STD 12 - Nuclei PYQs: JEE Mains Physics

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1. 1. 7.9 MeV \( \alpha \)-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) __________m.
   \(\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 Nm ^2 / C ^2\right.\) and electron charge \(\left.=1.6 \times 10^{-19} C \right]\) 2026 Medium
2. 2. A nucleus has mass number \(\alpha\) and radius \(R_{\alpha}\). Another nucleus has mass number \(\beta\) and radius \(R_{\beta}\). If \(\beta = 8\alpha\) then \(R_{\alpha}/R_{\beta}\) is : 2026 Medium
3. 3. An atom \({ }_3^8 X\) is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by : 2026 Medium
4. 4. Assuming the experimental mass of \({}^{12}_{6}C\) as \(12\text{ u}\), the mass defect of \({}^{12}_{6}C\) atom is _______ \(\text{MeV}/c^2\).
   (Mass of proton \(= 1.00727\text{ u}\), mass of neutron \(= 1.00866\text{ u}\), \(1\text{ u} = 931.5\text{ MeV}/c^2\) and \(c\) is the speed of the light in vacuum). 2026 Hard
5. 5. 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 transforms to nuclei with greater binding energy per nucleon.
   In the light of the above statements, choose the correct answer from the options given below: 2026 Hard
6. 6. The average energy released per fission for the nucleus of \({ }_{92}^{235} U\) is 190 MeV . When all the atoms of 47 g pure \({ }_{92}^{235} U\) undergo fission process, the energy released is \(\alpha \times 10^{23} MeV\). The value of \(\alpha\) is ___________.
   (Avogadro Number \(=6 \times 10^{23}\) per mole) 2026 Easy
7. 7. The binding energy for the following nuclear reactions are expressed in MeV .
   \({ }_2 He ^3+{ }_0 n ^1 \rightarrow{ }_2 He ^4+20 MeV\)
   \({ }_2 He ^4+{ }_0 n ^1 \rightarrow{ }_2 He ^5-0.9 MeV\)
   If \(X _3, X _4, X _5\) denote the stability of \({ }_2 He ^3,{ }_2 He ^4\) and \({ }_2 He ^5\), respectively, then the correct order is : 2026 Medium
8. 8. The binding energy per nucleon of \(^{209}_{83}Bi\) is _______ MeV.
   \([\text{Take } m(^{209}_{83}Bi) = 208.980388 \, u, \, m_p = 1.007825 \, u, \, m_n = 1.008665 \, u, \, 1 \, u = 931 \, \text{MeV}/c^2]\) 2026 Medium
9. 9. The energy released if hydrogen atoms are combined to form \(^{4}_{2}\text{He}\) is __________ MeV. (Take binding energies per nucleon of \(^{2}_{1}\text{H}\) and \(^{4}_{2}\text{He}\) as \(1.1\) MeV and \(7.2\) MeV, respectively) 2026 Medium
10. 10. The energy released when \(\dfrac{7}{17.13}\) kg of \(^{7}_{3}\text{Li}\) is converted into \(^{4}_{2}\text{He}\) by proton bombardment is \(\alpha \times 10^{32}\) eV. The value of \(\alpha\) is _______. (Nearest integer) (Mass of \(^{7}_{3}\text{Li} = 7.0183\) u, mass of \(^{4}_{2}\text{He} = 4.004\) u, mass of proton \(= 1.008\) u and \(1\) u \(= 931\) MeV/c\(^2\) and Avogadro number \(= 6.0 \times 10^{23}\)) 2026 Hard
11. 11. The minimum frequency of photon required to break a particle of mass 15.348 amu into 4\( \alpha \) particles is __________ kHz.
    [mass of He nucleus = 4.002 amu,
    \(1 amu =1.66 \times 10^{-27} kg, h =6.6 \times 10^{-34} J . s\) and \(c =\) \(\left.3 \times 10^8 m / s \right]\) 2026 Medium
12. 12. Two nuclei of mass number \(3\) combine with another nucleus of mass number \(4\) to yield a nucleus of mass number \(10\). If the binding energy per nucleon for the mass numbers \(3\), \(4\) and \(10\) are \(5.6\) MeV, \(7.4\) MeV and \(6.1\) MeV, respectively, then in the process, \(\Delta Mc^2 = \) _____ MeV. 2026 Medium
13. 13. Two radioactive substances A and B of mass numbers \(200\) and \(212\) respectively, shows spontaneous \(\alpha\)-decay with same \(Q\) value of \(1\) MeV. The ratio of energies of \(\alpha\)-rays produced by A and B is ________. 2026 Medium
14. 14. Which of the following pair of nuclei are isobars of the element? 2026 Easy
15. 15. A radioactive nucleus \(n_2\) has 3 times the decay constant as compared to the decay constant of another radioactive nucleus \(n_1\). If initial number of both nuclei are the same, what is the ratio of number of nuclei of \(n_2\) to the number of nuclei of \(n_1\), after one half-life of \(n_1\) ? 2025 Medium
16. 16. Choose the correct nuclear process from the below options.
    [p: proton, n : neutron, \(\mathrm{e}^{-}\): electron, \(\mathrm{e}^{+}\): positron, \(v:\) neutrino, \(\bar{v}\) : antineutrino] 2025 Easy
17. 17. Energy released when two deuterons \(\left({ }_1 \mathrm{H}^2\right)\) fuse to form a helium nucleus \(\left({ }_2 \mathrm{He}^4\right)\) is :
    (Given : Binding energy per nucleon of \({ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}\) and binding energy per nucleon of \({ }_2 \mathrm{He}^4=7.0 \mathrm{MeV}\)) 2025 Easy
18. 18. For a nucleus of mass number \(A\) and radius \(R\), the mass density of nucleus can be represented as how? 2025 Easy
19. 19. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : The density of the copper \(\left({ }_{29}^{64} \mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({ }_6^{12} \mathrm{C}\right)\) nucleus.
    Reason (R): The nucleus of mass number A has a radius proportional to \(\mathrm{A}^{1 / 3}\).
    In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Easy
20. 20. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170.
    Reason (R): Nuclear force is long range.
    In the light of the above statements, choose the correct answer from the options given below : 2025 Easy
21. 21. Match the LIST-I with LIST-II.

    LIST-I	LIST-II
    (A) \(_0^1n + _{92}^{235}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + 2_0^1n\)	(I) Chemical reaction
    (B) \(2H_2 + O_2 \rightarrow 2H_2O\)	(II) Fusion with +ve Q value
    (C) \(_1^2H + _1^2H \rightarrow _2^3He + _0^1n\)	(III) Fission
    (D) \(_1^1H + _1^3H \rightarrow _1^2H + _1^2H\)	(IV) Fusion with -ve Q value

    
    Choose the correct answer from the options given below : 2025 Medium
22. 22. The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation. 2025 Easy
23. 23. A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :- 2024 Hard
24. 24. A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If relation between mass number is \(A_2=4 A_1\), then \(\frac{V_2}{V_1}=\)_______. 2024 Hard
25. 25. A star has \(100 \%\) helium composition. It starts to convert three \({ }^4 \mathrm{He}\) into one \({ }^{12} \mathrm{C}\) via triple alpha process as \({ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}\). The mass of the star is \(2.0 \times 10^{32} \mathrm{~kg}\) and it generates energy at the rate of \(5.808 \times 10^{30} \mathrm{~W}\). The rate of converting these \({ }^4 \mathrm{He}\) to \({ }^{12} \mathrm{C}\) is \(\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}\), where \(\mathrm{n}\) is _______. [Take, mass of \({ }^4 \mathrm{He}=4.0026 \mathrm{u}\), mass of \({ }^{12} \mathrm{C}=12 \mathrm{u}\)] 2024 Hard
26. 26. Binding energy of a certain nucleus is \(18 \times 10^8 J\). How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus? 2024 Medium
27. 27. From the statements given below :
    \((A)\) The angular momentum of an electron in \(n^{\text {th }}\) orbit is an integral multiple of \(h\).
    \((B)\) Nuclear forces do not obey inverse square law.
    \((C)\) Nuclear forces are spin dependent.
    \((D)\) Nuclear forces are central and charge independent.
    \((E)\) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below : 2024 Hard
28. 28. If \(M_0\) is the mass of isotope \({ }_5^{12} B, M_p\) and \(M_n\) are the masses of proton and neutron, then nuclear binding energy of isotope is _______. 2024 Hard
29. 29. If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _______ \(\times 10^{-2} \mathrm{MeV}\). (Given \(1 \mathrm{u}=931 \mathrm{MeV} / \mathrm{c}^2\), atomic mass of helium \(=4.002603 \mathrm{u}\) ) 2024 Hard
30. 30. In a hypothetical fission reaction \({ }_{92} \mathrm{X}^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} \mathrm{Z}^{92}+3 \mathrm{R}\) The identity of emitted particles \((R)\) is _______. 2024 Hard
31. 31. In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6\  \mathrm{MeV} /\) Nucleon dissociated into middle mass nuclides \((A \approx 118)\), having binding energy of \(8.6 \ \mathrm{MeV} / \mathrm{Nucleon}\). The energy released in the process would be \(\mathrm{MeV}\). 2024 Hard
32. 32. In a nuclear fission reaction of an isotope of mass \(M\), three similar daughter nucler of same mass are formed. The speed of a daughter nuclei in terms of mass defect \(\Delta \mathrm{M}\) will be _______. 2024 Hard
33. 33. The atomic mass of \({ }_6 \mathrm{C}^{12}\) is \(12.000000\ \mathrm{u}\) and that of \({ }_6 \mathrm{C}^{13}\) is \(13.003354 \ \mathrm{u}\). The required energy to remove a neutron from \({ }_6 \mathrm{C}^{13}\), if mass of neutron is \(1.008665 \ \mathrm{u}\), will be : 2024 Hard
34. 34. The disintegration energy \(Q\) for the nuclear fission of \({ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+\mathrm{n}\) is _______ \(\mathrm{MeV}\). Given atomic masses of \({ }^{235} \mathrm{U}: 235.0439 \mathrm{u},{ }^{140} \mathrm{Ce} ; 139.9054 \mathrm{u},\) \({ }^{94} \mathrm{Zr}: 93.9063 \mathrm{u} ; \mathrm{n}: 1.0086 \mathrm{u},\) Given Value of \(\mathrm{c}^2=931 \mathrm{MeV} / \mathrm{u}\) 2024 Hard
35. 35. The energy equivalent of \(1 \mathrm{~g}\) of substance is _______. 2024 Medium
36. 36. The energy released in the fusion of \(2 \mathrm{~kg}\) of hydrogen deep in the sun is \(\mathrm{E}_{\mathrm{H}}\) and the energy released in the fission of \(2 \mathrm{~kg}\) of \({ }^{235} \mathrm{U}\) is \(E_U\). The ratio \(\frac{E_H}{E_U}\) is approximately _______. (Consider the fusion reaction as \(4{ }_1^1 \mathrm{H}+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 \mathrm{v}+6 \gamma+26.7 \mathrm{MeV}\), energy released in the fission reaction of \({ }^{235} \mathrm{U}\) is \(200 \mathrm{MeV}\) per fission nucleus and \(\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}\) ) 2024 Hard
37. 37. The explosive in a Hydrogen bomb is a mixture of \({ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3\) and \({ }_3 \mathrm{Li}^6\) in some condensed form. The chain reaction is given by \( { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \) \( { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1\) During the explosion the energy released is approximately [Given : \(\mathrm{M}(\mathrm{Li})=6.01690\  \mathrm{amu} . \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \  amu.\) \(\mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388\  \mathrm{amu}\),\( and\ \)\(1 \ \mathrm{amu}=931.5\) \(\mathrm{MeV}]\) 2024 Hard
38. 38. The mass defect in a particular reaction is \(0.4 \mathrm{~g}\). The amount of energy liberated is \(\mathrm{n} \times 10^7 \mathrm{kWh}\), where\(\mathrm{n}=\)________. (speed of light \(=3 \times 10^8 \mathrm{~m} / \mathrm{s}\) ) 2024 Hard
39. 39. The mass number of nucleus having radius equal to half of the radius of nucleus with mass number \(192\) is _______. 2024 Hard
40. 40. The radius of a nucleus of mass number \(64\) is \(4.8\) fermi. Then the mass number of another nucleus having radius of \(4\) fermi is \(\frac{1000}{x}\), where \(x\) is _______. 2024 Hard
41. 41. Which of the following nuclear fragments corresponding to nuclear fission between neutron \(\left({ }_0^1 \mathrm{n}\right)\) and uranium isotope \(\left({ }_{92}^{235} \mathrm{U}\right)\) is correct: 2024 Hard
42. 42. \({ }_{92}^{238} A \rightarrow{ }_{90}^{234} B +{ }_2^4 D + Q\) In the given nuclear reaction, the approximate amount of energy released will be \(.....\,MeV\) \(\text { [Given, mass of }{ }_{92}^{238} A =238.05079 \times 931.5\,MeV / c ^2\) \(\text { mass of }{ }_{90}^{234} B =234.04363 \times 931.5\,MeV / c ^2\) \(\text { mass of } \left.{ }_2^4 D =4.00260 \times 931.5\,MeV / c ^2\right]\) 2023 Easy
43. 43. A common example of alpha decay is \({ }_{82}^{238} U \longrightarrow{ }_{80}^{234} Th +{ }_2 He ^4+ Q\).  ( Given : \({ }_{92}^{238} U =238.05060 u ,\) \({ }_{90}^{234} Th =234.04360 u ,\) \({ }_2^4 He =4.00260 u \text {, and }\) \(1 u =931.5 \frac{ MeV }{ c ^2} )\). The energy released \((Q)\) during the alpha decay of \({ }_{92}^{238} U\) is \(......\,MeV\) 2023 Medium
44. 44. A free neutron decays into a proton but a free proton does not decay into neutron. This is because 2023 Medium
45. 45. A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is \(1: 2^{1 / 3}\).Their respective speed have a ratio of \(n: 1\). The value of \(n\) is \(.....\). 2023 Medium
46. 46. A nucleus disintegrates into two smaller parts, which have their velocities in the ratio \(3: 2\). The ratio of their nuclear sizes will be \(\left(\frac{x}{3}\right)^{\frac{1}{3}}\). The value of ' \(x\) ' is : 2023 Medium
47. 47. A nucleus with mass number \(242\) and binding energy per nucleon as \(7.6\,MeV\) breaks into fragment each with mass number \(121\) . If each fragment nucleus has binding energy per nucleon as \(8.1\,MeV\), the total gain in binding energy is \(........MeV\) 2023 Medium
48. 48. A radio-active material is reduced to \(1 / 8\) of its original amount in \(3\) days. If \(8 \times 10^{-3}\,kg\) of the material is left after \(5\) days. The initial amount of the material is \(.......\,g\) 2023 Medium
49. 49. A radioactive element \({ }_{92}^{242} X\) emits two \(\alpha\)-particles, one electron and two positrons. The product nucleus is represented by \({ }_{ P }^{234} Y\). The value of \(P\) is \(..................\) 2023 Medium
50. 50. A radioactive nucleus decays by two different process. The half life of the first process is \(5\) minutes and that of the second process is \(30\,s\). The effective half-life of the nucleus is calculated to be \(\frac{\alpha}{11}\,s\). The value of \(\alpha\) is \(..............\) 2023 Medium

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