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NUCLEI QUIZ-12

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JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts.



Q1 A□(→┴( λ ) B□(→┴( 2λ ) )) C T=0 N_0 0 0 T N_1 N_2 N_3 The ratio of N_1 to N_2 when N_2 is maximum is
  •   At no time this is possible
  •   2
  •   1/2
  •   ln⁡2/2
Solution




Q2. Two radioactive materials X_1 and X_2 have decay constants 10λ and λ, respectively. If initially they have the same number of nuclei, the ratio of the number of nuclei of X_1 to that of X_2 will be 1/e after a time
  •   1/10λ
  •   1/11λ
  •   11/10λ
  •   1/9λ
Solution




Q3. Number of nuclei of a radioactive substance are 1000 and 900 at times t=0 and time t=2 s. Then, number of nuclei at time t=4 s will be
  •   800
  •   810
  •   790
  •   700
Solution 
(b) In 2 s only 90% nuclei are left behind. Thus, in next 2 s 90% of 900 or 810 nuclei will be left



Q4 Gold _79^198 Au undergoes β^- decay to an excited state of _80^198 Hg. If the excited state decays by emission of a γ-photon with energy 0.412 MeV, the maximum kinetic energy of the electron emitted in the decay is (This maximum occurs when the antineutrino has negligible energy. The recoil energy of the _80^198 Hg nucleus can be ignored. The masses of the neutral atoms in their ground states are 197.968225 u for _79^198 Au and 197.966752 u for _79^198 Hg.)
  •   0.412 MeV
  •   1.371 MeV
  •   0.959 MeV
  •   1.473 MeV
Solution



Q5. The mean life time of a radionuclide, if its activity decreases by 4% for every 1 h, would be [product is non-radioactive, i.e., stable]

  •   25 h
  •   1.042 h
  •   2 h
  •   30 h
Solution



Q6. A radioactive nucleus decay by two different processes. The mean value period for the first process is t_1 and that for the second process is t_2. The effective mean value period for the two processes is
  •   (t_1+t_2)/2
  •   t_1+t_2
  • √(t_1 t_2 )
  •   (t_1 t_2)/(t_1+t_2 )
Solution



Q7. A radioactive isotope is being produced at a constant rate X. Half-life of the radioactive substance is Y. After some time, the number of radioactive nuclei become constant. The value of this constant is

  •   XY/ln⁡〖(2)〗
  •   XY
  •   (XY) ln⁡〖(2)〗
  •   X/Y
Solution




Q8 A certain radioactive material can undergo three different types of decay, each with a different decay constant λ, 2λ and 3λ. Then, the effective decay constant λ_eff is
  •  
  •  
  •  
  •  
Solution



Q9 The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is
  •   1215 Å
  •   1640 Å
  •   2430 Å
  •   4687 Å
Solution




Q10 The ratio of molecular mass of two radioactive substances is 3/2 and the ratio of their decay constants is 4/3. Then, the ratio of their initial activity per mole will be
  •   2
  •   8/9
  • 4/3
  • 9/8

Solution


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