Nuclei-Quiz-14

NUCLEI QUIZ-14

Dear Readers,

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 largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer is)

•   802 nm
•   823 nm
•   1882 nm
•   1648 nm

Solution

Q2.  The activity of a radioactive substance is R_1 at time t_1 and R_2 at time t_2 (>t_1). Its decay constant is λ. Then

•   R_1 t_1
•   R_2=R_1 e^(λ(t_1-t_2))
•   (R_1-R_2)/(t_2-t_1 )=constant
•   R_2=R_1 e^(λ(t_2-t_1))

Solution

Q3. The nuclear radius of a nucleus with nucleon number 16 is 3×10^(-15)m. Then, the nuclear radius of a nucleus with nucleon number 128 is

•   3×10^(-15) m
•   1.5×10^(-15) m
•   6×10^(-15) m
•   4.5×10^(-15) m

Solution

Q4. A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass numbers 80 and 120. If binding energy per nucleon for parent atom is 6.5 MeV and for daughter nuclei is 7 MeV and 8 MeV, respectively, then the energy released in the decay will be

•   200 MeV
•   -200 MeV
•   220 MeV
•   180 MeV

Solution
(c) Energy released is (80×7+120×8-200×6.5)=220 MeV

Q5. Why is a _2^4 He nucleus stable than a _3^4 Li nucleus?

•  The strong nuclear force is larger when the neutron to proton ratio is higher
•   The laws of nuclear physics forbid a nucleus from containing more protons than neutrons
•   Forces other than the strong nuclear force make the lithium nucleus less stabl
•   None of the above

Solution
(c) All neutrons attract each other with the same strong nuclear force. So, the strong nuclear force holds together three protons and one neutron (_3^4 Li) just as vigourously as it holds together two protons and two neutrons (_2^4 He). Specifically, protons electrostastically repel other protons. This repulsion tries to make a nucleus fly apart. Since _2^4 He contains only two protons, the attractive strong nuclear forces overcome the repulsion of the protons. Hence, the nucleus holds together. But in _3^4 Li, the mutual repulsion of the three protons overcomes the strong nuclear attractions and the nucleus falls apart (or undergoes radioactive decay into a more stable nucleus). Therefore, the answer will be (c)

Q6. The half-life of At is 100 μs. The time taken for the radioactivity of a sample of At to decay to 1/16th of its initial value is

•  400 μs
•   6.3 μs
• 40 μs
•   300 μs

Solution

Q7. A radioactive nucleus ‘X’ decays to a stable nucleus ‘Y’. Then, time graph of rate of formation of ‘Y’ against time ‘t’ will be:

•  
  
•  
  
•  
  
•  
  

Solution

Q8. A radioactive substance is being consumed at a constant rate of 1 s^(-1). After what time will the number of radioactive nuclei become 100. Initially, there were 200 nuclei present

•   1 s
•   1/ln⁡〖(2)〗 s
•   ln⁡〖(2)〗 s
•   2 s

Solution

Q9. A nucleus moving with velocity v ⃗ emits an α- particle. Let the velocities of the α-particle and the remaining nucleus be (v_1 ) ⃗ and (v_2 ) ⃗ and their masses be m_1 and m_2, then

•   v ⃗,v ⃗_1 and v ⃗_2 must be parallel to each other
•   None of the two of 〖v ⃗,v ⃗〗_1 and v ⃗_2 should be parallel to each other
•   v ⃗_1+ v ⃗_2 must be parallel to v ⃗
•   m_1 v ⃗_1+m_2 v ⃗_2 must be parallel to v ⃗

Solution

Q10. Certain radioactive substance reduces to 25% of its value in 16 days. Its half-life is

•  32 days
•  8 days
• 64 days
• 28 day
  
  

Solution