[Note] In the questions Y-N means that the mass number of nuclide Y is N.

Transcription

1 Problem Set #1: Nuclear Transformations [Note] In the questions Y-N means that the mass number of nuclide Y is N. 1. Among the following physical units, which is not the unit of energy? a) Joule, J b) Calorie, Cal c) Watt, W d) Electron volt, ev 2. Suppose that an electron was placed on the negative electrode. A static electric potential of 100 V is applied between the negative and positive electrode. The final energy that the electron achieves was 100 ev. What is the final energy of the proton if a proton is placed on the positive electrode instead of an electron? 3. The atomic weight of C-12 is What is the mass of C-12 in atomic mass unit (amu)? What is the mass in MeV? 4. An activity of 3.7x10 7 Bq corresponds to a) 1 mci b) 10 mci c) 100 mci d) 1 Ci e) None of the above. 5. You need a 30 mci of Cs-137 source for radiotherapy. To order the source to a manufacture, you have to tell the activity in Becquerel. What do you tell the company? 6. You have a Co-60 source, whose activity is 5000 Ci today. What is the activity of the Co- 60 source one month from today? 7. A nuclide has the atomic number of 92 and the mass number of 238. How many neutrons does this nuclide have? What is the name of this isotope? What is the most likely decay mode if it ever decays? 8. When radioactive equilibrium is established between parent and daughter in a sealed container: a) The parent decays with the half-life of the daughter. b) The parent and daughter emit gammas of the same energy. c) The activity of the daughter increases while that of the parent decreases. d) The daughter appears to decay with the half-life of the parent. 9. Polonium, Po, has the atomic number of 84. Which is the stable isotope of Po? a) Po-168 b) Po-209 c) Po-210 d) None of the above 1 of 4 YW: 9/24/2009

2 10. In alpha decay a) A changes by 2 b) Z changes by 4 c) Nuclei with A < 82 are most likely candidates d) An energetic helium nucleus is emitted e) Charge is not conserved. 11. Which isotope does not decay via alpha-decay process? a) Ra-226 b) Rn-222 c) U-235 d) O A nuclide decays into a product isotope (the daughter) via beta-minus decay. Which statement is correct? a) The atomic number of the daughter is larger than that of the parent. b) The atomic number of the daughter is smaller than that of the parent. c) The mass number of the daughter is smaller than that of the parent. d) The energy of beta-minus (or electron) has a fixed kinetic energy. 13. In the decay scheme shown in the diagram below, the total energy emitted in the pathway that includes β 1 and γ 3 is divided among: a) Two gamma-rays b) Two gamma-rays and one beta-ray c) One gamma-ray, one beta-ray and one antineutrino d) One beta-ray and one antineutrino e) Two beta-rays and three gamma-rays β 1 β 2 γ 1 γ 3 γ Positron emission tomography (PET) uses positrons emitted from C-11. Which statement is correct? a) The mass of positron is greater than the mass of electron. b) Detectors are used to detect positrons in PET. c) The positron kinetic energy is distributed over a wide energy range. d) The daughter isotope of this decay has the mass number of of 4 YW: 9/24/2009

3 15. Sources of photon radiation following the decay of atom X to atom Y by positron emission include: 1) Gamma radiation from X 2) Gamma radiation from Y 3) X-ray radiation from X 4) X-ray radiation from Y 5) Annihilation photons A. 1, 3 B. 2, 4 C. 1, 3, 5 D. 2, 4, 5 E. 1, 2, Be-7 (Beryllium) decays into the ground state of Li-7 (Lithium) by capturing an electron in the K-shell. Which of the following will not happen next? a) An electron in the L-shell of Li-7 jumps into the hole in the K-shell, emitting characteristic x-ray. b) Gamma-ray is emitted. c) An Auger electron is emitted. d) A neutrino is emitted spontaneously. 17. Regarding the gamma emission, which statement is correct? a) The gamma emission is one of primary radioactive decay processes similar to α- decay, β-decay, and electron capture b) The gamma ray is emitted when a nucleus in an excited state transits into a lower energy state. c) The gamma ray energy is continuously distributed over certain energy range. d) The gamma ray energy is usually in the order of 10 ev. 18. Br-80 (Bromine) decays into an excited state of Kr-80 (Krypton) by emitting an electron, whose maximum energy is 1.38 MeV. The excited state transits to the ground state with emission of a 0.62 MeV gamma ray. Br-80 also decays directly decays into the ground state of Kr-80 with emission of an electron. What is the maximum kinetic energy of this electron? 19. In how many days will 100 mci of I-125 (half-life=60days) decay to 60 mci? 20. If a radionuclide decay at 1% per day, about how long will it take to decay to half its original activity? a) 0.25 month b) 0.5 month c) 1.0 month d) 2.0 months e) 4.0 months [Raphex 2007, G25] 21. How many U-238 nuclides are in 1 gram of U-238? (Atomic mass of U-238 = amu). 3 of 4 YW: 9/24/2009

4 22. P-32 (Phosphorus-32) disintegrates into S-32 (Sulfur-32) by beta-minus decay. What energy is available as the kinetic energy of electron and neutrino? The atomic masses of P-32 and S-32 are amu and amu respectively. 23. N-13 (Nitrogen-13) disintegrates into C-13 (Carbon-13) by beta-plus decay. What energy is available as the kinetic energy of electron and neutrino? The atomic masses of N-32 and C-32 are amu and amu respectively mg of radium (Ra-226) decays for 1 day. How many 0.18MeV gamma rays will be emitted? [Jones and Cunnigham, 4 th ed. Chapter 3, page 100, Problem 7]. 4 of 4 YW: 9/24/2009

5 Problem Set #2: Nuclear Transformations [Note] In the questions Y-N means that the mass number of nuclide Y is N. 1. During nuclear reactions, which of the following physical properties is not conserved? a) Electric charge b) Linear momentum c) temperature d) The number of nucleons 2. A proton bombards a nuclide X with atomic number Z and mass number A. The reaction produces a neutron. What is Z and A of the reaction product nuclide Y? a) Z =Z and A =A b) Z =Z -1 and A =A c) Z =Z+1 and A =A d) Z =Z-1 and A =A-1 3. A 10 MeV neutron flies through a lead shield. The total cross section of neutrons, σ, with lead for that energy is 5 barns. The density of lead is 3.3x10 22 cm -3. What is the number of the neutron interactions with lead within 10 cm of the neutron flight path in the lead shield? 4. A deuterium (H-2) hits Be-9 (beryllium nine) and undergoes (d,n) reactions producing a neutron and B-10 (boron ten). If al the nuclear energy produced by this reaction is carried by the neutron, what is the energy of the neutron? The atomic weight in amu units of deuterium, Be-9, and B-10 are , , and , respectively. 5. Neutrons (or photoneutrons) are produced in a linear accelerator room where an x-ray beam is produced for radiation therapy. Which of the following is not correct? a) The reactions are called photo disintegration. b) Photons with any energy can produce neutrons through this reaction. c) The product material can be radioactive. d) The average energy of the photoneutrons is about 2 MeV. 6. A 1 g of Co-59 is irradiated with neutrons in a nuclear reactor. The neutron flux is cm -2 s -1. If irradiation is continued for 10 years by leaving the Co-59 sample, what is the activity of the product? 7. Co-59 is irradiated with a neutron beam. The reactions between the Co-59 and the neutron are absorption reactions (n,γ). What are the atomic number and the mass number of the product nuclide? 1 of 2 YW: 9/24/2009

6 8. Palladium-103 (Pd-103) disintegrates with electron capture. Z of Pd-103 is 46. The daughter nuclide is a) Rh-103 b) Ag-103 c) Pd-104 d) Rh U-235 is a fissile material and undergoes nuclear fission reactions. The energy generated by fission reactions are in the many forms. Which particles carry the most of the energy? a) Neutrons. b) Protons c) Fission fragments d) neutrinos 10. Match the following terms with the appropriate nuclides. A. Isotopes B. Isotones C. Isomers D. Isobars i. ii. iii. iv. 99 Tc/ 99m Tc 131 I/ 123 I 14 N/ 14 C 3 H/ 4 He 11. Which of the following statements is correct regarding reactor byproduct materials? a) Radioactive material is produced in a nuclear reactor by bombarding material with charged particle. b) Byproduct materials are fission products. They are radioactive and may be daughters of the fission products. c) Reactor byproduct is produced by placing samples in a nuclear reactor and irradiating with neutrons. d) Most of positron emitting nuclides used with positron emission tomography are reactor byproducts. 12. Calculate the energy produced when two hydrogen atoms fuse together. The atomic mass of H-1 is A 1 MeV neutron enters a shielding wall made of pure lead (Pb). The scattering cross section of neutron-pb interaction is 10 barns. What is the mean path of neutrons in the lead? 14. From literature, obtain the energy diagram for Cs-131 decay process. What is the photon energy produced by Cs-131? 2 of 2 YW: 9/24/2009

7 Answers to Problem Set #1: Nuclear Transformations 1. c ev amu, x =11178 MeV= x x10-27 = x10-26 kg. 4. a GBq. 6. T1/2 of Co-60 = 5.26 years=5.26x12=63.12 months. The activity = 5000xexp( x1/63.12)=5000x =4945 Ci. 7. The number of neutrons = =146. Uranium (or Uranium-238). Alpha-decay. 8. d. 9. d. 10. d. 11. d. 12. a. 13. c. 14. c. 15. d. 16. b. 17. b =2.0 MeV days. 20. D. 0.99=exp(-λx1) => 69 days x10 21 U-238 nuclides. 22. ( )*931.5 = 1.71 MeV. 23. Answer: Eq.(1): 13N7 -> 13C6 + positron + neutrino The mass in amu is the mass of the atom (or the atomic weight Aw). This means that it includes the mass of orbital electrons. Hence, The mass of nucleus of 13N7 = Atomic weigh of 13N7, Aw(13N7), 7 * the mass of electron (mc^2) The mass of nucleus of 13C6 = Atomic weight of 13C6, Aw(13C6), - 6 * mc^2. The mass of position is mc^2 and the mass of neutrino is 0 (almost). 1 of 2 yw:9/24/2009

8 So, from equation (1) above, the kinetic energy of position and neutrino, T, is given by T=Aw(13N7) 7mc^2 [Aw(13C6)-6mc^2+mc^2+0]=Aw(13N7)-Aw(13C6)-2*mc^2. Here is MeV is the mass of electron or positron in MeV. So, T=( )* *0.511=1.198 MeV. Note that AW is in amu and 1 amu = MeV. 24. The initial activity of 1 mg of Ra-226 is the same as 1 mci (=3.7x10 10 *10-3 Bq or dps). The half-life of Ra-226 is 1600 years. Hence, we can assume that the activity of Ra-226 does not change in 1 day. Thus, the number of disintegrations in one day is 3.7x10 7 *24*60*60=3.2* From the energy level diagram, we know that one disintegration only produces MeV gamma rays. Therefore, the number of 0.18 MeV gamma rays emitted in one day is 1.75x of 2 yw:9/24/2009

9 Answers to Problem Set #2: Nuclear Transformations 1. c. 2. c. 3. The number of interactions = 5x10-24 [cm 2 ] x 3.3x10 22 [cm -3 ] x10 [cm] = MeV. Q-value calculation 1 amu = MeV Pre Post isotope mass isotope mass H n Be B total Q = MeV 5. b x10 22 x 37x10-24 == 3.77x10 14 s -1 =10,000 Ci 7. Co a. 9. c. 10. The correspondences are A. ii. B. iv. C. i. D. iii. 11. b MeV Pre Post isotope mass isotope mass H electron 5.49E-04 H H total Q = MeV 1 of 2 yw:9/24/2009

10 13. The mass density of lead is 11.3 g/cm 3. The atomic mass is Hence, the number of lead atoms per 1 cm 3 of lead is 6.02x10 23 *11.3/(207.2)=3.28x The mean free path is 1/(10x10-24 *3.28x10 22 )= The mean free path is 3.05 cm. 14. Cs-131 decays to Xe-131 via K-electron capture. There is no gamma ray produced with this process. Fluorescent x-rays are produced when an electron in higher energy states falls to the hole in the K-shell. The measured energies of the x-rays are 29 kev and 34 kev. [Refs] M.K.Murphy et al. Med Phys 31, 1529 (2004); C.M.Lederer and V.S/Shirley, Table of Isotopes, 7 th ed.,john Wiley&Sons, Inc., New York (1978).] 2 of 2 yw:9/24/2009