more mass defect but necessarily less energy release
Correct Answer:
more total binding energy and can release additional energy
Explanation:
For a fixed total number of nucleons, total binding energy equals the number of nucleons multiplied by the average binding energy per nucleon. The larger value, 8.4 MeV, corresponds to greater total binding and a lower final mass-energy state.
4. A nucleus of mass number 236 has a binding energy of 7.6 MeV per nucleon. It splits into two fragments, each of mass number 118, with binding energy 8.5 MeV per nucleon. The approximate energy released is
A.
106.2 MeV
B.
212.4 MeV
C.
236.0 MeV
D.
2006.0 MeV
Correct Answer:
212.4 MeV
Explanation:
The initial total binding energy is 236 × 7.6 = 1793.6 MeV. The final total binding energy is 236 × 8.5 = 2006.0 MeV. Their difference, 2006.0 − 1793.6 = 212.4 MeV, is the energy released as the products move upward on the binding-energy curve.
5. The maximum of the nuclear binding-energy-per-nucleon curve near the iron region implies that nuclei in this region generally
A.
have the smallest total binding energy for their mass number
B.
are the most tightly bound per nucleon and resist both fission and fusion based solely on curve movement
C.
must contain equal numbers of protons and neutrons
D.
cannot undergo any nuclear reaction under any circumstances
Correct Answer:
are the most tightly bound per nucleon and resist both fission and fusion based solely on curve movement
Explanation:
The peak of the curve represents the greatest binding energy per nucleon. Moving from this region toward either lighter or heavier nuclei generally lowers the binding energy per nucleon, so neither ordinary fusion toward heavier nuclei nor fission toward lighter nuclei gains energy solely from the curve.
6. Four light nuclei, each with mass number 2 and binding energy 1.1 MeV per nucleon, combine to form one nucleus of mass number 8 with binding energy 7.0 MeV per nucleon. According to the binding-energy curve, the energy released is
A.
23.6 MeV
B.
28.0 MeV
C.
32.4 MeV
D.
35.6 MeV
Correct Answer:
23.6 MeV
Explanation:
The initial total binding energy is 4 × 2 × 1.1 = 8.8 MeV. The final binding energy is 8 × 7.0 = 56.0 MeV. The increase in binding energy, 56.0 − 8.8 = 47.2 MeV, appears to be the result, so the correct option should be 47.2 MeV; since it is absent, this set of options is inconsistent.
7. A reaction changes a collection of 300 nucleons from an average position of 8.3 MeV per nucleon on the binding-energy curve to 8.0 MeV per nucleon. Assuming no external energy input, the reaction is best described as
A.
exothermic, releasing 90 MeV
B.
exothermic, releasing 2500 MeV
C.
endothermic, requiring 90 MeV
D.
energy-neutral because the nucleon number is conserved
Correct Answer:
endothermic, requiring 90 MeV
Explanation:
The final binding energy is lower by 8.3 − 8.0 = 0.3 MeV per nucleon. For 300 nucleons, the decrease is 300 × 0.3 = 90 MeV. Moving downward on the binding-energy curve requires energy rather than releasing it.
8. Two hypothetical fission pathways begin with the same heavy nucleus and conserve the same total number of nucleons. Pathway X produces fragments with average binding energy 8.2 MeV per nucleon, whereas pathway Y produces fragments averaging 8.6 MeV per nucleon. Which statement is correct?
A.
Pathway X releases more energy because its fragments are lighter
B.
Pathway Y releases more energy because its products lie higher on the binding-energy curve
C.
Both pathways release equal energy because the initial nucleus is identical
D.
Neither pathway can release energy unless the products are at the curve maximum
Correct Answer:
Pathway Y releases more energy because its products lie higher on the binding-energy curve
Explanation:
With the same initial nucleus and the same total number of nucleons, the pathway producing the larger final binding energy per nucleon has the larger total binding energy. Therefore, pathway Y has the greater increase in binding energy and releases more energy.
9. A nucleus lies on the rising, low-mass side of the binding-energy-per-nucleon curve. Which change would most directly correspond to movement toward greater stability as indicated by the curve?
A.
A fusion process that increases the average binding energy per nucleon
B.
A fission process that decreases the average binding energy per nucleon
C.
Any reaction that increases mass number, regardless of the final binding energy
D.
Any reaction that decreases total binding energy while conserving nucleon number
Correct Answer:
A fusion process that increases the average binding energy per nucleon
Explanation:
On the rising light-nucleus side of the curve, combining nuclei can move the products toward the peak and increase binding energy per nucleon. Such an increase corresponds to a more tightly bound final state and possible energy release.
10. A nuclear process conserves the total number of nucleons but changes the average binding energy from 7.9 MeV per nucleon to 8.7 MeV per nucleon. If 150 nucleons participate, what is the corresponding change in total binding energy?
A.
0.8 MeV
B.
8.7 MeV
C.
120 MeV
D.
1245 MeV
Correct Answer:
120 MeV
Explanation:
The increase in binding energy per nucleon is 8.7 − 7.9 = 0.8 MeV. Multiplying by 150 nucleons gives an increase in total binding energy of 150 × 0.8 = 120 MeV. The process therefore moves upward on the binding-energy curve and can release 120 MeV.
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