STD 12 - Nuclei PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 135 questions

51. 51. Assume that protons and neutrons have equal masses. Mass of a nucleon is \(1.6 \times 10^{-27}\,kg\) and radius of nucleus is \(1.5 \times 10^{-15} A ^{1 / 3}\,m\). The approximate ratio of the nuclear density and water density is \(n \times 10^{13}\). The value of \(n\) is \(.................\) 2023 Medium
52. 52. Consider the following radioactive decay process  \({ }_{84}^{218} A \stackrel{\alpha}{\longrightarrow} A_1 \stackrel{\beta^{-}}{\longrightarrow} A_2 \stackrel{\gamma}{\longrightarrow} A_3 \stackrel{\alpha}{\longrightarrow} A_4 \stackrel{B^{+}}{\longrightarrow} A_5 \stackrel{\gamma}{\longrightarrow} A_6\) The mass number and the atomic number \(A _6\) are given by  2023 Medium
53. 53. Experimentally it is found that \(12.8\,eV\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{ x } \times 10^{-10}\,m\). The value of the \(x\) is \(\left(1\,eV =1.6 \times 10^{-19}\,J , \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\,Nm ^2 / C ^2\right.\) and electronic charge \(=1.6 \times 10^{-19}\,J\,C\) ) 2023 Medium
54. 54. For a nucleus \({ }_Z^A X\) having mass number \(A\) and atomic number \(Z\) \(A.\) The surface energy per nucleon \(\left(b_s\right)=a_1 A^{2 / 3}\) \(B.\) The Coulomb contribution to the binding energy \(b_c=-a_2 \frac{Z(Z-1)}{A^{4 / 3}}\) \(C.\) The volume energy \(b_v=a_3 A\) \(D.\) Decrease in the binding energy is proportional to surface area. \(E.\) While estimating the surface energy, it is assumed that each nucleon interacts with \(12\) nucleons, \(\left(a_1, a_2\right.\) and \(a _3\) are constants) Choose the most appropriate answer from the options given below: 2023 Hard
55. 55. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : The nuclear density of nuclides \({ }_5^{10} B ,{ }_3^6 Li ,{ }_{26}^{56} Fe ,{ }_{10}^{20} Ne\) and \({ }_{83}^{209} Bi\) can be arranged as \(\rho_{ Bi }^{ N }>\rho_{ Fe }^{ N }>\rho_{ Ne }^{ N }>\rho_{ B }^{ N }>\rho_{ Li }^{ N }\). Reason \(R\) : The radius \(R\) of nucleus is related to its mass number \(A\) as \(R=R_0 A^{1 / 3}\), where \(R_0\) is a constant. In the light of the above statement, choose the correct answer from the options given below : 2023 Medium
56. 56. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range \(30\) to \(170\). Reason \(R\) : Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below on 2023 Medium
57. 57. If a radioactive element having half-life of \(30\,min\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90\,min\). will be : 2023 Easy
58. 58. Nucleus a having \(Z=17\) and equal number of protons and neutrons has \(1.2\,MeV\) binding energy per nucleon.Another nucleus \(B\) of \(Z=12\) has total \(26\) nucleons and \(1.8\,MeV\) binding energy per nucleons.The difference of binding energy of \(B\) and \(A\) will be \(...........MeV\). 2023 Medium
59. 59. Substance \(A\) has atomic mass number \(16\) and half life of \(1\) day. Another substance \(B\) has atomic mass number \(32\) and half life of \(\frac{1}{2}\) day. If both \(A\) and \(B\) simultaneously start undergo radio activity at the same time with initial mass \(320\,g\) each, how many total atoms of \(A\) and \(B\) combined would be left after \(2\) days \(.........\times 10^{24}\) 2023 Medium
60. 60. The decay constant for a radioactive nuclide is \(1.5 \times 10^{-5} s ^{-1}\). Atomic of the substance is \(60\,g\) mole \(^{-1},\left( N _{ A }=6 \times 10^{23}\right)\). The activity of \(1.0\,\mu g\) of the substance is \(.......\,\times 10^{10}\,Bq\) 2023 Hard
61. 61. The energy released per fission of nucleus of \({ }^{240} X\) is \(200 MeV\). The energy released if all the atoms in \(120 g\) of pure \({ }^{240} X\) undergo fission is \(........\times 10^{25}\,MeV\).\(\left(\right.\) Given \(\left.N_A=6 \times 10^{23}\right)\) 2023 Medium
62. 62. The half-life of a radioactive nucleus is \(5\) years, The fraction of the original sample that would decay in \(15\) years is 2023 Medium
63. 63. The half-life of a radioactive substance is \(T\). The time taken, for disintegrating \(\frac{7}{8}\) th part of its original mass will be 2023 Medium
64. 64. The mass of proton, neutron and helium nucleus are respectively \(1.0073\,u , 1.0087\,u\) and \(4.0015\,u\). The binding energy of helium nucleus is \(.........\,MeV\) 2023 Medium
65. 65. The ratio of the density of oxygen nucleus \(\left({ }_8^{16} O \right)\) and helium nucleus \(\left({ }_2^4 He \right)\) is 2023 Medium
66. 66. Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_A\) and \(\lambda_B\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options. 2023 Easy
67. 67. A freshly prepared radioactive source of half life \(2\) hours \(30\) minutes emits radiation which is \(64\) times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours. 2022 Medium
68. 68. A radioactive nucleus can decay by two different processes. Half-life for the first process is \(3.0\, hours\) while it is \(4.5\, hours\) for the second process. The effective half- life of the nucleus will be \(.........\,hours.\) 2022 Medium
69. 69. A radioactive sample decays \(\frac{7}{8}\) times its original quantity in \(15\) minutes. The half-life of the sample is \(......min\) 2022 Medium
70. 70. A sample contains \(10^{-2}\, kg\) each of two substances A and \(B\) with half lives \(4 \,s\) and \(8 \,s\) respectively. The ratio of then atomic weights is \(1: 2\) The ratio of the amounts of \(A\) and \(B\) after \(16 \,s\) is \(\frac{x}{100}\). the value of \(x\) is........ 2022 Medium
71. 71. How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ? 2022 Medium
72. 72. In the following nuclear rection, \(D \stackrel{\alpha}{\longrightarrow} D _{1} \stackrel{\beta-}{\longrightarrow} D _{2} \stackrel{\alpha}{\longrightarrow} D _{3} \stackrel{\gamma}{\longrightarrow} D _{4}\) Mass number of \(D\) is \(182\) and atomic number is \(74\) . Mass number and atomic number of \(D _{4}\) respectively will be 2022 Medium
73. 73. Mass numbers of two nuclei are in the ratio of \(4: 3\). Their nuclear densities will be in the ratio of 2022 Medium
74. 74. Nucleus A is having mass number \(220\) and its binding energy per nucleon is \(5.6 \,MeV\). It splits in two fragments '\(B\)' and '\(C\)' of mass numbers \(105\) and \(115\) The binding energy of nucleons in '\(B\)' and '\(C\) ' is \(6.4 \,MeV\) per nucleon. The energy \(Q\) released per fission will be............\(MeV\) 2022 Medium
75. 75. Read the following statements: \((A)\) Volume of the nucleus is directly proportional to the mass number. \((B)\) Volume of the nucleus is independent of mass number. \((C)\) Density of the nucleus is directly proportional to the mass number. \((D)\) Density of the nucleus is directly proportional to the cube root of the mass number. \((E)\) Density of the nucleus is independent of the mass number. Choose the correct option from the following options. 2022 Medium
76. 76. The activity of a radioactive material is \(2.56 \times 10^{-3} \,Ci\). If the half life of the material is \(5\) days, after how many days the activity will become \(2 \times 10^{-5} \,Ci\) ? 2022 Medium
77. 77. The activity of a radioactive material is \(6.4 \times 10^{-4}\) curie. Its half life is \(5\; days\). The activity will become \(5 \times 10^{-6}\) curie after \(.......day\) 2022 Medium
78. 78. The disintegration rate of a certain radioactive sample at any instant is \(4250\) disintegrations per minute.\(10\) minutes later, the rate becomes \(2250\) disintegrations per minute. The approximate decay cons \(.........\min^{-1}\) 2022 Medium
79. 79. The half life of a radioactive substance is \(5\) years. After \(x\) years a given sample of the radioactive substance gest reduced to \(6.25 \%\) of its initial value of \(x\) is ............... 2022 Medium
80. 80. The half life period of a radioactive substance is 60 days. The time taken for \(\frac{7}{8}\) th of its original mass to disintegrate will be \(......days\)  2022 Medium
81. 81. The \(Q\)-value of a nuclear reaction and kinetic energy of the projectile particle, \(K _{ p }\) are related as 2022 Medium
82. 82. Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below: \({ }_{1}^{2} X +{ }_{1}^{2} X ={ }_{2}^{4} Y\) The binding energies per nucleon \({ }_{1}^{2} X\) and \({ }_{2}^{4} Y\) are \(1.1\,MeV\) and \(7.6\,MeV\) respectively. The energy released in this process is \(MeV\). 2022 Medium
83. 83. Two radioactive materials \(A\) and \(B\) have decay constants \(25 \lambda\) and \(16 \lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \(B\) to that of \(A\) will be "\(e\)" after a time \(\frac{1}{a \lambda}\). The value of \(a\) is \(......\) 2022 Medium
84. 84. What is the half-life (in years) period of a radioactive material if its activity drops to \(1 / 16^{\text {th }}\) of its initial value of \(30\) years? 2022 Medium
85. 85. A nucleus of masss \(M\) emits \(\gamma\)-ray photon of frequency \('v'.\) The loss of internal energy by the nucleus is: 2021 Hard
86. 86. A nucleus with mass number \(184\) initially at rest emits an \(\alpha\)-particle. If the \(Q\) value of the reaction is \(5.5\, {MeV}\), calculate the kinetic energy of the \(\alpha-\) particle. (In \({MeV}\)) 2021 Hard
87. 87. 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 which one third of the material remains? (Take In \(3=1.1\) ) (In \(years\)) 2021 Hard
88. 88. 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 2021 Medium
89. 89. A radioactive sample has an average life of \(30\, {ms}\) and is decaying. A capacitor of capacitance \(200\, \mu\, {F}\) is first charged and later connected with resistor \(^{\prime}{R}^{\prime}\). If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of \(^{\prime}R^{\prime}\) should be \(....\,\Omega\) 2021 Hard
90. 90. A radioactive sample is undergoing \(\alpha\) 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? 2021 Hard
91. 91. A radioactive substance decays to \(\left(\frac{1}{16}\right)^{t h}\) of its initial activity in \(80\, days.\) The half life of the radioactive substance expressed in days is ... . 2021 Medium
92. 92. Calculate the time (in \(minutes\)) interval between \(33 \,\%\) decay and \(67\, \%\) decay if half-life of a substance is \(20\, minutes.\) 2021 Hard
93. 93. Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below  2021 Hard
94. 94. 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 \(....\,{sec}.\)
    2021 Medium
95. 95. From the given data, the amount of energy required to break the nucleus of aluminium \({ }_{13}^{27} {Al}\) is \(....\,x \times 10^{-3} {J}\) Mass of neutron \(=1.00866 \,{u}\) Mass of proton \(=1.00726 \,{u}\) Mass of aluminium nucleus \(=27.18846\, {u}\) (Assume \(1\,u\) corresponds to \(x\,J\) of energy) (Round off to the nearest integer) 2021 Medium
96. 96. If \('f^{\prime}\) denotes the ratio of the number of nuclei decayed \(\left(N_{d}\right)\) to the number of nuclei at \(t=0\) \(\left({N}_{0}\right)\) then for a collection of radioactive nuclei, the rate of change of \('f'\) with respect to time is given as: \([\lambda\) is the radioactive decay constant] 2021 Medium
97. 97. 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 \(\lambda\) is the decay constant) 2021 Hard
98. 98. The decay of a proton to neutron is : 2021 Medium
99. 99. 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 ..... \(\times 10^{12}\,disintegration/second\) 2021 Hard
100. 100. The half-life of \(Au ^{198}\) is \(2.7\, days.\) The activity of \(1.50\, mg\) of \(Au ^{198}\) if its atomic weight is \(198\, g mol ^{-1}\) is .......\(Ci\) \(\left( N _{ A }=6 \times 10^{23}\, / mol \right)\) 2021 Hard

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