Nuclei PYQs Set 4 (PDF)

Set 4 of 8 · Questions 91-120 of 240

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Mere Teacher · Previous Year Questions JEE Main Physics · Nuclei · Set 4 (Q91-120)
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91. $There are 1 0^{10} radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? (2 = 1.414)$ (1) $2 \times 1 0^{10}$ (2) $7 \times 1 0^{9}$ (3) $1 0^{5}$ (4) $4 \times 1 0^{10}$ 92. $The binding energy per nucleon of_{3}^{7} Li and_{2}^{4} H nuclei are 5.60 MeV and 7.06 MeV respectively In the nuclear reaction_{3}^{7} Li +_{1}^{1} H \to_{2}^{4} He +_{2}^{4} He + Q the value of energy Q released is$ (1) $19.6 MeV$ (2) $- 2.4 MeV$ (3) $8.4 MeV$ (4) $17.3 MeV$ 93. $The radius of_{29} Cu^{64} nucleus in Fermi is (given R_{0} = 1.2 \times 10^{- 15} m)$ (1) $4.8$ (2) $1.2$ (3) $7.7$ (4) $9.6$ 94. $The nucleus having highest binding energy per nucleon is$ (1) $_{8}^{16} O$ (2) $_{26}^{56} Fe$ (3) $_{84}^{208} Pb$ (4) $_{2}^{4} He$ 95. $Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei ofA to those of B will be (1/ e) 2 after a time interval$ (1) $4 λ$ (2) $2 λ$ (3) $1/2 λ$ (4) $1/4 λ .$ 96. $An alloy is composed of two radioactive materials A and B having equal weight. The half life of A and B are 10 yrs and 20 yrs respectively. After time t, the alloy was found to consist of (\frac{1}{e}) kg of A and 1 kg of B . If the atomic weight of A and B are same, then the value of t is (Assume, n 2 = 0.7)$ (1) $200 7 yrs$ (2) $10 7 yrs$ (3) $7 yrs$ (4) $70 yrs$ 97. $In the nuclear reaction,_{6}^{11} C \to_{5}^{11} B + β + X, X stands for$ (1) $a neutron$ (2) $an electron$ (3) $a neutrino$ (4) $an anti-neutrino$ 98. $Half‐lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes. Initially the samples of A and B have equal number of nuclei. After 80 minutes the ratio of remaining numbers of A and B nuclei is$ (1) $1 : 4$ (2) $4: 1$ (3) $1: 16$ (4) $1: 1$ 99. $A nucleus has mass number A_{1} and volume V_{1} . Another nucleus has mass number A_{2} and volume V_{2} . If the relation the mass numbers is A_{2} = 3 A_{1}, then \frac{V _{1}}{V _{2}} =$ (1) $3^{\frac{1}{3}}$ (2) $(\frac{1}{3})^{\frac{1}{3}}$ (3) $\frac{1}{3}$ (4) $\frac{1}{3}$ 100. $In the reaction_{1}^{2} H +_{1}^{3} H \to_{1}^{4} He +_{0}^{1} n, if the binding energies of_{1}^{2} H,_{1}^{3} H and_{2}^{4} He are respectively a, b and c (in MeV), then the energy (in MeV ) released in this reaction is$ (1) $a + b + c$ (2) $a + b - c$ (3) $c - a - b$ (4) $c + a - b .$ 101. $The mass density of a nucleus varies with mass number A as$ (1) $A^{2}$ (2) $A$ (3) $constant$ (4) $1/ A$ 102. $In a radioactive material, fraction of active material remaining after time is . The fraction that was remaining after is$ (1) $\frac{3}{4}$ (2) $\frac{4}{5}$ (3) $\frac{3}{5}$ (4) $\frac{7}{8}$ 103. $Decay constants of two radio-active samples A and B are 15 x and 3 x respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in A and B after a time 1/6 x is$ (1) $e$ (2) $e^{2}$ (3) $e^{- 1}$ (4) $e^{- 2}$ 104. $Two radioactive materials R_{1} and R_{2} have decays constants 6 λ and λ, respectively. The half life of R_{2} is 1.4 \times 10^{17} s . Initially they contain some number of nuclei. The time at which the ratio of the remaining nuclie of R_{2} to that of R_{1} will be e is (Let ln 2 = 0.7)$ (1) $2 \times 10^{16} s$ (2) $4 \times 10^{16} s$ (3) $3 \times 10^{16} s$ (4) $5 \times 10^{16} s$ 105. $Calculate the time interval between 33 % decay and 67 % decay if half-life of a substance is 20 minutes.$ (1) $60 minutes$ (2) $20 minutes$ (3) $40 minutes$ (4) $13 minutes$ 106. $A radioactive element has half-life of 15 years. What is the fraction that will decay in 30 years?$ (1) $0.75$ (2) $0.85$ (3) $0.25$ (4) $0.5$ 107. $If 'f' denotes the ratio of the number of nuclei decayed (N_{d}) to the number of nuclei at t = 0 (N_{0}) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as: [λ is the radioactive decay constant]$ (1) $- λ (1 - e^{- λt})$ (2) $λ (1 - e^{- λt})$ (3) $λ e^{- λt}$ (4) $- λ e^{- λd}$ 108. $When an α ‐particle of mass m moving with velocity v bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as$ (1) $\frac{1}{m ^{2}}$ (2) $m$ (3) $\frac{1}{m}$ (4) $\frac{1}{m}$ 109. $You are given that Mass of_{3}^{7} Li = 7.0160 u Mass of_{2}^{4} He = 4.0026 u and Mass of_{1}^{1} H = 1.0079 u When 20 g of_{3}^{7} Li is converted into_{2}^{4} He by proton capture, the energy liberated, (in kWh), is: [Mass of nudeon (= 1 GeV / c^{2})$ (1) $1.33 \times 10^{6}$ (2) $4.5 \times 10^{5}$ (3) $8 \times 10^{6}$ (4) $6.82 \times 10^{5}$ 110. $A radioactive element has half life period 800 years. After 6400 years what amount will remain7.$ (1) $1/2$ (2) $1/16$ (3) $1/8$ (4) $1/256$ 111. $Which of the following are suitable for the fusion process?$ (1) $light nuclei$ (2) $heavy nuclei$ (3) $element lying in the middle of the periodic table$ (4) $middle elements, which are lying on binding energy curve.$ 112. $What is the binding energy of_{14}^{29} Si, whose atomic mass is 28.976495 u ? Mass of proton = 1.007276 u Mass of neutron = 1.008664 u (Neglect the electron mass) (Assume, 1 u = 931.5 MeV)$ (1) $237.84 MeV$ (2) $421.72 MeV$ (3) $387.21 MeV$ (4) $116.35 MeV$ 113. $The electron in the hydrogen atom jumps from excited state (n = 3) to its ground state (n = 1) and the photons thus emitted irradiate a photosensitive material. If the work function of the material is 5.1 eV , the stopping potential is estimated to be (the energy of the electron in n^{t h} state E_{n} = - \frac{13.6}{n ^{2}} eV$ (1) $5.1 V$ (2) $12.1 V$ (3) $17.2 V$ (4) $7 V$ 114. $If the nuclear radius of^{27} Al is 3.6 fermi, the approximate nuclear radius of^{64} Cu in fermi is$ (1) $2.4$ (2) $1.2$ (3) $4.8$ (4) $3.6$ 115. $A sample of radioactive element has a mass of 10 g at an instant t = 0 . The approximate mass of this element in the sample after two mean lives is$ (1) $1.35 g$ (2) $2.50 g$ (3) $3.70 g$ (4) $6.30 g$ 116. $A sample of radioactive element containing 4 \times 1 0^{16} active nuclei. Half life of element is 10 days, then number of decayed nuclei after 30 days$ (1) $0.5 \times 1 0^{16}$ (2) $2 \times 1 0^{16}$ (3) $3.5 \times 1 0^{16}$ (4) $1 \times 1 0^{16}$ 117. $If the nucleus_{13}^{27} Al has a nuclear radius of about 3.6 fm , then_{32}^{125} Te would have its radius approximately as$ (1) $9.6 fm$ (2) $12.0 fm$ (3) $4.8 fm$ (4) $6.0 fm .$ 118. $Which of the following values is the correct order of nuclear density?$ (1) $5 \times 10^{5} kg m^{- 3}$ (2) $9 \times 10^{10} kg m^{- 3}$ (3) $3 \times 10^{21} kg m^{- 3}$ (4) $2 \times 10^{17} kg m^{- 3}$ 119. $The energy equivalent to a substance of mass 1 g is$ (1) $18 \times 10^{13} J$ (2) $9 \times 10^{13} J$ (3) $18 \times 10^{6} J$ (4) $9 \times 10^{6} J$ 120. $Pick out the correct statement from the following.$ (1) $Energy released per unit mass of the reactant is less in case of fusion reaction.$ (2) $Packing fraction may be positive or may be negative.$ (3) $Pu^{239} is not suitable for a fission reaction.$ (4) $For stable nucleus, the specific binding energy is low.$