NUCLEI, RADIOACTIVITY AND NUCLEAR REACTIONS

NUCLEI, RADIOACTIVITY AND NUCLEAR REACTIONS VERY SHORT ANSWER QUESTIONS Q-1. Which of the two is bigger 1 kwh or 1 MeV? Q-2. What should be the approximate minimum energy of a gamma ray photon for pair production? Q-3. Who discovered the neutron? Q-4. What is the mass of an electron in amu? Q-5. What is the mass of a proton in amu? Q-6. Q-7. Name three nuclei which are on the bottom points of binding energy curve. Name five nuclei which lie on the peaks in binding energy curve. Q-8. Why electron capture is more common in heavy atoms? Q-9. How many joule are contained in 1 kwh? Q-10. What exactly makes large nuclei unstable? Q-11. What is one roentgen? Q-12. Name two elementary particles which have almost infinite life time. Q-13. Is free neutron a stable particle? Q-14. Cadmium rods are provided in a reactor. Why? Q-15. How many electrons, protons and neutrons are there in a nucleus of atomic number 11 and mass number 24? Q-16. How are the two units of radioactivity related to each other? Q-17. How many kg are there in one atomic mass unit? Q-18. Q-19. You are given two nuclides X 3 7 and Y 3 4. Are they isotopes of the same element? Why? Write one equation representing nuclear fusion reaction. Q-20. Which of the following will be affected by electric and magnetic fields? Q-21. Name two radioactive elements which are not found in observable quantities in nature. Why is it so? 1

Q-22. How many joule are contained in 1 MeV? Q-23. What is Einstein s mass-energy relation? Q-24. How is mass defect related to the binding energy of a nucleus? Q-25. What is atomic mass unit? Q-26. Q-27. Write down the radioactive rays in the order of increasing penetrating power. Give an equation representing the decay of a free neutron. Q-28. What is the relation between disintegration constant and half life of a radioactive material? Q-29. 7 When 3Li is bombarded with a certain particle, two alpha particles are produced. Identify the bombarding particle. Q-30. What are isotopes? Q-31. What is the essential difference between an electron and a β particle? Q-32. You are given two nuclides X 3 7 and Y 3 4. Which one of the two is likely to be more stable? Give reason. Q-33. Select the pairs of isobars and isotones from the following nuclei : 14 6 C, 13 7 N, 14 7 N, O Q-34. Select the pairs of isotopes and isotones from the following nuclei : 13 6 C, 14 7 N, 30 P, P Q-35. What holds nucleons together in a nucleus? Q-36. How is half-life of a radioactive substance related to its average life? 15 16 8. 15 31. Q-37. Define binding energy of a nucleus. Q-38. What are isotones? Q-39. Q-40. Explain whether the neutron-proton ratio increases or decreases during beta decay. A radioactive nuclide has a decay constant equal to λ. Give the formula for the (i) half-life (ii) mean life of this nuclide. Q-41. A nucleus of mass number A has a mass defect m. Give the formula for the binding energy per nucleon of this nucleus. 32 Q-42. Write the nuclear decay process for β decay of 15P. Q-43. What is the source of solar energy? 2

Q-44. What is the ratio of kwh to MeV? Q-45. Define half-life of a radioactive material. Q-46. What is nuclear holocaust? Q-47. Q-48. Define Q-value of a nuclear reaction. Arrange radioactive radiations in the increasing order of their ionizing power. Q-49. What do you mean by mass defect of nucleus? Q-50. What is the ratio of nuclear densities of two nuclei having mass number in the ratio of 1 : 3? Q-51. What is the ratio of the two nuclei of mass numbers A 1 and A 2? Q-52. Why have nuclei invariably mass less than the sum of the masses of the individual nucleous in them? Q-53. Why does the binding energy per nucleon decrease with increase in mass number for heavy nuclei like 235U? Q-54. What is an exoergic nuclear reaction? Q-55. What is an edoergic nuclear reaction? Q-56. Define the term activity of a radionuclide. Write its SI unit. Q-57. Why is nuclear fusion not possible in laboratory? SHORT ANSWER QUESTIONS Q-58. Q-59. In a natural uranium reactor, heavy water is a preferred moderator to ordinary water. Very high temperature as those obtained in the interior of the sun are required for fusion reaction to take place. Q-60. When energies of electrons emitted in beta decay were first measured, it was found that in the decay of same species, the electrons coming out had varying energies ; the energy varied from zero to maximum. Initially the researchers felt that energy was not conserved in beta decay. If energy was conserved, they argued that, the electrons should have fixed energy, as do the alpha particles in alpha decay. Can you explain why the argument is not true? 3

Q-61. The half-lives of radioactive nuclides that emit -rays vary from microsecond to billion years. What is the reason for this large variation in the half-life of -emitters? Q-62. A radioactive nucleus undergoes a series of decays according to the following scheme : A A A A A If the mass number and atomic number of A are 180 and 1 2 3 4 72 respectively, what are these number for A 4? Q-63. Q-64. 7 Which of the two is more stable 3Li or 3Li 4? It is said that a very powerful crane is required to lift a nuclear mass of microscopic size. Comment on this. Q-65. How are β-particles different from electron emitted in thermionic emission and photoelectric effect? Q-66. Give the order of magnitude of nuclear mass density and average atomic mass density. Compare these densities with the typical mass density of solids, liquids and gases (at ordinary temperatures and pressures). 197 Q-67. Obtain approximately the ratio of the nuclear radii of the gold isotope 79 Au and the silver isotope 107 Ag. What is the approximate ratio of their nuclear mass densities? 47 Q-68. Safety of nuclear reactors is an important issue that has attracted much attention recently. Guess some of the safety problems that a nuclear engineer must cope with in reactor design.[a proper view of this issue can be obtained only by reading a standard text on the subject.] Q-69. The -particle faces a Coulomb barrier. A neutron, being uncharged, faces no such barrier. When does the nucleus 238 U not decay spontaneously by emitting a neutron? 92 [m( 237 ) = 237.04874u, m n = 1.000867u]. U 92 Q-70. If the -decay of 238 U is energetically allowed (i.e., the decay products have a total mass less than the mass of 238 U), what prevents 238 U from decaying all at once? Why is its half-life so large? Q-71. If a neutron is unstable with a half-life of about 917 s, why all the neutrons of nucleus do not decay eventually into protons? How can a nucleus of Z protons and (A Z) neutrons ever remain stable if the neutrons themselves are unstable? 4

Q-72. In a nuclear reactor, explain clearly the role of delayed neutrons. 238 Q-73. What are the number of protons and the number of neutrons in a nucleus of 92 U? Q-74. The half-life period of a radioactive substance is 30 days. What is the time taken for 3 th of its original 4 mass to disintegrate? Q-75. A certain radioactive substance has a half-life period of 30 days. What is the disintegration constant? Q-76. A radioactive substance having N nuclei has activity A. What is the expression for its half-life in terms of A and N? Q-77. In a nuclear reactor, explain clearly the role of control rods. (Why are they made of cadmium?) Q-78. Why -particles have a high ionizing power? Q-79. Complete the following nuclear reaction Q-80. A radioactive nucleus A decays as follows : A A1 A2 If the mass number and atomic number of A 2 are 176 and 71 respectively, what are the mass number and atomic number of A 1 and A? Which of these three elements are isobars? Q-81. Why ionic crystals are poor conductors of electricity? Q-82. Q-83. Express 16 mg mass into equivalent energy in electron volt. 3 Tritium ( 1H) has a half-life of 12.5 years against beta-decay. What fraction of a sample of pure tritium will remain undecayed after 25 years? 238 Q-84. Why 92 U is not suitable for chain reaction? Q-85. Compare the radii of two nuclei with mass numbers 1 and 27 respectively. Also compare their nuclear densities. Q-86. Q-87. Q-88. What is nuclear fission? Give one representative equation. A 4 What is alpha particle? In the reactions, X Y + He, give the atomic number and mass number of Y. Z 2 A nucleus makes a transition from one permitted energy level to another level of lower energy. Name the region of the electromagnetic spectrum to which the emitted photon belongs. What is the order of its energy in ev? Write four characteristics of nuclear forces. 5

Q-89. Q-90. Express one joule in ev. Taking 1 amu = 931 MeV, calculate the mass of C 12 atom. Give the mass number and atomic number of elements on the right-hand side of the decay process 220 86 Rn Po + He. Q-91. Why is it said that nuclear forces are saturated forces? Q-92. Show that the decay rate R of a sample of a radionuclide is related to the number of radioactive nuclei N at the same instant by the expression R = λn. 60 Q-93. Draw the energy level diagram showing the emission of β-particles followed by γ-rays by a 27 Co nucleus. Q-94. Define atomic mass unit. Find its energy equivalent in MeV. 204 32 Q-95. Write the nuclear reactions for the following : (i) -decay of 84 Po (ii) β-decay of P (iii) β + 11 -decay of 6 C 15 Q-96. Why is the mass of a nucleus always less than the sum of the masses of its constituents, neutrons and protons? Q-97. What do you mean by the charge-independent nature of nuclear forces? Q-98. Q-99. Q-100. Write three characteristic properties of nuclear force which distinguish it from the electrostatic force. Plot the distribution of kinetic energy of β-particles and state why the energy spectrum is continuous. Draw a graph showing the variation of potential energy of a pair of nucleons as a function of their separation. Indicate the regions in which nuclear force is (i) attractive (ii) repulsive. Q-101. Draw the graph showing the variation of binding energy per nucleon with mass number of different atomic nuclei. Give the reason for the decrease of binding energy per nucleon for nuclei with high mass numbers. Q-102. Distinguish between isotopes and isobars. Give one example for each of the species. SHORT ANSWER QUESTIONS Q-103. We know that atomic mass of an element is the weighted average of the atomic masses of different isotopes of that element. This explains why atomic masses of many elements show large departures from 6

integral values. However, even if we consider masses of individual isotopes, they are not strictly integral multiples of the mass of a hydrogen ( H 1 1 ) atom. How do you account for this fact? 16 8 Q-104. The isotope 8 O has 8 protons, 8 neutrons and 8 electrons, while 4 Be has 4 protons, 4 neutrons and 4 electrons. Yet the ratio of their atomic masses is not exactly 2. Why? Q-105. 4 238 Obtain the approximate value of the radius of (a) a nucleus of 2 He and (b) a nucleus of U. (c) What is 92 the ratio of these radii? (Assume R 0 = 1.2 10-15 m.) Q-106. An electron which is emitted in beta decay comes out of the nucleus. It is not one of the atomic electrons revolving around the nucleus. This fact led some scientists to conjecture that electrons are constituents of the nucleus. Later this conjecture proved to be incorrect. Try to collect some arguments which show that this conjecture is indeed incorrect. Q-107. Answer the following questions : Are the equations of nuclear reactions balanced in the sense a chemical equation (e.g., 2H 2 + O 2 2H 2 O) is? If not, in what sense are they balanced on both sides? Q-108. If both the number of protons and the number of neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Q-109. A general impression is that mass-energy inter-conversion takes place only in nuclear reactions and never in chemical reactions. This is strictly speaking incorrect. Explain Q-110. Give reasons for the following. Lighter elements are better moderators for a nuclear reactor than heavier elements. Q-111. A free proton cannot decay into n + e + + v, because such decay is not energetically allowed. Yet we observed in nature beta decay with positron emission. How do we understand the emission of positrons from nuclei? Q-112. The observed decay products of a free neutron are a proton and an electron. The emitted electrons are found to have a continuous distribution of kinetic energy with a maximum of (m n m p m e ) c 2. Explain clearly why the presence of a continuous distribution of energy is a pointer to the existence of other unobserved product(s) in the decay. 7

Q-113. In a nuclear reactor, explain clearly the role of moderator (why is heavy water used as a moderator?) Q-114. Explain, with the help of a nuclear reaction in each of the following cases, how the neutron to proton ratio changes during (i) alpha decay (ii) beta decay? Q-115. Prove that the instantaneous rate of change of the activity of a radioactive substance is inversely proportional to the square of its half-life. Q-116. Four nuclei of an element fuse together to form a heavier nucleus. If the process is accompanied by release of energy, which of the two-the parent or the daughter nucleus would have a higher binding energy / nucleon? Q-117. A radioactive material is reduced to 1 begin with so that 4 10-3 kg of the material is left after 6 days? 16 of its original amount in 4 days. How much material should one Q-118. Define the term Activity of a radioactive substance. State its SI unit. Two different radioactive elements with half-lives T 1 and T 2 have N 1 and N 2 (undecayed) atoms respectively present at a given instant. Determine the ratio of their activities at this instant. CONCEPTUAL PROBLEMS Q-119. Name one physical quantity which can be said to be the source of binding energy. Q-120. What is the mass in g of a radioactive element whose activity is equal to 1 curie? Q-121. Can the atomic spectrum of two isotopes be the same? Q-122. The atomic masses are generally not whole numbers. Why? Q-123. Is it possible that a nucleus has negative mass defect? Q-124. A velocity selector selects positive ions of certain velocity. Can the same selector be used to select negative ions of the same velocity? Q-125. An element emits in succession 2 -particles and 1 β-particle. What is the change in mass number? Q-126. Why heavy stable nucleus must contain more neutrons than protons? Q-127. Which property of nuclear forces is responsible for the constancy of binding energy per nucleon? 8

235 Q-128. In a particular fission reaction, a 92 U nucleus captures a slow neutron. The fission products are three neutrons, a 142 La nucleus and a fission product Z X. What is the value of Z? 57 Q-129. Which has greater ionizing power : alpha particles or beta particles? Q-130. A point source of γ-radiation has a half-life of 30 minutes. The initial count rate, recorded by Geiger counter, placed 2 m from the source is 360s -1. The distance between the counter and the source is altered. After 1.5 hours, the count rate recorded is 5 s -1. What is the new distance between the counter and the source? Q-131. Energy released per fission of a nucleus is of the order of 200 MeV whereas that per fusion is of the order of 10Mev. But a fusion bomb (Hydrogen bomb) is said to be more powerful than a fission bomb. Explain why? Q-132. With respect to power generation, what are the relative advantages and disadvantages of Fusion type and Fission type reactors? Q-133. A radioactive isotope decays in the following sequence : 1 0 n A A A 1 2 If the mass number and atomic number of A 2 are 176 and 71 respectively, find the mass number and atomic number of A and A 1. Q-134. Define half-life and average life of a radioactive substance. What is the relation between the two? Q-135. Which law is violated in the following nuclear reaction? n H + e 20 40 Q-136. M1 and M2 represent the masses of 10 Ne and 20 Ca nuclei respectively. State whether M 2 = 2M 1 or M 2 > 2M 1 or M 2 < 2M 1? 1 0 1 1 1 0 Q-137. The half-life period of radioactive element A is the same as the mean life time of another radioactive element B. Initially both of them have same number of atoms. The radioactive element B decays faster than A. Explain, why? Q-138. What is meant by critical mass? Q-139. What are thermal neutrons? Why are neutrons considered as ideal particles for nuclear fission? Q-140. Comment on the statement A nucleus contains no electrons and can eject them. 9

Q-141. The sequence of stepwise decays of a radioactive nucleus is D D1 D2 D3 If the nucleon number and atomic number for D 2 are 176 and 71 respectively, what are the corresponding values of D and D 3? Q-142. If the total number of neutrons and protons in a nuclear reactions is conserved how then is the energy absorbed or evolved in the reaction? Explain. Q-143. Define disintegration constant and mean life of a radioactive substance. Give the unit for each. 235 Q-144. The nucleus of an atom of 92 Y. Initially at rest, decays by emitting an -particle as per the equation : 235 Y 231 x + 4 He + Energy. It is given that the binding energies per nucleon of the parent and the 92 90 2 daughter nuclei are 7.8 MeV and 7.835 MeV respectively and that of -particle is 7.07 MeV/ nucleon. Assuming the daughter nucleus to be formed in the unexcited state and neglecting its share in the energy of the reaction, calculate the speed of the emitted -particle. Take mass of -particle to be 6.68 10-27 kg. LONG ANSWER QUESTIONS Q-145. Q-146. Q-147. What are nuclear forces? State their six important properties. Explain the possible cause of these forces. Distinguish between nuclear fusion and nuclear fission reactions by giving examples. Define the terms half-life period and decay constant of a radioactive substance. Write their SI units. Establish the relationship between the two. Q-148. Draw a graph showing the variation of binding energy per nucleon with mass number for different nuclei. Explain, with the help of this graph, the release of energy by the process of nuclear fusion. Q-149. Define binding energy per nucleon. Draw a graph showing the variation of binding energy per nucleon with mass number of different nuclei. What is its significance? Q-150. Draw the curve showing variation of binding energy/nucleon with mass number of different nuclei. Briefly state, how nuclear fusion and nuclear fission can be explained on the basis of this graph. Q-151. What is nuclear reaction? Give one example of it. How can a nuclear reaction be identified? Mention two laws which are obeyed by these reactions. 10

Q-152. Define binding energy and mass defect. Obtain an expression for binding energy per nucleon and state the importance of binding energy per nucleon. Q-153. What are alpha particles? Explain alpha decay giving an example. What is the magnitude of electric charge possessed by an alpha particle? 11