## NUCLEI QUIZ-11

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.If the decay or disintegration constant of a radioactive substance is λ, then its half life and mean life are respectively
•   1/λ and log_e⁡2/λ
•   log_e⁡2/λ and 1/λ
•   λ log_e⁡2 and 1/λ
•   λ/log_e⁡2 and 1/λ
Solution

Q2. Rank the following nuclei in order from largest to smallest value of the binding energy per nucleon: (i) _2^4 He , (ii) _24^52 Cr, (iii) _62^152 Sm, (iv) _80^100 Hg, (v) _92^252 Cf
•   E_((v))>E_((iv))>E_((iii))>E_((ii))>E_((i))
•   E_((i))>E_((ii))>E_((iii))>E_((iv))>E_((v))
•   E_((ii))>E_((iii))>E_((iv))>E_((v) )>E_((i))
•   E_((i))=E_((ii))=E_((iii))=E_((iv))=E_((v))
Solution
(c) The binding energy per nucleon is lowest for very light nuclei such as _2^4 He, is greatest around A=60, and then decreases with increasing A

Q3 Plutonium has atomic mass 210 and a decay constant equal to 5.8×10^(-8) s^(-1). The number of α-particles emitted per second by 1 mg Plutonium is (Avogadro’s constant =6.0×10^23)
•   1.7×10^9
•   1.7×10^11
•   2.9×10^11
•   3.4×10^9

Q4 Neutron decay in the free space is given as follows:〖 _0 n〗^1→〖 _1 H〗^1+〖 _(-1) e〗^0+[ ] Then, the parenthesis represents
•   Photon
•   Graviton
•   Neutrino
•   Antineutrino
Solution
(d) The emission of antineutrino is a must for the validity of different laws

Q5. U-235 can decay by many ways, let us here consider only two ways A and B. In decay of U-235 by means of A, the energy released per fission is 210 MeV while in B it is 186 MeV. Then, the uranium 235 sample is more likely to decay by

•   Scheme A
•   Scheme B
•   Equally likely for both schemes
•   It depends on half-life of schemes A and B
Solution
(a) Since scheme A releases more energy than scheme B, scheme A is more likely to occur. This is because the more the energy released, the more stable the daughter nucleus is. A heavy nucleus undergoes fission such that its products will be more stable than the parent nucleus

Q6 The decay constant of a radioactive sample is λ. The half-life and mean-life of the sample are, respectively, given by
•   1/λ and (ln⁡〖2)/λ〗
•   (In⁡2)λ and 1/λ
• λ(In⁡2 ) and 1/λ
•   λ/(In⁡2) and 1/λ
Solution

Q7. The half-life of ^131 I is 8 days. Given a sample of ^131 I at time t=0, we can assert that

•   No nucleus will decay before t=4 days
•   No nucleus will decay before t=8 days
•   all nuclei will decay before t=16 days
•   A given nucleus may decay at any time after t=0
Solution
(d) As we regard the decay process as a spontaneous and statistical process, therefore the decay can start any time after t=0. Therefore, the answer is (d)

Q8 In the disintegration series _92^238 U□(→┴( α ) X〖□(→┴〖 β〗^- )〗_( Z)^( A) Y) The values of Z and A, respectively, will be
•   92, 326
•   88, 230
•   90, 234
•   91, 234
Solution
(d) α-decay decreases mass number by 4 and reduces charge number by 2. β-decay keeps mass number unchanged and increases charge by 1. Clearly, option (d) is the right choice

Q9 The nuclear radius of _8 O^16 is 3×10^(-15) m. If an atomic mass unit is 1.67×10^(-27) kg, then the nuclear density is approximately?
•   2.35×10^17 g cm^(-3)
•   2.35×10^17 kg m^(-3)
•   2.35×10^17 g m^(-3)
•   2.35×10^17 kg mm^(-3)

Q10There are two radioactive substances A and B. Decay constant of B is two times that of A. Initially, both have equal number of nuclei. After n half-lives of A, rates of disintegration of both are equal. The value of n is
•  1
•  2
• 4
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