## NUCLEI QUIZ-15

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.The half-life of a certain radioactive isotope is 32 h. What fraction of a sample would remain after 16 h?
•   0.25
•   0.71
•   0.29
•   0.75
Solution

Q2. A helium atom, a hydrogen atom and a neutron have masses of 4.003 u, 1.008 u and 1.009 u (unified atomic mass units), respectively. Assuming that hydrogen atoms and neutrons can fuse to form helium, what is binding energy of a helium nucleus?
•   2.01 u
•   3.031 u
•   1.017 u
•   0.031 u
Solution
(d) Refer to the definition of mass defect

Q3.The rest mass of a deuteron is equivalent to an energy of 1876 MeV, that of a proton to 939 MeV and that of a neutron to 940 MeV A deuteron may disintegrate to a proton and a neutron if it
•   Emits an X-ray photon of energy 2 MeV
•   Captures an X-ray photon of energy 2 MeV
•   Emits an X-ray photon of energy 3 MeV
•   Captures an X-ray photon of energy 3 MeV
Solution

Q4. The activity of a radioactive element decreases to one-third of the original activity A_0 in a period of 9 years. After a further lapse of 9 years, its activity will be
•   A_0
•   2/3 A_0
•   A_0/9
•   A_0/6
Solution

Q5. There are n number of radioactive nuclei in a sample that undergoes beta decay. If from the sample, n’ number of Î²-particles are emitted every 2 s, then half-life of nuclei is

•   n^'/2
•   0.693×(2n/n')
•   0.693 ln(2n/n')
•   0.693×n/n'
Solution
(b) t(1/2)=0.639/Î»

Q6. A radioactive nucleus undergoes a series of decays according to the scheme A□(→┴( Î± ) A_1 □(→┴( Î² ) A_2 □(→┴( Î± ) A_3 □(→┴( Î³ ) A_4 )) ) ) If the mass number and atomic number of A are 180 and 72, respectively, then what are these number for A_4?
•  172 and 69
•  174 and 70
•  176 and 69
•  176 and 70
Solution
(a) Two Î±-particles reduce mass number by 8 Therefore, new mass number =180-8=172 Emission of two Î±-particles reduces charge number by 4 Emission of Î²-particles increases charge number by 1 Therefore, the new charge number =72-4+1=69

Q7. When an atom undergoes Î²^+ decay,:

•  A neutron ‘changes into’ a proton
•  A proton ‘changes into’ a neutron
•  A neutron ‘changes into’ an antiproton
•  A proton ‘changes into’ an antineutron
Solution
(b) A nucleus contains protons and neutrons with no antiprotons and antineutrons. Hence, answer can be either (b) or (d). Due to conservation of spin, the answer is (b)

Q8. From a newly formed radioactive substance (Half life 2 hours), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is
•   6 hours
•   12 hours
•   24 hours
•   128 hours
Solution

Q9. Stationery nucleus ^238 U decays by a emission generating a total kinetic energy T: _92^238 U → _90^234 Th+ _2^4 Î± What is the kinetic energy of the Î±-particle?
•   Slightly less than T/2
•   T/2
•   Slightly less than T
•   Slightly greater than T
Solution

Q10. A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is
•  6 h
•  12 h
• 24 h
• 28 h

Solution

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