Nuclei PYQs Set 7 (PDF)

Set 7 of 8 · Questions 181-210 of 237

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Mere Teacher · Previous Year Questions NEET Physics · Nuclei · Set 7 (Q181-210)
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181. $The radius of the first permitted Bohr orbit for the electron, in a hydrogen atom equals 0.51Å and its ground state energy equals -13.6 eV. If the electron in the hydrogen atom is replaced by muon (μ^{- 1}) [Charge same as electron and mass 207 m_{e}], the first Bohr radius and ground state energy will be [NEET 2019]$ (1) $0.53 \times 10^{- 13} m, - 3.6 eV$ (2) $25.6 \times 10^{- 13} m, - 28 eV$ (3) $2.56 \times 10^{- 13} m, - 2.8 keV$ (4) $2.56 \times 10^{- 13} m, - 13.6 eV$ 182. $In a reactor, 2 kg of_{92} U^{235} fuel is fully used up in 30 days. The energy released per fission is 200 MeV . Given that the Avogadro number, N = 6.023 \times 10^{26} per kilo mole and 1 eV = 1.6 \times 10^{- 19} J . The power output of the reactor is close to$ (1) $125 MW$ (2) $35 MW$ (3) $60 MW$ (4) $54 MW$ 183. $A certain radioactive element disintegrates with a decay constant of 7.9 \times 10^{- 10} / s . At a given instant of time, if the activity of the sample is equal to 55.3 \times 10^{11} disintegration/second, then number of nuclei at that instant of time is$ (1) $7.0 \times 10^{21}$ (2) $4.27 \times 10^{13}$ (3) $4.27 \times 10^{3}$ (4) $6 \times 10^{23}$ 184. $An electron of mass m and a photon have same energy E. The ratio of de-Brogli wavelengths associated with them is:$ (1) $\frac{1}{c} (\frac{2 m}{E})^{\frac{1}{2}}$ (2) $\frac{1}{c} (\frac{E}{2 m})^{\frac{1}{2}}$ (3) $(\frac{E}{2 m})^{\frac{1}{2}}$ (4) $c (2 mE)^{1/2}$ 185. $The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be$ (1) $150 years$ (2) $200 years$ (3) $250 years$ (4) $100 years$ 186. $Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R . At time t = 0, number of P species are 4 N_{0} and that of Q are N_{0} Half‐life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal the number of nuclei of R present in the sample would be$ (1) $2 N_{0}$ (2) $3 N_{0}$ (3) $\frac{9 N _{0}}{2}$ (4) $\frac{5 N _{0}}{2}$ 187. $A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500 disintegrations per minute. The decay constant per minute is$ (1) $0.2 log_{e} 2$ (2) $0.5 log_{e} 2$ (3) $0.6 log_{e} 2$ (4) $0.8 log_{e} 2$ 188. $The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is$ (1) $\frac{1}{4}$ (2) $\frac{1}{2 2}$ (3) $\frac{1}{2}$ (4) $\frac{1}{2}$ 189. $In the following equation representing β decay, the number of neutrons in the nucleus X is_{83}^{210} Bi \to X + e^{- 1} + v$ (1) $126$ (2) $127$ (3) $125$ (4) $84$ 190. $An electron of mass m with an initial velocity V = V_{0} i (V_{0} > 0) enters an electric field E = - E_{0} i (E_{0} = constant > 0) at t = 0 . If λ_{0} is its de-Broglie wavelength at time t = 0, then its wavelength at any instant t will be$ (1) $\frac{λ _{0}}{( 1 + \frac{eE _{0}}{mV _{0}} t )}$ (2) $λ_{0}$ (3) $λ_{0} t$ (4) $λ_{0} (1 + \frac{e E _{0}}{m V _{0}} t)$ 191. $For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately:$ (1) $9.15sec$ (2) $6.93 sec$ (3) $2.62 sec$ (4) $4.62 sec$ 192. $Assume the graph of specific binding energy versus mass number is as shown in the figure. Using this graph, select the correct choice from the following:$ (1) $Fusion of two nuclei of mass number lying in the range of 100 < A < 200 will release energy.$ (2) $Fusion of two nuclei of mass number lying in the range of 51 < A < 100 will release energy.$ (3) $Fusion of two nuclei of mass number lying in the range of 1 < A < 50 will release energy.$ (4) $Fission of the nucleus of mass number lying in the range of 100 < A < 200 will release energy when broken into two fragments.$ 193. $the binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is$ (1) $23.6 MeV$ (2) $2.2 MeV$ (3) $28.0 MeV$ (4) $30.2 MeV$ 194. $Which graph in the following diagram correctly represents the potential energy of a pair of nucleons as a function of their separation?$ (1) (2) (3) (4) 195. $How does the Binding Energy per nucleon vary with the increase in the number of nucleons?$ (1) $Decrease continuously with mass number.$ (2) $First decreases and then increases with increase in mass number.$ (3) $First increases and then decreases with increase in mass number.$ (4) $Increases continuously with mass number.$ 196. $A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B vesus time is: (Assume that at t=0, there are no B atoms in the sample)$ (1) (2) (3) (4) 197. $A nucleus with mass number 184 initially at rest emits an α -particle. If the Q value of the reaction is 5.5MeV, calculate the kinetic energy of the α -particle.$ (1) $5.0MeV$ (2) $5.5MeV$ (3) $0.12MeV$ (4) $5.38MeV$ 198. $The rate of disintegration of a radioactive sample is R and the number of atoms present at any time t is N . When \frac{R}{N} is taken along Y -axis and t is taken along X -axis, the correct graphs is$ (1) (2) (3) (4) 199. $Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives T_{\frac{1}{2}} (A) : T_{\frac{1}{2}} (B) : T_{\frac{1}{2}} (C) are in the ratio$ (1) $02 : 01 : 03$ (2) $04 : 03 : 01$ (3) $02 : 01 : 01$ (4) $03 : 02 : 01$ 200. $A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after the which one third of the material remains? (Take ln3 = 1.1)$ (1) $1110 years$ (2) $700 years$ (3) $340 years$ (4) $740 years$ 201. $The angle made by orbital angular momentum of electron with the direction of the orbital magnetic moment is$ (1) $120^{\circ}$ (2) $60^{\circ}$ (3) $180^{\circ}$ (4) $90^{\circ}$ 202. $A nucleus of uranium decays at rest into nuclei of thorium and helium. Then$ (1) $The helium nucleus has more momentum than the thorium nucleus.$ (2) $The helium nucleus has less kinetic energy than the thorium nucleus.$ (3) $The helium nucleus has more kinetic energy than the thorium nucleus.$ (4) $The helium nucleus has less momentum than the thorium nucleus.$ 203. $Which one of the following nuclei has shorter mean life?$ (1) $C$ (2) $A$ (3) $Same for all$ (4) $B$ 204. $The figure shows standing de Broglie waves due to the revolution of electron in a certain orbit of hydrogen atom. Then the expression for the orbit radius is (all notations have their usual meanings)$ (1) $\frac{h ^{2} ϵ _{0}}{πm e ^{2}}$ (2) $\frac{36 h ^{2} ϵ _{0}}{πm e ^{2}}$ (3) $\frac{9 h ^{2} ϵ _{0}}{πm e ^{2}}$ (4) $\frac{16 h ^{2} ϵ _{0}}{πm e ^{2}}$ 205. $Consider the nuclear fission Ne^{20} \to 2 He^{4} + C^{12} Given that the binding energy/nucleon of Ne^{20}, He^{4} and C^{12} are, respectively, 8.03 MeV, 7.07 MeV and 7.68 MeV identify the correct statement:$ (1) $energy of 12.4 MeV will be supplied$ (2) $8.3 MeV energy will be released$ (3) $energy of 3.6 MeV will be released$ (4) $energy of 11.9 MeV has to be supplied$ 206. $The radius of nucleus of mass number 27 is R . Which of the following is true about a nucleus whose radius is 2 R ?$ (1) $It is stable in nature$ (2) $Its mass number is 54$ (3) $It is likely to undergo fission reaction$ (4) $It is likely to undergo fusion reaction$ 207. $Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as:(where λ is the decay constant)$ (1) $\frac{1}{2} \frac{ln 2}{λ}$ (2) $\frac{ln 2}{λ}$ (3) $\frac{2 ln 2}{λ}$ (4) $\frac{l n \frac{3}{2}}{λ}$ 208. $A sample of radioactive material A, that has an activity of 10 mCi (1 Ci = 3.7 \times 10^{10}) decays, has twice the number of nuclei as another sample of a different radioactive material B which has an acitvity of 20mCi. The correct choices for half-lives of A and B would then be respectively:$ (1) $5 days and 10 days$ (2) $10 days and 40 days$ (3) $20 days and 5 days$ 209. $The range of the nuclear force is$ (1) $10^{- 18} m$ (2) $10^{- 16} m$ (3) $10^{- 15} m$ (4) $10^{- 13} m$ 210. $The nuclear forces are$ (1) $long range repulsive forces$ (2) $long range attractive forces$ (3) $short range attractive forces$ (4) $short range repulsive forces$