## NUCLEI QUIZ-21

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.Statement 1: In alpha decay of different radioactive nuclides, the energy of alpha particles has been compared. It is found that as the energy of alpha particle increases the half-life of the decay goes on decreasing
Statement 2: More is the energy in any decay process, more is the probability of decaying the nuclide which leads to faster rate of decay
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution
(a) Statement II is correctly explaining Statement I More probability of decay means faster decay process and hence shorter half-life

Q2. Statement 1: (A) Fission of(_92^( 235))U is brought about by thermal neutron, whereas that of (_92^( 238))U is brought about by a fast neutron.
Statement 2: (_92^( 235))Uis an even-odd nucleus, whereas (_92^( 238))U is an even-even nucleus.
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution
(b) Fission of U^235 occurs by slow neutrons only (of energy about 1 eV) or even by thermal neutrons (of energy bout 0.025eV). Fission of (_92^( 238))U is brought about by a fast neutron.(_92^( 235))U has odd mass number and even atomic number, hence it is an even-odd nucleus whereas (_92^( 238))U has even mass number and even atomic number, hence it is an even-even nucleus.

Q3.Statement 1: For the scattering of Î±-particles at large angles, only the nucleus of the atom is responsible
Statement 2: Nucleus is very heavy in comparison to electrons
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution (a) We know that an electron is very light particle as compared to an Î±-particle. Hence electron cannot scatter the Î±-particle at large angles, according to law of conservation of momentum. On the other hands, mass of nucleus is comparable with the mass of Î±-particle, hence only the nucleus of atom is responsible for scattering of Î±-particles

Q4.Statement 1: The mass of a nucleus can be either less than or more than the sum of the masses of nucleons present in it
Statement 2: The whole mass of the atom is considered in the nucleus
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution
(d) The whole mass of the atom is concentrated at nucleus and M_nucleus< (Sum of the masses of nucleons) because, when nucleons combine some energy is wasted

Q5. Statement 1: The amount of energy required to remove an average nucleon from different nuclei having different mass numbers is approximately the same, while to remove an average electron from atoms having different mass numbers widely varying amounts of energies are required
Statement 2: Nucleons in a nucleus are bounded by short-range nuclear force while in a electrons in an atom are bounded by long-range Coulomb’s forces

•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution
(a) As in a nucleus, nucleons are bounded by short-range nuclear force, so a given nucleon is in interaction only with neighboring nucleons. So, detaching a nucleon from a nucleus is irrespective of the fact that how many nucleons are present in the nucleus. Moreover, due to short-range nuclear force only, the E_b/A versus A curve is slowly varying for A>40 While, in atoms electrons are bound with nucleus by Coulomb’s force which is a long-range force and depends on the number of protons in the nucleus and electron separation from the nucleus. If we take the average of the energies required to detach all the electrons from the outermost shell to the innermost K shell, then this average increases rapidly with increase in atomic number

Q6.Statement 1: The force of repulsion between atomic nucleus and Î±-particle varies with distance according to inverse square law
Statement 2: Rutherford did Î±-particle scattering experiment
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
• Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Solution
(b) Rutherford confirmed that the repulsive force on Î±-particle due to nucleus varies with distance according to inverse square law and that the positive charges are concentrated at the centre and not distributed throughout the atom

Q7.Statement 1: Half-life of a certain radioactive element is 100 days. After 200 days, fraction left undecayed will be 50%
Statement 2: N/N_0 =(1/2)^n, where symbols have usual meaning.

•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution

Q8. Statement 1: A nucleus having energyE_1 decays be Î²^- emission to daughter nucleus having energy E_2, but the Î²^- rays are emitted with a continuous energy spectrum having end point energy E_1-E_2.
Statement 2: To conserve energy and momentum in Î²-decay at least three particles must take part in the transformation.
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution (c) In particle situation , at least three particles take place in transformation, so energy for Î²-particle+ energy of third particle=E_1 –E_2 Hence, energy of Î²-particle ≤E_1 –E_2

Q9. Statement 1: Energy is released when heavy nuclei undergo fission of light nuclei undergo fusion.
Statement 2: For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is False
•   Statement 1 is False, Statement 2 is True
Solution
(a) Here, statement I is correct and Statement II is wrong can be directly concluded from binding energy/nucleon curve.

Q10. Statement 1: The nucleus _Z^A X is having atomic mass as well as its mass number as A Statement 2: Mass number of an element is an integer that specifies an isotope and has no units, while atomic mass is generally not an integer
•   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
• Statement 1 is True, Statement 2 is False
• Statement 1 is False, Statement 2 is True

Solution
(d) Atomic mass and mass number are different. Mass number is simply representing number of nucleons, while atomic mass is the average of the masses of isotopes of a given element and has units of u (atomic mass unit)

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