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

19 NEET-UG practice questions on Nuclei, part of Physics. The first 19 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
Question 7 · Hard
Samples of two radioactive nuclides X and Y start with equal numbers of nuclei. X has a half-life of 2 h and Y a half-life of 4 h. After how long will the number of undecayed X nuclei be one quarter of the number of undecayed Y nuclei?
1. A8 h
2. B2 h
3. C4 h
4. D16 h
Answer and explanation in LearnFree account
Question 8 · Medium
A radioactive nuclide has a half-life of 6.93 days. What are its decay constant and mean life?
1. A10 per day and 0.1 day
2. B0.1 per day and 4.8 days
3. C0.693 per day and 10 days
4. D0.1 per day and 10 days
Answer and explanation in LearnFree account
Question 9 · Medium
Why does the fission of a heavy nucleus such as uranium-235 release energy?
1. AThe fragments have a lower binding energy per nucleon than the parent nucleus
2. BThe fragments have a higher binding energy per nucleon than the parent nucleus
3. CThe number of nucleons increases during fission
4. DSome protons change into neutrons during fission
Answer and explanation in LearnFree account
Question 10 · Easy
How does the density of nuclear matter in a heavy nucleus such as uranium compare with that in a light nucleus such as carbon?
1. AIt is greater in uranium by a factor equal to the ratio of their mass numbers
2. BIt is nearly the same
3. CIt is much greater in carbon
4. DIt is much greater in uranium
Answer and explanation in LearnFree account
Question 11 · Medium
Nuclear radius follows R = R₀A^(1/3). What is the ratio of the radius of an aluminium-27 nucleus to that of a tellurium-125 nucleus?
1. A5 : 3
2. B3 : 5
3. C27 : 125
4. D9 : 25
Answer and explanation in LearnFree account
Question 12 · Medium
Two deuterium nuclei fuse to form a helium-4 nucleus. Taking the binding energy per nucleon as 1.1 MeV for ²H and 7.0 MeV for ⁴He, how much energy is released in each fusion?
1. A25.8 MeV
2. B28 MeV
3. C5.9 MeV
4. D23.6 MeV
Answer and explanation in LearnFree account
Question 13 · Easy
Which description of the nuclear force that binds protons and neutrons is correct?
1. ALong-ranged and falling as the inverse square of distance, like gravitation
2. BAttractive at every separation, however small
3. CActing only between protons, and not on neutrons
4. DShort-ranged, much stronger than the Coulomb force, and nearly independent of charge
Answer and explanation in LearnFree account
Question 14 · Medium
In the fusion reaction ²H + ²H → ³He + n, the masses are ²H = 2.014102 u, ³He = 3.016029 u and n = 1.008665 u. Taking 1 u = 931.5 MeV/c², how much energy is involved in each reaction?
1. A3.27 MeV released
2. B6.54 MeV released
3. C3.27 MeV absorbed
4. D1.63 MeV released
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Question 15 · Medium
Taking the mass of a hydrogen atom as 1.007825 u, that of a neutron as 1.008665 u, the mass of a ¹²C atom as exactly 12 u, and 1 u = 931.5 MeV/c², what is the binding energy per nucleon of ¹²C?
1. AAbout 15.4 MeV
2. BAbout 0.0082 MeV
3. CAbout 7.7 MeV
4. DAbout 92 MeV
Answer and explanation in LearnFree account
Question 16 · Medium
The activity of a radioactive sample falls from 800 Bq to 50 Bq in 20 days. What is its half-life?
1. A5 days
2. B1.25 days
3. C10 days
4. D6.7 days
Answer and explanation in LearnFree account
Question 17 · Easy
Isotones are nuclides with the same number of neutrons. Which pair are isotones?
1. A³H and ⁴He
2. B²H and ⁴He
3. C³H and ³He
4. D¹H and ²H
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Question 18 · Hard
In a radioactive sample, the ratio of decayed nuclei to undecayed nuclei is 15 after 8 hours. What was this ratio after 4 hours?
1. A4
2. B3
3. C1
4. D7.5
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Question 19 · Medium
Assertion A: Nuclear fusion needs an extremely high temperature, of the order of 10⁷ K as in the core of the Sun. Reason R: At such a temperature the nuclei have enough kinetic energy to overcome the attractive nuclear force between them. Choose the correct answer.
1. AA is correct but R is not correct
2. BA is not correct but R is correct
3. CBoth A and R are correct and R is the correct explanation of A
4. DBoth A and R are correct but R is not the correct explanation of A
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?

Samples of two radioactive nuclides X and Y start with equal numbers of nuclei. X has a half-life of 2 h and Y a half-life of 4 h. After how long will the number of undecayed X nuclei be one quarter of the number of undecayed Y nuclei?

A radioactive nuclide has a half-life of 6.93 days. What are its decay constant and mean life?

Why does the fission of a heavy nucleus such as uranium-235 release energy?

How does the density of nuclear matter in a heavy nucleus such as uranium compare with that in a light nucleus such as carbon?

Nuclear radius follows R = R₀A^(1/3). What is the ratio of the radius of an aluminium-27 nucleus to that of a tellurium-125 nucleus?

Two deuterium nuclei fuse to form a helium-4 nucleus. Taking the binding energy per nucleon as 1.1 MeV for ²H and 7.0 MeV for ⁴He, how much energy is released in each fusion?

Which description of the nuclear force that binds protons and neutrons is correct?

In the fusion reaction ²H + ²H → ³He + n, the masses are ²H = 2.014102 u, ³He = 3.016029 u and n = 1.008665 u. Taking 1 u = 931.5 MeV/c², how much energy is involved in each reaction?

Taking the mass of a hydrogen atom as 1.007825 u, that of a neutron as 1.008665 u, the mass of a ¹²C atom as exactly 12 u, and 1 u = 931.5 MeV/c², what is the binding energy per nucleon of ¹²C?

The activity of a radioactive sample falls from 800 Bq to 50 Bq in 20 days. What is its half-life?

Isotones are nuclides with the same number of neutrons. Which pair are isotones?

In a radioactive sample, the ratio of decayed nuclei to undecayed nuclei is 15 after 8 hours. What was this ratio after 4 hours?

Assertion A: Nuclear fusion needs an extremely high temperature, of the order of 10⁷ K as in the core of the Sun. Reason R: At such a temperature the nuclei have enough kinetic energy to overcome the attractive nuclear force between them. Choose the correct answer.