Nuclei PYQs Set 1 (PDF)

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Mere Teacher · Previous Year Questions JEE Main Physics · Nuclei · Set 1 (Q1-30)
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1. $A radioactive nucleus can decay by two different processes. The half lives of the first and second decay processes are 5 \times 10^{3} and 10^{5} years respectively. Then, the effective half-life of the nucleus is$ (1) $105 \times 10^{5} yr$ (2) $4762 yr$ (3) $10^{4} yr$ (4) $47.6 yr$ 2. $α -decay of a parent nucleus X results in a daughter nucleus Y. If m_{x}, m_{y} and m_{a} are the masses of the parent nucleus, the daughter nucleus and the α - particle respectively, then the net kinetic energy gained in the process is$ (1) $(m_{x} + m_{a} - m_{y}) c^{2}$ (2) $(m_{x} - m_{y} - m_{a}) c^{2}$ (3) $(m_{x} + m_{y} + m_{a}) c^{2}$ (4) $(m_{x} + m_{y} - m_{a}) c^{2}$ 3. $Half life of a radioactive element is 12.5 hour and its quantity is 256 g . After how much time its quantity will remain 1 g ?$ (1) $50 hrs$ (2) $100 hrs$ (3) $150 hrs$ (4) $200 hrs$ 4. $The activity of a radioactive sample is measured as N_{0} counts per minute at t = 0 and N_{0} / e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is$ (1) $lo g_{e} \frac{2}{5}$ (2) $\frac{5}{lo g _{e} 2}$ (3) $5 lo g_{10} 2$ (4) $5 lo g_{e} 2$ 5. $A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energy in the process is [NEET 2021]$ (1) $0.9 MeV$ (2) $9.4 MeV$ (3) $804 MeV$ (4) $216 MeV$ 6. $A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2 : 1 . What will be the ratio of their nuclear size (nuclear radius)?$ (1) $3^{1/2} : 1$ (2) $1 : 3^{1/2}$ (3) $2^{1/3} : 1$ (4) $1 : 2^{1/3}$ 7. $Fusion reaction takes place at high temperature because$ (1) $nuclei break up at high temperature$ (2) $atoms get ionized at high temperature$ (3) $kinetic energy is high enough to overcome the coulomb repulsion between nuclei$ (4) $molecules break up at high temperature$ 8. $The graph of ln (\frac{R}{R _{o}}) versus ln A is where R is radius of a nucleus, A is its mass number, and R_{0} is constant$ (1) $A straight line$ (2) $A circle of radius R$ (3) $A parabola$ (4) $An ellipse$ 9. $Activity of a radioactive sample decreases to (1/3)^{rd} of its original value in 3 days. Then, in 9 days its activity will become$ (1) $(1/27) of the original value$ (2) $(1/9) of the original value$ (3) $(1/18) of the original value$ (4) $(1/3) of the original value.$ 10. $A nucleus with mass number 220 initially at rest emits an alpha particle. If the Q value of reaction is 5.5 MeV, calculate the value of kinetic energy of alpha particle.$ (1) $6.5 MeV$ (2) $5.4 MeV$ (3) $7.4 MeV$ (4) $4.5 MeV$ 11. $Two radioactive materials A and B have decay constants 10 λ and λ, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/ e after a time:$ (1) $\frac{1}{9 λ}$ (2) $\frac{1}{11 λ}$ (3) $\frac{11}{10 λ}$ (4) $\frac{1}{10 λ}$ 12. $The relation between half life (T) and decay constant (λ) is$ (1) $λT = log_{e} 2$ (2) $λT = 1$ (3) $λ = log 2 T$ (4) $λT = 1 2$ 13. $β decay means emission of electron from$ (1) $innermost electron orbit$ (2) $a stable nucleus$ (3) $outermost electron orbit$ (4) $radioactive nucleus.$ 14. $A nucleus of mass 20 u emits a γ photon of energy 6 MeV . If the emission assume to occur when nucleus is free and at rest, then the nucleus will have kinetic energy nearest to (take 1 u = 1.6 \times 10^{- 27} kg)$ (1) $10 keV$ (2) $1 keV$ (3) $0.1 keV$ (4) $100 keV$ 15. $The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 \times 10^{- 15}) A^{1/3} m It follows that the mass density of a nucleus is of the order of (M_{prot .} ≅ M_{neut .} = 1.67 \times 10^{- 27} kg)$ (1) $10^{24} kgm^{- 3}$ (2) $10^{10} kgm^{- 3}$ (3) $10^{17} kgm^{- 3}$ (4) $10^{3} kgm^{- 3}$ 16. $The half life of a stream of radioactive particles moving along a straight path with a constant kinetic energy of 4 eV is 1 minute. The percentage of particles which decay before travelling a distance of 3.6 km is (Mass of the radioactive particles = 3.2 \times 10^{- 21} kg and charge of the electron = 1.6 \times 10^{- 19} C).$ (1) $87.5$ (2) $175$ (3) $37.5$ (4) $75$ 17. $The mass number and the volume of a nucleus is M and V, respectively. If the mass number is increased to 2 M, then the volume is changed to$ (1) $4 V$ (2) $\frac{V}{2}$ (3) $2 V$ (4) $8 V$ 18. $Nuclear fission and fusion can be explained on the basis of$ (1) $Einstein's theory of relativity$ (2) $Einstein specific heat equation$ (3) $Einstein mass-energy equation$ (4) $Einstein photoelectric equation$ 19. $The rate of radioactive disintegration at an instant for a radioactive sample of half life 2.2 \times 1 0^{9} s is 1 0^{10} s^{- 1} . The number of radioactive atoms in the sample at that instant is,$ (1) $3.17 \times 1 0^{20}$ (2) $3.17 \times 1 0^{17}$ (3) $3.17 \times 1 0^{18}$ (4) $3.17 \times 1 0^{19}$ 20. $The binding energy of deuteron is 2.2 MeV and that of_{2}^{4} He is 28 MeV .If two deuterons are fused to form one_{2}^{4} He then the energy released is$ (1) $30.2 MeV$ (2) $25.8 MeV$ (3) $23.6 MeV$ (4) $19.2 MeV$ 21. $In a radioactive decay, an element_{z} X^{A} emits four α -particles, three β -particles and eight gamma photons. The atomic number and mass number of the resulting final nucleus are$ (1) $Z - 11, A - 16$ (2) $Z - 5, A - 13$ (3) $Z - 5, A - 16$ (4) $Z - 8, A - 13$ 22. $Half life of radioactive element is 1600 years. The fraction of sample remains undecayed after 6400 years will be$ (1) $\frac{1}{16}$ (2) $\frac{1}{4}$ (3) $\frac{1}{8}$ (4) $\frac{1}{24}$ 23. $Two radioactive substances X and Y originally have N_{1} and N_{2} nuclei respectively. Half life of X is half ofthe half life of Y . After there half lives of Y, number of nuclei of both are equal. The ratio \frac{N _{1}}{N _{2}} will be equal to:$ (1) $\frac{8}{1}$ (2) $\frac{1}{8}$ (3) $\frac{3}{1}$ (4) $\frac{1}{3}$ 24. $The half-life of^{198} Au is 3 days. If atomic weight of^{198} Au is 198 g / mol then the activity of 2 mg of^{198} Au is [in disintegration/second]:$ (1) $2.67 \times 10^{12}$ (2) $6.6 \times 10^{18}$ (3) $32.36 \times 10^{12}$ (4) $16.18 \times 10^{12}$ 25. $A nucleus A, with a finite de-broglie wavelength λ_{A}, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B . the de-Broglie wavelengths λ_{B} and λ_{C} of B and C are respectively:$ (1) $λ_{A}, 2 λ_{A}$ (2) $2 λ_{A}, λ_{A}$ (3) $λ_{A}, \frac{λ _{A}}{2}$ (4) $\frac{λ _{A}}{2}, λ_{A}$ 26. $A and B are the two radioactive elements. The mixture of these elements show a total activity of 1200 disintegrations/minute. The half life of A is 1 day and that of B is 2 days. What will be the total activity after 4 days? Given: The initial number of atoms in A and B are equal.$ (1) $200 dis / min$ (2) $250 dis / min$ (3) $500 dis / min$ (4) $150 dis / min$ 27. $Which of the following statement is incorrect?$ (1) $Conservation laws have deep connection with symmetric of nature.$ (2) $Weak nuclear force is weakest among all fundamental forces of nature.$ (3) $A conservation law is hypothesis based on observations and experiments.$ (4) $In a nuclear process mass gets converted to energy of vice-versa.$ 28. $The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is:$ (1) $\frac{h}{mkT}$ (2) $\frac{h}{3 mkT}$ (3) $\frac{2 h}{3 mkT}$ (4) $\frac{2 h}{mkT}$ 29. $A radioactive material whose half life period is 2 years weighs 1 g and is stored in the laboratory for 4 years. Then the amount of remaining radioactive material is$ (1) $0.5 g$ (2) $0.125 g$ (3) $0.25 g$ (4) $0.0625 g$ 30. $The half life of a radioactive nucleus is 50 days. The time interval (t_{2} - t_{1}) between the time t_{2} when \frac{2}{3} of it has decayed and the time t_{1} when \frac{1}{3} of it had decayed is$ (1) $30 days$ (2) $50 days$ (3) $60 days$ (4) $15 days$