## NUCLEI QUIZ-17

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 radium is 1500 years. In how many years will 1 g of pure radium be reduced to one centigram?
•   3.927×10^2 years
•   9.972×10^2 years
•   99.927×10^2 years
•   0.927×10^2 years
Solution

Q2. If the Q value of an endothermic reaction is 11.32 MeV, then the minimum energy of the reactant nuclei to carry out the reaction is (in laboratory frame of reference)
•   11.32 MeV
•   Less than 11.32 MeV
•   Greater than 11.32 MeV
•   Data is insufficient
Solution
(c) The minimum energy needed to carry out an endothermic reaction is greater than the Q value of the reaction. This is because to conserve the momentum some extra energy has to be provided KE_min (1+m/M)×|Q|, where m is the mass of the incident particle and M is the mass of target

Q3.If a nucleus such _ ^226 Ra that is initially at rest undergoes alpha decay, then which of the following statements is true?
•   The alpha particle has more kinetic energy than the daughter nucleus
•   The alpha particle has less kinetic energy than the daughter nucleus
•   The alpha particle and daughter nucleus both have same kinetic energy
•   We cannot say anything about kinetic energy of alpha particle and daughter nucleus
Solution

Q4. Two radioactive materials X_1 and X_2 have decay constants 10Î» and Î», respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X_1 to that of X_2 will be 1/e after a time
•   1/10Î»
•   1/11Î»
•   11/10Î»
•   1/9Î»
Solution

Q5. On an average, a neutron loses half of its energy per collision with a quasi-free proton. To reduce a 2 MeV neutron to a thermal neutron having energy 0.04 eV, the number of collisions required is nearly

•   50
•   52
•   26
•   15
Solution

Q6.A container is filled with a radioactive substance for which the half-life is 2 days. A week later, when the container is opened, it contains 5 g of the substance. Approximately how many grams of the substances were initially placed in the container?
•  40
•  60
•  80
•  100
Solution
(c) For this substance 7 days correspond to 3.5 half-lives. Over 3 half-lifes the sample reduces to 1/2^3 =1/8 of its initial mass. After 4 half-lifes, the sample has only 1/2^4 =1/16 of its initial mass. Hence, after 3.5 half-lives the sample must contain somewhere between 1/8 and 1/16 of its initial mass Hence, 5 g is somewhere between 1/8 and 1/16 of the initial mass So, the initial mass is somewhere between 8×5=40 g and 16×5=80 g

Q7. In a sample of a radioactive substance, what fraction of the initial nuclei will remain undecayed after a time t=T/2, where T= half-life of radioactive substance?

•  1/√(2 )
•   1/(2√(2 ))
•   1/4
•   1/(√(2 )-1)
Solution

Q8. Binding energy per nucleon vs. mass number curve for nuclei is shown in W,X,Y and Z are four nuclei indicated on the curve. The process that would release energy is
•   Y→2Z
•   W→X+Z
•   X→Y+Z
•   X→Y+Z
Solution

Q9. A certain radioactive element has half-life of 4 days. The fraction of material that decays in 2 days is
•   1/2
•   1/√2
•
•   (√2-1)/√2
Solution

Q10. The half-life of a radioactive decay is x times its mean life. The value of x is
•  0.3010
•  0.6930
• 0.6020
• 1/0.6930

Solution

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