Nuclei PYQs Set 6 (PDF)

Set 6 of 8 · Questions 151-180 of 240

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Mere Teacher · Previous Year Questions JEE Main Physics · Nuclei · Set 6 (Q151-180)
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151. $The radius of germanium (Ge) nuclide is measured to be twice the radius of_{4}^{9} Be The number of nucleons in Ge are$ (1) $72$ (2) $73$ (3) $74$ (4) $75$ 152. $In the nuclear fission of one nucleus of U^{235} the energy released is 188 MeV . The energy released in the nuclear fission of 235 g of U^{235} is nearly (Avogadro number = 6.02 \times 10^{23} mol^{- 1})$ (1) $28.8 \times 10^{12} J$ (2) $23.5 \times 10^{12} J$ (3) $36.2 \times 10^{12} J$ (4) $18.11 \times 10^{12} J$ 153. $Energy released in nuclear fission is due to$ (1) $some mass is converted into energy$ (2) $total binding energy of fragments is more than the binding energy of parental element$ (3) $total binding energy of fragments is less than the binding energy of parental element$ (4) $total binding energy of fragments is equal to the binding energy of parental element.$ 154. $A radioactive nucleus of mass M emits a photon of frequency u and the nucleus recoils. The recoil energy will be$ (1) $M c^{2} - h ν$ (2) $h^{2} ν^{2} /2 M c^{2}$ (3) $zero$ (4) $h ν$ 155. $For a radioactive material, half‐life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is$ (1) $20$ (2) $10$ (3) $30$ (4) $15$ 156. $In a nuclear reactor the activity of a radioactive substance is 2000/s. If the mean life of the product is 50 minutes, then in the steady power generation, the number of radio nuclides is$ (1) $12 \times 10^{5}$ (2) $60 \times 10^{5}$ (3) $90 \times 10^{5}$ (4) $15 \times 10^{5}$ 157. $The relation between the mean life time τ and the half life time T_{1/2} of a radioactive substance is$ (1) $T_{1/2} = τ log_{e} 2$ (2) $T_{1/2} = τ log_{10} 2$ (3) $T_{1/2} = τ$ (4) $T_{1/2} = 2 τ log_{e} 2$ 158. $The energy equivalent of 0.5 g of a substance is [NEET 2020]$ (1) $4.5 \times 10^{13} J$ (2) $1.5 \times 10^{13} J$ (3) $0.5 \times 10^{13} J$ (4) $4.5 \times 10^{16}$ 159. $If r_{1} and r_{2} are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio (r_{1} / r_{2}) is$ (1) $\frac{64}{125}$ (2) $\frac{64}{125}$ (3) $\frac{5}{4}$ (4) $\frac{4}{5}$ 160. $Half-life of a radioactive substance A is two times the half-life of another radioactive substance B . Initially the number of nuclei of A and B are N_{A} and N_{B} respectively. After three half-lives of A, the number of nuclei of both are equal. Then \frac{N _{A}}{N _{B}} is$ (1) $\frac{1}{3}$ (2) $\frac{1}{4}$ (3) $\frac{1}{6}$ (4) $\frac{1}{8}$ 161. $In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B . If V and B are kept constant, the ratio (\frac{chargeontheion}{massoftheion}) will be proportional to$ (1) $1/ R^{2}$ (2) $R^{2}$ (3) $R$ (4) $1/ R .$ 162. $Two radioactive materials X_{1} and X_{2} have decay constants 5 λ and λ respectively If initially they have the same number of nuclei, then the ratio of the number of nuclei of X_{1} to that X_{2} will be 1 le after a time$ (1) $1/4 λ$ (2) $e / λ$ (3) $λ$ (4) $\frac{1}{2} λ$ 163. $In a nuclear reactor the function of the moderator is to decrease$ (1) $number of neutrons$ (2) $speed of neutrons$ (3) $escape of neutrons$ (4) $temperature of the reactor$ 164. $A radioactive substance emits 100 beta particles in the first 2 seconds and 50 beta particles in the next 2 seconds. The mean life of the sample is$ (1) $4 seconds$ (2) $2 seconds$ (3) $\frac{2}{0.693} seconds$ (4) $2 \times 0.693 seconds$ 165. $Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to$ (1) $1.83$ (2) $2.3$ (3) $3.67$ (4) $1.07$ 166. $Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the materials is:$ (1) $4 \times 10^{15} Hz$ (2) $5 \times 10^{15} Hz$ (3) $1.6 \times 10^{15} Hz$ (4) $2.5 \times 10^{15} Hz$ 167. $Pick out the correct statement/s from the following. (A) Electron emission during β-decay is always accompanied by neutrino. (B) Nuclear force is charge independent. (C) Fusion is the chief source of stellar energy.$ (1) $(A), (B) are correct$ (2) $(A), (C) are correct$ (3) $Only (A) is correct$ (4) $(B), (C) are correct$ 168. $For a radioactive substance, fraction of its initial quantity which will disintegrate in its average life time is about ( )$ (1) $(\frac{1}{3}) N_{0}$ (2) $(\frac{2}{3}) N_{0}$ (3) $(0.9) N_{0}$ (4) $(\frac{1}{2}) N_{0}$ 169. $Energy released in the fission of a single_{92}^{235} U nucleus is 200 MeV The fission rate of_{92}^{235} U filled reactor operating at a power level of 5 W is$ (1) $1.56 \times 10^{- 10} s^{- 1}$ (2) $1.56 \times 10^{11} s^{- 1}$ (3) $1.56 \times 10^{- 16} s^{- 1}$ (4) $1.56 \times 10^{- 17} s^{- 1}$ 170. $A nucleus_{n}^{m} X emits one α particle and two β^{-} particles. The resulting nucleus is$ (1) $_{n - 4}^{m - 6} Z$ (2) $_{n}^{m - 6} Z$ (3) $_{n}^{m - 4} X$ (4) $_{n - 2}^{m - 4} Y$ 171. $In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled then the energy of the electron in the first orbit is$ (1) $- 27.2 eV$ (2) $- 13.6 eV$ (3) $- 6.8 eV$ (4) $- 3.4 eV$ 172. $What is the mass number of nucleus having radius equal to \frac{1}{3} of that of O_{S}^{189} ?$ (1) $20$ (2) $7$ (3) $12$ (4) $14$ 173. $Given the masses of various atomic particles m_{p} = 1.0072 u, m_{n} = 1.0087 u, m_{e} = 0.000548 u n \equiv neutron, e \equiv electron, v \equiv antineutrino and d \equiv deuteron. Which of the following process is allowed by momentum and energy conservation?$ (1) $n + n \to deuterium atom (electron bound to the nucleus)$ (2) $n + p \to d + γ$ (3) $p \to n + e^{+} + v$ (4) $e^{+} + e^{-} \to γ$ 174. $The decay constant of a radio isotope is λ . If A_{1} and A_{2} are its activities at times t_{1} and t_{2} respectively, the number of nuclei which have decayed during the time (t_{1} - t_{2})$ (1) $A_{1} t_{1} - A_{2} t_{2}$ (2) $A_{1} - A_{2}$ (3) $A_{1} - A_{2} /λ$ (4) $λ A_{1} - A_{2}$ 175. $The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then:$ (1) $x -will decay faster than y .$ (2) $y - will decay faster than x .$ (3) $x and y have same decay rate initially and later on different decay rate.$ (4) $x and y decay at the same rate always.$ 176. $At time t = 0, activity of radioactive substance is 1600 Bq and at t = 8 s activity falls to 100 Bq . The activity at t = 2 s is$ (1) $400 Bq$ (2) $800 Bq$ (3) $200 Bq$ (4) $600 Bq$ 177. $For photoelectric emission from certain metal the cutoff frequency is v . If radiation of frequency 2 v impinges on the metal plate the maximum possible velocity of the emitted electron will be (m is the electron mass):$ (1) $hv / m$ (2) $2 hv / m$ (3) $2 hv / m$ (4) $hv / (2 m)$ 178. $A radioactive sample disintegrates via two independent decay processes having half lives T_{1/2}^{(1)} and T_{1/2}^{(2)} respectively. The effective half- life T_{1/2} of the nuclei is:$ (1) $T_{1/2} = \frac{T _{1/2}^{(1)} + T _{1/2}^{(2)}}{T _{1/2}^{(1)} - T _{1/2}^{(2)}}$ (2) $T_{1/2} = T_{1/2}^{(1)} + T_{1/2}^{(2)}$ (3) $T_{1/2} = \frac{T _{1/2}^{(1)} T _{1/2}^{(2)}}{T _{1/2}^{(1)} + T _{1/2}^{(2)}}$ (4) $None of the above$ 179. $Which of the following interaction is responsible for beta decay?$ (1) $Gravitational$ (2) $Weak$ (3) $Electromagnetic$ (4) $Strong$ 180. $A radioactive source has a half-life of 6 h . A freshly prepared sample of the same exhibits radioactivity 32 times the permissible safe value. The minimum time after which it would be possible to work safely with the source is$ (1) $30 h$ (2) $24 h$ (3) $18 h$ (4) $12 h$