Nuclei-Quiz-4

NUCLEI QUIZ-4

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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 star initially has 10^40 deutrons. It produces energy via the processes 〖 _1 H〗^2+〖 _1 H〗^2→〖 _1 H〗^2+p and 〖 _1 H〗^2+〖 _1 H〗^3→〖 _2 He〗^4+n If the average power radiated by the star is 10^16 W, the deuteron supply of the star is exhausted in a time of the order of [The mass of the nuclei are as follows: M(H^2 )=2.014 a.m.u..M(n)=1.008 a.m.u.. M(p)=1.007 a.m.u..M(He^4 )=4.001 a.m.u..]">

•  [M⁰ L⁰ T⁰], [M⁰ L⁰ T^-1]
•  [MLT^-2], [M⁰ L^-1 T⁰]
•  [M⁰ L⁰ T⁰], [M⁰ LT^-1]
•  [M⁰ L¹ T^-1], [M⁰ L⁰ T⁰]

Solution

Q2 After an interval of one day, 1/16th initial amount of a radioactive material remains in a sample. Then, its half-life is

•  6 h
•  12 h
•  1.5 h
•  3 h

Solution

Q3 In the following atoms and molecules for the transition from n=2 to n=1, the spectral line of minimum wavelength will be produced by

•   Hydrogen atom
•   Deuterium atom
•   Uni-ionized helium
•  De-ionized lithium 

Solution (d) 1/λ=RZ^2 (1/1^2 -1/2^2 ) For di-ionised lithium the value of Z is maximum

Q4 ^238 U decays with a half-life of 4.5×10^9 years, the decay series eventually ending at ^206 Pb, which is stable. A rock sample analysis shows that the ratio of the number of atoms of ^206 Pb and ^238 U is 0.0058. Assuming that all the ^206 Pb is produced by the decay of ^238 U and that all other half-lives on the chain are negligible, the age of the rock sample is (ln⁡〖1.0058=5.78×10^(-3))〗

•  38×10^8 years
•  38×10^6 years
•  19×10^8 years
•  19×10^6 years

Solution

Q5. Samples of two radioactive nuclides, X and Y, each have equal activity  at time . X has a half-life of 24 years and Y a half-life of 16 years. The samples are mixed together. What will be the total activity of the mixture at  years?

•   1/2 A_0
•   1/4 A_0
•   3/16 A_0
•   3/8 A_0

Solution

Q6 In a problem 43, number of atoms decayed between time interval t_1 and t_2 are

• ln⁡(2)/λ(R_1 R_2)
• R_1 e^(-λt_2 )-R_2 e^(-λt_2 )
• λ(R_1-R_2)    
• ( (R_1-R_2)/λ) 

Solution

Q7. ^22 Ne nucleus, after absorbing energy, decays into two α-particles and an unknown nucleus. The unknown nucleus is

•  Nitrogen
•  Carbon
•  Boron
•  Oxygen

Solution

Q8. In an α-decay, the kinetic energy of α-particle is 48 MeV and Q value of the reaction is 50 MeV. The mass number of the mother nucleus is (assume that daughter nucleus is in ground state)

•  96
•  100
•  104
•  None of the above

Solution

Q9. If 10% of a radioactive substance decays in every 5 years, then the percentage of the substance that will have decayed in 20 years will be

•  40%
•  50%
•  65.6%
•  34.4%

Solution

Q10 Half-life of a radioactive substance A is two times the half-life of another radioactive substance B. Initially, the number of A and B are N_A and N_B, respectively. After three half-lives of A, number of nuclei of both are equal. Then, the ratio N_A/N_B is

•  1/4
•  1/8
• 1/3
• 1/6

Solution