Chapter #13 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 3rd Edition

 

1. Write down the precise nuclide identification for the missing element x for the following reactions. ... Get solution

1q. Rutherford was able to initiate nuclear reactions with α particles before 1920. Why wasn’t he able to initiate nuclear reactions with protons? Get solution

2. For each of the reactions listed in Problem 1, write down one other possible exit channel. Reference of problem 1. Write down the precise nuclide identification for the missing element x for the following reactions. ... Get solution

2q. In Example 13.2 we learned that the 12C(α, n)15O cross section is much larger than the 12C(α, p)15N reaction for Eα = 14.6 MeV. We believe this is evidence of a resonance in 16O. If it is a resonance, why aren’t both neutron and proton exit channels strongly populated? Why do we conclude the difference must be due to quantum numbers in the exit channel? Can the Coulomb barrier in the exit channels make a difference? ... Get solution

3. The cross section for a 2-MeV neutron being absorbed by a 238U nucleus and producing fission is 0.6 barn. For a pure 258U sample of thickness 3 cm, what is the probability of a neutron producing fission? (...for uranium) Get solution

3q. Why do the lifetimes of nuclear excited states decrease for higher excitation energies? Get solution

4. List at least three entrance channels using stable nuclei that can produce the exit channel d + 20Ne. Get solution

4q. Why is the density of nuclear excited states larger for higher excitation energies? Get solution

5. The cross section for neutrons of energy 10 eV being captured by silver (ρ = 10.5 g/cm3) is 17 barns. What is the probability of a neutron being captured as it passes through a layer of silver 2 mm thick? Get solution

5q. Both deuterons and alpha particles can cause direct reactions by stripping. Which are more effective? Explain. Get solution

6. In order to measure the cross section of the ... ... reaction of Example 13.2, a detector subtending a solid angle of ... is used at the scattering angle ... particles is incident on a12C target of thickness ... for one hour. If the differential cross section is 0.2 mb/sr, how many protons are detected at the angle θ? Get solution

6q. Discuss the changes in the cross section for neutron-induced and proton-induced reactions as the initial kinetic energy is decreased from 50 MeV. Ignore resonances. Get solution

7. Write the complete reaction for an 16O target for the following reactions. List which products are stable. ... Get solution

7q. Think about how a chain reaction could be controlled without delayed neutrons. Is it possible? What would be the difficulties? Get solution

8. Calculate the ground state Q values for the following reactions. Are the reactions endothermic or exothermic? (a) 16O(d, α)14N, (b) 12C(12C, d)22Na, and (c) 23Na(p, 12C)12C. Get solution

8q. Think carefully about the fi ssion process. Does it seem peculiar that symmetric fission is not the most probable? Does the distribution shown in Figure 13.8 seem reasonable? Explain. Get solution

9. For the endothermic reactions of Problem 8, calculate the threshold kinetic energy. Problem 8 Calculate the ground state Q values for the following reactions. Are the reactions endothermic or exothermic? (a) 16O(d, α)14N, (b) 12C(12C, d)22Na, and (c) 23Na(p, 12C)12C. Get solution

9q. Why is it useful to slow down neutrons produced by fission in a nuclear reactor? Get solution

10. A state in 16O* at an excitation energy of 9.63 MeV has a broad width ... = 510 keV. It is indicated in Figure 13.6 by hatch marks. In the excitation functions for 12C(α, γ)12C and 12C(α, γ)16O shown in Figure 13.6, broad peaks reflect this state. (a) At what laboratory bombarding energy Kα will the resonance be observed? (The actual peak may be shifted slightly because of interference effects.) (b) What is the approximate lifetime of this excited state? ... Get solution

10q. All the moderators mentioned in this chapter to slow down neutrons are light nuclei. Why are light nuclei used for moderators instead of heavy nuclei? Get solution

11. In a certain nuclear reaction initiated by 5.5-MeV α particles, the outgoing particles are measured to have kinetic energies of 1 .1 MeV and 6.4 MeV. (a) What is the Q value of the reaction? (b) If exactly the Same reaction were initiated by 10-MeV a particles, what is the Q value? (The outgoing energies will change.) Get solution

12. Calculate the Q value and threshold energy for the 20Ne(α, 12C)12C reaction. What will be the sum of the kinetic energies of the 12C nuclei if the alpha particle initially has 45 MeV of kinetic energy in the lab? Get solution

12q. Discuss how each of the following sources of energy is ultimately derived from the sun: wood, coal, gas, oil, water, and wind. Get solution

13. The threshold kinetic energy is calculated nonrelativistically in Equation (13.10). For the reaction A (a, b) B show that the threshold kinetic energy calculated relativistically is ... ... Get solution

13q. Why does a star’s temperature increase as fusion proceeds? Why are higher temperatures required for the carbon cycle than for the proton-proton chain? Get solution

14. A slow neutron is absorbed by 10B in the reaction 10B(n, γ)11B. What is the energy of the γ ray? Get solution

14q. The fusion process continues in a very massive star until its core consists of nuclei near 56Fe. Explain why this occurs. Get solution

15. In a PuBe source, plutonium produces α particles of about 5 MeV. These α particles interact with beryllium by the ... reaction. How much kinetic energy do the reaction products have? Get solution

15q. The first wall of a magnetic fusion containment vessel has been said to contain the most hostile environment yet designed by man. Justify this statement. Get solution

16. Calculate the ground state Q value and the threshold kinetic energy for the reactions (a) 16O(α, p)19F and (b) 12C(d, 3He)11B. Get solution

16q. Neutron-activation analysis is much more widely used than charged-particle activation. Why do you suppose that is true? Get solution

17. 60Co is produced by neutron activation of 59Co placed in a nuclear reactor where the neutron flux is 1.0 × 1018 neutrons/m2 . s. The cross section is 20 b, and the sample of 59Co has mass 40 mg. (a) If the 59Co is left in the reactor for one week, how many 60Co nuclei are produced? (b) What would be the activity of the 60Co? (density of cobalt = 8.9 g/cm3) (c) Describe a procedure for producing 1.0 × 1014 Bq of 60Co for medical use. Get solution

17q. Explain in your own words the origin of the names of elements 97 through 102; that is, who or what the elements were named after and the reasons for doing so. Get solution

18. Consider the reaction X(x,y)Y depicted in Figure 13.4, where the target X is at rest. The energy of the center of mass is given by ... where vcm is the speed of the center of mass given by Equation (13.8). Show that the energy available in the center-of-mass system K’cm is given by Equation (13.12): ... where K lab = Mxvx 2/2. ... ... Get solution

18q. Explain in your own words the origin of the names of elements 103 through 108—that is, who or what the elements were named after and the reasons for doing so. Get solution

19. A 7.7-MeV alpha particle initiates the ... reaction in air. What is the excitation energy of the com-pound nucleus18F? Get solution

19q. Explain in your own words the origin of the names of elements 109 through 114—that is, who or what the elements were named after and the reasons for doing so. You can skip those elements for which International Union of Pure and Applied Chemistry has not yet officially assigned a name. Get solution

20. A 14-MeV neutron is captured by a 208Pb nucleus. (a) At what excitation energy is the resulting 209Pb? (b) What decay mechanism would you expect for this highly excited 209Pb nucleus? Get solution

20q. How many new elements have been discovered that are not mentioned in this textbook? Discuss them. Get solution

21q. Small research nuclear reactors, like those mostly used in universities, are often submerged in concrete structures that look like swimming pools. The water serves as a moderator of the neutrons. They often have a blue glow in the swimming pool around the reactor. What is the origin of the blue color? Hint: Look up Cerenkov radiation. Get solution

22. The ground state of 17Ne is unstable. Its half-life has been measured to be 109 ms. (a) What is the energy width of the state? (b) List two possible decay mechanisms. Get solution

23. The first excited state of 17F is at 0.495 MeV. Can the p + 16O reaction populate this state? Give your reasons. Get solution

25. List as many nuclear reactions as you can that use deuterons and alpha particles for projectiles with stable targets that will populate 22Ne as the final state in direct reactions. Get solution

26. Calculate how much energy is released when 239Pu absorbs a thermal neutron and fissions in the reaction ... Get solution

27. A sample of shale contains 0.04% 238U by weight. Calculate the number of spontaneous fissions in one day in a 106-kg pile of the shale by determining (a) the mass of 238U present, (b) the number of 238Uatoms, (c) the fission activity, and finally (d) the number of fissions. The density of uranium is 19 g/cm3. The spontaneous fission activity rate is 0.69 fissions/kg • s. Get solution

28. Calculate the percentage abundance of ... 2 billion years ago if the abundance today is 0.7% and 99.3%, respectively. The higher percentage of 235U probably allowed natural nuclear reactors to occur. Explain why such a reaction could not occur today. Get solution

29. Use the information in Figure 13.8 to write at least three common sets of fission fragments for the fission products of 236U (that is, the unstable nuclide present after 235U has absorbed a neutron and has undergone fission). ... Get solution

30. A fission reactor operates at the 1000-MWc level. Assume all this energy comes from the 200 MeV released by fission caused by thermal neutron absorption by 235U. At what daily rate is the mass of 235U used? (In practice, of course, the energy conversion is not 100% efficient, nor is all the 235U in a fuel cell used.) Get solution

31. Calculate the energy released in kilowatt hours from the fission of 1.0 kg of 235U. Compare this with the energy released from the combustion of 1.0 kg of coal. The heat of combustion of coal is given in Table 13.1. ... Get solution

32. Neutrons in equilibrium with their surroundings at temperature T are called thermal neutrons and have an average kinetic energy ... kT. Calculate the thermal neutron energy for (a) room temperature (300 K) and (b) the sun (15 × 106 K). Get solution

33. Determine the ground-state Q values for each of the reactions in the carbon cycle and show that the overall energy released is the same as for the proton-proton chain (26.7 MeV). Get solution

34. There is a bottleneck in producing masses higher than 4He, because there are no mass-5 or mass-8 stable nuclides. For older stars with high densities and high temperatures (T >100 million K), three alpha particles can form 12C. This occurs by two alpha particles first forming 8Be, and 8Be reacting with another alpha particle to form 12C before 8Be can decay back to two alpha particles. (a) Explain why this has to happen for very hot stars and high density. (b) Calculate how much energy is given up when three alpha particles form 12C. Get solution

35. Following the triple-alpha process to form 12C (see the previous problem), a variety of nuclear reactions can form heavier nuclide masses. In one of them ..., , the temperature must be greater than about 3 billion K. (a) Why does the temperature have to be so high? (b) Calculate how much energy is released in the reaction. It is reactions like this that allow nuclei in the iron region to be formed. Problem 36 There is a bottleneck in producing masses higher than 4He, because there are no mass-5 or mass-8 stable nuclides. For older stars with high densities and high temperatures (T >100 million K), three alpha particles can form 12C. This occurs by two alpha particles first forming 8Be, and 8Be reacting with another alpha particle to form 12C before 8Be can decay back to two alpha particles. (a) Explain why this has to happen for very hot stars and high density. (b) Calculate how much energy is given up when three alpha particles form 12C. Get solution

36. One of the fusion reactions that goes on in massive stars is silicon burning ..., This reaction is how fusion reactions eventually reach the most stable iron/nickel region. It is also a precursor to the end of a star’s life and may lead to a supernova, if the star’s mass is sufficient. (a) Calculate the ignition temperature required for this reaction. (b) How much energy is expended in this reaction? Get solution

37. One of the fusion reactions that goes on in massive stars is carbon burning, ... (a) Calculate the ignition temperature required for this reaction. (b) How much energy is expended in this reaction? Get solution

38. Assume that two thirds of Earth’s surface is covered with water to an average depth of 3 km. Calculate how many nuclei of deuterium exist (2H is 0.015% abundant). Estimate using reaction (13.22) how much energy is available through fusion. ... Get solution

39. The ignition temperature of fusion reactions is referred to in both temperature and kinetic energy. (a) Explain why this is done. (b) What is the relation between the two? (c) At what temperature is the energy 6.0 keV? Get solution

40. The following reactions may be useful in producing energy for fusion reactions. Find their Q values. ... Get solution

41. Determine how hot the environment must be for the first reaction of the CNO cycle to occur. (Hint: First find the threshold kinetic energy for the proton and the Coulomb barrier. After determining the kinetic energy, determine the temperature.) Get solution

42. One of the possibilities for producing energy in a star after the hydrogen has burned to helium is ... (that is, three alpha particles react to form 12C). How much energy is released in this process? Get solution

43. For a thermal neutron (300 K), find its (a) energy, (b) speed, and (c) de Broglie wavelength. Get solution

44. To determine the wear of an automobile engine, a steel compression ring is placed in a nuclear reactor, where it becomes neutron activated because of the formation of 59Fe(t1/2 = 44.5 days, β-). The activity of the ring when placed in the engine is 4.0 × 105 Bq. Over the next 60 days, the car is driven 100,000 km on a test track. The engine oil is extracted, and the activity rate of the oil is measured to be 512 β-/min. What fraction of the ring was worn off during the test? Get solution

45. (a) Why does a 99mTc generator need to be shipped once a week to hospitals? (b) What is the activity of a 1011-Bq 99mTc generator source 9 days after it was produced? (c) If the activity is 0.9 × 1011 Bq on Monday morning when it arrives, what will be the activity at the same time on Friday morning, the last day of the working week? Get solution

46. The Los Angeles County Police want to use neutron activation analysis to look for a tiny residue of barium in gunpowder. The suspected residue is placed in a nuclear reactor, where it is activated by the neutron flux. Natural barium contains 71.7% 138Ba. The β- emitter 139Ba is produced in the 138Ba(n, γ ) 139Ba reaction. The half-life of 139Ba is 83.1 min. 139Ba beta decays to 139La, 72% going to the ground state and 27% going to the first excited state at 0.166 MeV. Scientists think they need a count rate for the 166-keV γ ray (decay to the ground state) of at least 1000 Bq 30 min after the residue is removed from the reactor in order to make a positive identification of barium. (a) How many 139Ba nuclei must be present at the end of the activation? (Remember the decay and fraction going to the first excited state.) (b) How many grams of 139Ba must be produced? If the original amount of barium was 0.01 μg, what fraction of the 138Ba was activated? Get solution

47. A ... Am alpha source is used in a smoke alarm. The device is arranged so that 15% of the decay alphas are detected. (a) What current is detected? (B) If the introduction of smoke causes a 10% change in the intensity of the alpha particles, what sensitivity must the electronic circuit have to cause an alarm? Get solution

48. Consider a spacecraft’s power source consisting of 210Po, which emits a 5.3-MeV alpha particle, t1/2 = 138 days. (a) How many kg of 210Po are needed to initially produce a power source of 5.0 kW? (b) If the power source must produce 7.0 kW after 2.0 years in space, how much 210Po is needed? Get solution

49. A hospital has a 3.0 × 1014 Bq 60Co source for cancer therapy. What is the rate of γ rays incident on a patient of area 0.30 m2 located 4.0 m from the source? 60Co emits a 1.1- and a 1.3-MeV γ ray for each disintegration. Get solution

50. Rework Example 13.10 if the neutron is to probe the diameter of a 238U nucleus. Could neutrons from a nuclear reactor be used? Explain. ... ... Get solution

51. Assume that a 10.0-kg sample of 239Pu is used to produce electrical power from its α decay. If your device is 60% efficient in producing electrical power, how much power can be produced? Get solution

52. We mentioned several superheavy elements that had been observed but not yet confirmed or officially approved by the International Union of Pure and Applied Chemistry (IUPAC). (a) List those elements. (b) Research and discuss their status: Have they been confirmed? Has IUPAC approved them? Get solution

53. An inflated catheter is used in balloon angioplasty to open up arteries that are occluded with plaque formation. Stents are placed in the arteries to support the arterial wall. Radioisotopes have been incorporated into the stents to inhibit the reclosing of the artery (called restenosis). Almost a half million patients in the United States receive intravascular therapy each year. (a) Research the current status of using radioisotopes in this process. How many patients are treated in the United States each year using it? (b) Which radioisotopes are primarily used? Are they beta or gamma emitters? Why would one be favored over the other? Get solution

54g. Compare the following: (a) total atomic binding energy of 1.0 kg of hydrogen atoms, (b) nuclear binding energy of 1.0 kg of deuterons, and (c) annihilation energy of 0.50 kg of protons with 0.50 kg of antiprotons. (d) Comment on the relative orders of magnitudes of the energies you computed in (a), (b), and (c). Get solution

55g. One method used to determine unknown atomic masses consists of precisely measuring the kinetic energies of the particles involved in a nuclear reaction and using known atomic masses. The mass of 34Si is determined by the 30Si(18O, 14O)34Si reaction initiated by 100-MeV 18O particles. The outgoing particles have 86.63 MeV of energy, which can be determined only by measuring the 14O energy and using the conservation of momentum and energy. (a) What is the Q value of the reaction? (b) What is the mass of 34Si assuming the other three masses involved are known (see Appendix 8)? Get solution

56g. 90 90Sr is one of the most deadly products of nuclear fission. Assume that 4% of the fission fragment yield from a 235U atomic bomb is 90Sr. In a nuclear interchange on the planet Inhospitable, 1000 atomic bombs, each corresponding to the fission of 100 kg of 235U, are detonated. (a) How many atoms of 90Sr are released? (b) Assuming the 90Sr is spread evenly over the planet of diameter 12,000 km, what is the resulting activity for each m2? The half-life of 90Sr is 28.8 y. Get solution

57g. Assume a temperature of 2.0 × 108 K in a controlled thermonuclear reactor. (a) Calculate the most probable energy of deuterons at this temperature. (b) Use the Maxwell-Boltzmann distribution from Chapter 9 to determine the fraction of deuterons having an energy that is 2, 5, and 10 times the most probable energy. Get solution

58g. A PuBe source has a neutron activity of 105 Bq. The neutrons are produced by the ... reaction with an effective cross section of 90 mb and thickness of 3 cm. (a) What is the probability of an incident alpha particle interacting with a 9Be nucleus? (b) What must be the rate of alpha particles incident on 9Be? (c) What must be the amount of mass of the 239Pu producing the alpha particles? Get solution

59g. A typical person of mass 70 kg contains 0.35% potassium, by weight. Of the potassium, 0.012% is 40K, an unstable nucleus which decays through ... and electron capture ... What is the 40K activity due to ... decay in a typical per-son's body? Get solution

60g. The yields of nuclear fission bomb weapons are measured in terms of the equivalent amount of energy produced by 1 kiloton of TNT (1 kiloton TNT = 4.2 × 1012J). The bomb dropped on Hiroshima, Japan, on August 6, 1945, was believed to yield 15–20 kilotons. Assume that the bomb yield was 15 kilotons of TNT and that each fission reaction yields 200 MeV. What is the minimum mass of 235U that this bomb (called “Little Boy”) could have contained? Get solution