Assertion A: The mass of a stable nucleus is less than the sum of the masses of its nucleons when free. Reason R: Nuclear density is nearly the same for all nuclei. Choose the correct answer.

Both A and R are correct but R is not the correct explanation of A

A is correct but R is not correct

A is not correct but R is correct

Both A and R are correct and R is the correct explanation of A

Nuclei

6 NEET-UG practice questions on Nuclei, part of Physics. The first 6 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Easy
A radioactive isotope has a half-life of 5 years. What percentage of its nuclei remains undecayed after 15 years?
1. A33.3%
2. B25%
3. C6.25%
4. D12.5%
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Answer: D · 12.5%
Fifteen years is 3 half-lives, so the fraction left is (1/2)³ = 1/8, which is 12.5%.
- A: Decay was treated as a linear loss.
- B: This counts only 2 half-lives.
- C: This counts 4 half-lives.
Remember this
After n half-lives the fraction remaining is (1/2)ⁿ; decay is not a uniform loss per year.
Question 2 · Easy
Assertion A: The mass of a stable nucleus is less than the sum of the masses of its nucleons when free. Reason R: Nuclear density is nearly the same for all nuclei. Choose the correct answer.
1. ABoth A and R are correct but R is not the correct explanation of A
2. BA is correct but R is not correct
3. CA is not correct but R is correct
4. DBoth A and R are correct and R is the correct explanation of A
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Answer: A · Both A and R are correct but R is not the correct explanation of A
A is true: the mass defect corresponds to the binding energy released when the nucleus forms. R is also true, since the nuclear radius varies as A^(1/3), so density does not depend on A. But density is not the cause of the mass defect.
- B: R is true, since nuclear volume varies directly with A.
- C: A is true: this is the mass defect.
- D: Constant density does not cause the mass defect; binding energy does.
Remember this
Mass defect comes from binding energy, E = Δm c²; constant density comes from volume being proportional to A.
Question 3 · Hard
Two radioactive samples X and Y start with equal numbers of nuclei. Their half-lives are 1 hour and 2 hours respectively. What is the ratio of the activity of X to that of Y after 4 hours?
1. A1 : 4
2. B2 : 1
3. C1 : 2
4. D1 : 8
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Answer: C · 1 : 2
After 4 h, X has gone through 4 half-lives and Y through 2, so N_X/N_Y = (1/16)/(1/4) = 1/4. Activity is λN, with λ_X/λ_Y = 2, as λ varies as 1/T. So the ratio is 2 × 1/4 = 1/2.
- A: This compares only the surviving numbers, ignoring λ.
- B: This ignores the fall in the number of nuclei and uses only λ.
- D: The decay constant ratio has been inverted.
Remember this
Activity is λN, so compare both the surviving nuclei and the decay constants.
Question 4 · Medium
A nucleus with A = 220 and binding energy per nucleon 7.5 MeV splits into two nuclei with A = 100 (8.5 MeV per nucleon) and A = 120 (8.4 MeV per nucleon), with no free neutrons. How much energy is released?
1. A9.4 MeV
2. B198 MeV
3. C208 MeV
4. D1858 MeV
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Answer: C · 208 MeV
Total binding energy after = 100 × 8.5 + 120 × 8.4 = 850 + 1008 = 1858 MeV, and before = 220 × 7.5 = 1650 MeV. The energy released is 1858 - 1650 = 208 MeV.
- A: The per-nucleon values were combined without multiplying by A.
- B: 8.4 MeV was used for both product nuclei.
- D: This is the final total binding energy, before subtracting the initial.
Remember this
Q value is final total binding energy minus initial total binding energy, each found by multiplying by A.
Question 5 · Medium
Using the binding energy curve drawn, in which X and Y are two marked nuclei, which of these statements are correct? A. Splitting one X into two Y nuclei releases about 216 MeV. B. Nucleons are bound more firmly, on average, in Y than in X. C. The total binding energy of X is less than that of Y. D. Binding energy per nucleon is greatest near A = 56.
Figure: MedExams
1. AB, C and D only
2. BA, B and D only
3. CA, C and D only
4. DA and B only
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Answer: B · A, B and D only
A is true: 2 × 120 × 8.5 − 240 × 7.6 = 2040 − 1824 = 216 MeV, or 240 × 0.9 = 216 MeV. B is true since 8.5 > 7.6, and D is read from the curve's peak. C is false: X has 1824 MeV in all, Y only 1020 MeV.
- A: Accepts C and rejects A, a fission release that the curve gives.
- C: Accepts C by comparing per-nucleon values in place of totals, and leaves out B.
- D: Leaves out D, which the peak of the curve shows.
Remember this
Energy is released when products have higher B.E. per nucleon; total B.E. still grows with A.
Question 6 · Medium
A radioactive sample starts with N₀ nuclei at t = 0. Which graph shows ln N, the natural logarithm of the undecayed nuclei, against time t?
Figure: MedExams
1. AGraph B
2. BGraph A
3. CGraph C
4. DGraph D
Answer and explanation in LearnFree account

Nuclei

A radioactive isotope has a half-life of 5 years. What percentage of its nuclei remains undecayed after 15 years?

Assertion A: The mass of a stable nucleus is less than the sum of the masses of its nucleons when free. Reason R: Nuclear density is nearly the same for all nuclei. Choose the correct answer.

Two radioactive samples X and Y start with equal numbers of nuclei. Their half-lives are 1 hour and 2 hours respectively. What is the ratio of the activity of X to that of Y after 4 hours?

A nucleus with A = 220 and binding energy per nucleon 7.5 MeV splits into two nuclei with A = 100 (8.5 MeV per nucleon) and A = 120 (8.4 MeV per nucleon), with no free neutrons. How much energy is released?

A radioactive sample starts with N₀ nuclei at t = 0. Which graph shows ln N, the natural logarithm of the undecayed nuclei, against time t?