Nuclei PYQs Set 2 (PDF)

Set 2 of 8 · Questions 31-60 of 240

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Physics · Nuclei · Set 2 (Q31-60)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
31. $A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei, respectively is: [NEET 2022]$ (1) $4 : 5$ (2) $5 : 4$ (3) $25 : 16$ (4) $1 : 1$ 32. $Alpha rays emitted from a radioactive substance are$ (1) $negatively charged particles$ (2) $doubly ionised helium atoms$ (3) $ionised hydrogen nuclei$ (4) $uncharged particles$ 33. $If 200 MeV of energy is released in the fission of one nucleus of_{92}^{235} U, , then the number of nuclei that must undergo fission to release an energy of 1000 J is$ (1) $3.125 \times 10^{13}$ (2) $6.25 \times 10^{13}$ (3) $12.5 \times 10^{13}$ (4) $3.125 \times 10^{14}$ 34. $In a radioactive material the activity at time t_{1} is R_{1} and at a later time t_{2}, it is R_{2} . If the decay constant of the material is λ, then$ (1) $R_{1} = R_{2}$ (2) $R_{1} = R_{2} e-λt1-t2$ (3) $R_{1} = R_{2} eλt1-t2$ (4) $R_{1} = R_{2} t2lt1$ 35. $_{82}^{290} X \to α_{80}^{286} Y \to e^{+} Z \to β^{-} P \to e^{-} Q In the nuclear emission stated above, the mass number and atomic number of the product Q respectively are [NEET 2024]$ (1) $280,81$ (2) $286, 80$ (3) $288,82$ (4) $286, 81$ 36. $A radioactive element which can decay by two processes, has half-life t_{1} for first process and half-life t_{2} for second process. Let (t) be the effective average-life of this element. Which of the following is correct?$ (1) $⟨ t ⟩ < \frac{t _{1} t _{2}}{t _{1} + t _{2}}$ (2) $⟨ t ⟩ = \frac{t _{1} t _{2}}{t _{1} + t _{2}}$ (3) $⟨ t ⟩ > \frac{t _{1} t _{2}}{t _{1} + t _{2}}$ (4) $⟨ t ⟩ = ln 2 (\frac{t _{1} + t _{2}}{t _{1} t _{2}})$ 37. $The physics behind fusion test reactor is$ (1) $Newton's law of motion$ (2) $Trapping and cooling of atoms by laser beams and magnetic fields$ (3) $Magnetic confinement of plasma$ (4) $Motion of charged particles in electromagnetic fields$ 38. $The ratio of the nuclear radii of elements with mass numbers 216 and 125 is$ (1) $6 : 5$ (2) $216 : 125$ (3) $216 : 125$ (4) $none of these.$ 39. $If M (A; Z), M_{p} and M_{n} denote the masses of the nucleus_{Z}^{A} X, proton and neutron respectively in units of u (1 u = 931.5 MeV / c^{2}) and BE represents its binding energy in MeV, then$ (1) $M (A, Z) = Z M_{p} + (A - Z) M_{n} - BE$ (2) $M (A, Z) = Z M_{p} + (A - Z) M_{n} + \frac{BE}{c ^{2}}$ (3) $M (A, Z) = Z M_{p} + (A - Z) M_{n} - \frac{BE}{c ^{2}}$ (4) $M (A, Z) = Z M_{p} + (A - Z) M_{n} + BE$ 40. $A radioactive decay can form an isotope of the original nucleus with the emission of particles$ (1) $one α and two β$ (2) $four α and one β$ (3) $one α and four β$ (4) $one α and one β$ 41. $The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of_{2}^{4} He is(Given helium nucleus mass \approx 4.0015 u .)$ (1) $0.0305 J$ (2) $0.0305 erg$ (3) $28.4 MeV$ (4) $0.061 u$ 42. $In a radioactive decay process, the negatively charged emitted β ‐particles are$ (1) $the electrons produced as a result of the decay of neutrons inside the nucleus$ (2) $the electrons produced as a result of collisions between atoms$ (3) $the electrons orbiting around the nucleus$ (4) $the electrons present inside the nucleus.$ 43. $The count rate of a Geiger Muller counter for the radiation of a radioactive material of half‐life of 30 minutes decreases to 5 secon d^{- 1} after 2 hours. The initial count rate was$ (1) $80 secon d^{- 1}$ (2) $625 secon d^{- 1}$ (3) $20 secon d^{- 1}$ (4) $25 secon d^{- 1}$ 44. $Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:$ (1) $3 : 8$ (2) $1 : 8$ (3) $8 : 1$ (4) $9 : 8$ 45. $Radioactive material ' A ' has decay constant ' 8 λ' and material ' B ' has decay constant ' λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material ' A ' to that ' B ' will be \frac{1}{e} ?$ (1) $\frac{1}{λ}$ (2) $\frac{1}{7 λ}$ (3) $\frac{1}{8 λ}$ (4) $\frac{1}{9 λ}$ 46. $A nucleus z^{A} emits an α -particle with velocity v . The recoil speed of the daughter nucleus is$ (1) $\frac{A - 4}{4 v}$ (2) $\frac{4 v}{A - 4}$ (3) $v$ (4) $\frac{v}{4}$ 47. $The half‐life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is$ (1) $15$ (2) $30$ (3) $45$ (4) $60$ 48. $An alpha nucleus of energy \frac{1}{2} m v^{2} bombards a heavy nuclear target of charge Ze . Then the distance of closest approach for the alpha nucleus will be proportional to$ (1) $\frac{1}{Ze}$ (2) $v^{2}$ (3) $\frac{1}{m}$ (4) $\frac{1}{v ^{4}}$ 49. $Activity of a substance changes from 700 s^{- 1} to 500 s^{- 1} in 30 minute. Find its half-life in minutes$ (1) $66$ (2) $62$ (3) $56$ (4) $50$ 50. $The half-life period of element X is same as the mean life time of element Y . Assume initially X and Y have same number of atoms. Then$ (1) $Initially X and Y have same decay rates$ (2) $Always X and Y decay at same rate$ (3) $Y decays faster than X$ (4) $X decays faster than Y$ 51. $In any fission process the ratio \frac{mass of fission products}{mass of parent nucleus} is$ (1) $equal to 1$ (2) $greater than 1$ (3) $less than 1$ (4) $depends on the mass of the parent nucleus.$ 52. $The binding energy per nucleon is maximum in case of$ (1) $_{2}^{4} He$ (2) $_{26}^{56} Fe$ (3) $_{56}^{141} Ba$ (4) $_{92}^{235} U$ 53. $What is the respective number of α and β particles emitted in the following radioactive decay?^{200} X_{90} \to^{168} Y_{80}$ (1) $8 and 8$ (2) $8 and 6$ (3) $6 and 8$ (4) $6 and 6$ 54. $The mass of a \frac{7}{3} Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of_{3}^{7} Li nucleus is nearly$ (1) $46 MeV$ (2) $5.6 MeV$ (3) $3.9 MeV$ (4) $23 MeV$ 55. $A mixture consists of two radioactive materials A_{1} and A_{2} with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A_{1} and 160 g of A_{2} . The amount ofthe two in the mixture will become equal after$ (1) $60 s$ (2) $80 s$ (3) $20 s$ (4) $40 s$ 56. $The end product of decay of_{90} Th^{232} is_{82} Pb^{208} . The number of α and β particles emitted are respectively$ (1) $6,0$ (2) $3,3$ (3) $4,6$ (4) $6,4$ 57. $A radioactive sample is undergoing α decay. At any time t_{1}, its activity is A and another time t_{2} the activity is \frac{A}{5} . What is the average life time for the sample?$ (1) $\frac{t _{2} - t _{1}}{ln 5}$ (2) $\frac{1 n ( t _{2} + t _{1} )}{2}$ (3) $\frac{t _{1} - t _{2}}{1 n 5}$ (4) $\frac{1 n 5}{t _{2} - t _{1}}$ 58. $In the following nuclear reaction x stands for n \to p + e^{-} + x$ (1) $α -particle$ (2) $positron$ (3) $neutrino$ (4) $antinutrino$ 59. $In a radioactive decay chain, the initial nucleus is \frac{232}{90} Th . At the end there are 6 α -particles and 4 β -particles which areemitted. If the end nucleus is \frac{A}{Z} XA and Z are given by:$ (1) $A = 208; Z = 80$ (2) $A = 202; Z = 80$ (3) $A = 208; Z = 82$ (4) $A = 200; Z = 81$ 60. $Consider a nucleus_{30}^{60} x . It's approximate density is (Take 1 amu = 1.6 \times 10^{- 27} kg, R_{o} = 1.2 \times 10^{- 15} m .)$ (1) $1.2 \times 10^{18} kg / m^{3}$ (2) $8.5 \times 10^{19} kg / m^{3}$ (3) $3.3 \times 10^{16} kg / m^{3}$ (4) $2.2 \times 10^{17} kg / m^{3}$