Chapter #12 Solutions - Modern Physics for Scientists and Engineers - Andrew Rex, Stephen T. Thornton - 3rd Edition

 

1. Assume that gamma rays are Compton scattered by hydrogen. What energy gamma rays are necessary to produce 5.7-MeV protons? Get solution

1q. Explain why neutrons are not prohibited from being in the nucleus for the same three reasons, discussed in the text, that electrons are excluded. Get solution

2. Are the nuclear spins of the following nuclei integral or half-integral: 3He, 6Li, 7Li, 18F, 19F? Get solution

2q. Why does the atomic number Z determine the chemical properties of a nuclide? What differences in chemical properties would you expect for 16O, 17O, and 18O, which are all stable? What about 15O, which is unstable? Get solution

3. What are the number of protons, number of neutrons, mass number, atomic number, charge, and atomic mass for the following nuclei: ... ... Get solution

3q. Explain how the nuclear charge radius could be different from the nuclear mass or nuclear force radius. Get solution

4. What are the number of neutrons and protons for the following nuclides: ... Get solution

4q. Do you believe it is easier to measure atomic masses or nuclear masses? Explain how you could experimentally measure both for 2H. What about for 40Ca? Get solution

5. List from Appendix 8 all the isotopes, isobars, and isotones of ... Get solution

5q. Do you think it is signifi cant that the nucleus has a hard core? What would happen if it did not? Get solution

6. Write down the nuclidic symbol and percentage abundances of all the nuclides having atomic number 7, 23, and 38. Use Appendix 8. Get solution

6q. Is the nuclear potential shown in Figure 12.5 consistent with a short-range nuclear force? Explain. ... Get solution

7. Write down the nuclidic symbol and half-lives for the unstable nuclei having Z = 18 that undergo beta decay and for Z = 102 that undergo spontaneous fission. Use Appendix 8. Get solution

7q. How likely is it that there are additional, as-yet-undetected, stable nuclides that are not shown in Figure 12.6? Explain. ... Get solution

8. What is the ratio of density of the nucleus to that of water? Get solution

8q. Why does the binding energy curve of Figure 12.7 rise so fast for the light nuclei but fall off so slowly for the heavy nuclei? ... Get solution

9. What is the ratio of the magnetic moment of the proton to that of the electron? Get solution

9q. Hundreds of nuclides are known to decay by alpha emission. Why is decay by 3He emission never (or rarely) observed? Get solution

10. Calculate the density and mass of the nuclide 56Fe in SI units. Get solution

10q. For several decades it was believed that the neutrino was massless. If that were so, explain why it must still be distinct from a photon, despite the fact that both travel at the speed of light. Get solution

11. What is the ratio of the electron binding energy in deuterium to the rest energy of the deuteron? Is it reasonable to ignore electronic binding energies when doing nuclear calculations? Get solution

11q. Why is electron capture more probable than β+ decay for the very heavy radioactive elements? Get solution

12. Consider the photodisintegration of a deuteron at rest. Use both the conservation of energy and momentum to determine the minimum photon energy required. What percentage error does neglecting the conservation of momentum make? Get solution

12q. Why do unstable nuclei below the line of stability in Figure 12.6 undergo β+ decay, whereas unstable nuclei above the line of stability undergo β- decay? Get solution

13. Compute the gravitational and Coulomb force between two protons in 3He. Assume the distance between the protons is equal to the nuclear radius. The average nuclear potential energy is an attractive 40 MeV effective over a distance of 3.0 fm. Compare that energy with the potential energies associated with the gravitational and Coulomb forces at the same distance. Get solution

13q. Why are radioactive nuclei still producing heat inside Earth? Get solution

14. Consider two protons in the 27Al nucleus with their centers located 2.4 fm apart. How strong must the nuclear force be to overcome the Coulomb force? Get solution

15. (a) Show that the equation giving the binding energy of the last neutron in a nucleus ...is ... (b) Calculate the binding energy of the most loosely bound neutron of ... Get solution

16. (a) Show that the equation giving the binding energy of the last neutron in a nucleus AZ X is ... (b) Calculate the binding energy of the most loosely bound neutron of 8Be, 15O, and 32S. Get solution

17. What is the energy released when three alpha particles combine to form 12C? Get solution

18. Estimate the nuclear spins of the 3He and 4He nuclei. Explain your reasoning. Get solution

19. The energy required to remove an inner K-shell electron from a silver atom is 25.6 keV. Compare this electron binding energy (the most tightly bound electron) with the binding energy of the most loosely bound proton of .... Get solution

20. Compare the total Coulomb repulsion energy between protons for 4He, 40Ca, and 208Pb. Assume the protons in 4He are, on the average, a distance equal to the nuclear radius apart and use Equation (12.18) for the Coulomb repulsion of the larger nuclei. ... Get solution

21. Compare the total Coulomb repulsion energy between protons for 4He, 40Ca, and 208Pb. Assume the protons in 4He are, on the average, a distance equal to the nuclear radius apart and use Equation (12.18) for the Coulomb repulsion of the larger nuclei. ... Get solution

22. Explain why ... is stable, but ... is not. If ... is stable, why is ...unstable? Get solution

23. Use the von Weizsäcker semi-empirical mass formula to determine the mass (in both atomic mass units u and MeV/c2 ) of 48Ca. Compare this with the mass given in Appendix 8. Get solution

24. (a) Use the von Weizsäcker semi-empirical mass formula to determine the binding energy per nucleon for 18C, 18N, 18O, and 18Ne. (b) Which of these nuclides is the most stable? Is that consistent with what you expect? Explain. (c) Compare the von Weizsäcker B/A for 18O with the same value determined from the atomic masses in Appendix 8. Get solution

25. A radioactive sample of ... has a ... How many grams of ... are present? Get solution

26. An unknown radioactive sample is observed to decrease in activity by a factor of five in a one-hour period. What is its half-life? Get solution

27. Show that the mean (or average) lifetime of a radioactive sample is ... Get solution

28. For the reactor described in Example 12.12, compute the alpha activity of the 238U present in the fuel rod. Assume that the uranium has been enriched to 4% 235U, which is typical for a commercial power reactor fuel rod. ... Get solution

29. Potassium is a useful clement in the human body and is present at a level of about 0.3% of body weight. Calculate the ... activity in a 70-kg person. ... ... Get solution

30. The nuclide ... is a useful radioactive tracer for human consumption. An amount of 18F having an activity of ... is administered to a patient. What is the activity 48 hours later? Get solution

31. Tritium ... is mostly produced for military purposes. If we had stopped producing tritium in 1960 with a 2000-kg stockpile, how much would be left in the year 2010? Get solution

32. If we have the same mass quantities of the following nuclides, rank the activities of the following material: 3H (tritium), 222Rn (radon gas), and 239Pu (alpha source for power generation). Get solution

33. Use atomic masses to show that nucleon decay does not occur for ..., although this nuclide is highly unstable. If one could produce ..., do you believe it might nucleon decay? Explain. Get solution

34. In Example 12.13 we showed that ...does not decay by nucleon emission. What are the neutron and proton separation energies? ... Get solution

35. Show directly using masses that protons do not undergo any of the beta decays. Get solution

36. Calculate whether ...and ...may alpha decay. The natural abundance of 144Sm is 3.1% and that of 147Sm is 15.0%. How can this be explained? Get solution

37. How much kinetic energy does the daughter have when ...undergoes α decay from rest? Get solution

38. Show from the conservation of energy and momentum that if Equation (12.34) correctly describes the β- decay of 14C initially at rest, the electron energy spectrum must be monoenergetic and not like that shown in Figure 12.15. ... ... Get solution

39. Find which of the α and β decays are allowed for .... Get solution

40. Find which of the α and β decays are allowed for .... Get solution

41. Show that α, β-, β+, and EC decay are possible for the nucleus .... Get solution

42. List all the possible energies of γ decay for 230U based on Figure 12.16. ... Get solution

43. Calculate the partial pressure of helium gas for a volume of 1.0 × 10-6 m3 of ...gas after 6 days. The radon gas was originally placed in an evacuated container at 1.0 atm, and the temperature remains constant at 0°C. What is the partial pressure of the radon gas after 6 days? (t1/2 = 3.82 d for 222Rn) Calculate the partial pressure of helium gas for a volume of 1.0 × 10-6 m3 of ...gas after 6 days. The radon gas was originally placed in an evacuated container at 1.0 atm, and the temperature remains constant at 0°C. What is the partial pressure of the radon gas after 6 days? (t1/2 = 3.82 d for 222Rn) Get solution

44. The nuclide 60Co decays by β-. Yet 60Co is often used, especially in medical applications, as a source of γ rays. Explain how this is possible. Get solution

45. Explain why β- predominates over β+ decay in the natural radioactive decay chains of the heavy elements. Get solution

46. Give reasons why 14O can β+ decay, but the proton cannot. (Hint: Use masses to prove this.) Get solution

47. Two rocks are found that have different ratios R’ of 238U to 206Pb: R’ = 0.76 and 3.1. What are the ages of the two rocks? Did they likely have the same origin? Get solution

48. Use Table 12.2 to list some radioactive nuclides that may be useful for dating the age of Earth. ... Get solution

49. If scientists are only able to determine the ratio of R’ in Equation (12.50) to 0.01, what is the minimum time possible for dating? ... Get solution

50. If the age of Earth is 4.6 billion years, what should be the ratio of 206Pb/238U in a uranium-bearing rock as old as the Earth? Get solution

51. Use only Z and A values to calculate the number of α and β particles produced from the decay of ...to its stable end product.... Get solution

52. The Earth is about 4.5 billion years old. If 235U 1.3 is 0.72% abundant today, how abundant was it when the Earth formed? (Hint: Look in Appendix 8 for useful information.) Get solution

53. Consider 100 g of 252Fm, which decays in a sequence of five α decays to eventually reach 232Th. (a) How much of the original sample is 252Fm, and how much is 248Cf after one day? (b) After one month? (c) Explain why it is mostly curium after 5 years. (d) What isotope is it mostly after 100 years? (e) Approximate how much time it will take for the sample to be mostly thorium. Get solution

54. Note in Table 12.2 that the half-lives of two abundant isotopes of tellurium are more than 1021 years. (a) What is the decay rate per unit mass of 128Te, which decays by emitting two β-, in units of s-1 . kg-1? (b) How much mass of a natural sample of tellurium would it take to measure a decay rate of 10 β-/s for 128Te? ... Get solution

55g. Show that the total Coulomb self-energy of a sphere of radius R containing a charge Ze evenly spread throughout the sphere is given by ... Hint: Calculate the work done to bring a charge from infinity into a spherical shell of radius r and then integrate the spherical shell from 0 to R. Get solution

56g. Use the uncertainty principle ...to calculate the minimum kinetic energy of a nucleon known to be confined in 2H. What is the de Broglie wavelength of this nucleon? Is this reasonable? Get solution

57g. The nucleus 180 73Ta is unusual because it has both odd Z and odd N, yet it is barely unstable with a half-life of 8 hours. It has an isomeric state at excitation energy 0.075 MeV that experimental measurements indicate has a half-life greater than 1015 y. For many years it was believed that this long-lived excited state was the ground state and might be stable. All the stable odd Z and N nuclei are smaller than 16O. Why are all heavy elements with both odd Z and N unstable? The spins of the 180Ta ground state and isomeric states are believed to be 1+ and 9-, respectively. Explain why scientists may have believed for so long that 180Ta was stable. Get solution

58g. The only stable isotope of holmium is 165 67Ho. Explain this. Can 165Ho. α decay? Is it likely to α decay? Get solution

59g. The nuclide 226 88Ra decays to gaseous 222 86Rn with a t1/2 = 1600 y. The nuclide 222 86Rn in turn α decays with a shorter lifetime, t1/2 = 3.82 days. If radium is originally placed in an evacuated closed container, the amount of radon gas builds up and can be measured. It is found that radon gas builds up to a constant value and that as much 222Rn is being produced as decays. This process is called secular equilibrium, and the activities are equal. (a) Show that radon builds up at the rate dN2/dt = λ1N1 - λ2N2 where λ1, N1 and - λ2, N2 are the decay constants and number of nuclei present for radium and radon, respectively. (b) Because the decay of 226Ra is so slow, assume that N1 is constant and show that ... (c) Show that after a long time, secular equilibrium is reached. Get solution

60g. Rudolf Mössbauer discovered in 1957 that transitions from an excited nuclear state occur with negligible nuclear recoil when the nucleus is embedded in a large crystal lattice because the entire lattice absorbs the recoil. A transition like that in 191Ir from the 129- keV excited state to the ground state has a lifetime of 1.9 × 10-10 s. (a) Determine the energy width of the decay. (b) Similarly, if the photon is absorbed by 191Ir embedded in a crystal, the recoil is negligible. However, even a slight motion of the absorber will lead to a Doppler shift suffi cient to destroy the resonance absorption. Calculate the speed necessary to shift the energy absorption by 5 ..., where ... is the nuclear decay width. This effect is called the Mössbauer effect. Get solution

61g. Radon gas in the form of 222Rn is a health hazard because it is a gas that occurs as a result of one of the naturally occurring radioactive decay chains. It tends to collect in basements and can be inhaled by humans. (a) Which decay chain produces this isotope of radon? (b) Show that 222Rn produces five more disintegrations before a stable isotope is reached. (c) Choose one of the paths of the decay chain from 222Rn to the stable isotope and sum the half-lives. Approximate the number of days it would take for more than half these decays to occur for a given amount of radon. Get solution

62g. Just as there are atomic shell features, there are also nuclear shell structures. Certain values of the number of protons Z and neutrons N are called “magic,” because certain nuclides with these magic numbers are more tightly bound and have enhanced abundances. These numbers are 2, 8, 20, 28, 50, 82, and 126. (a) Use this fact to explain why 4He and 16O have peaks in the binding energy curve of Figure 12.7. (b) Explain why 208Pb is one of the heaviest stable nuclides. (c) Discuss the abundances of the calcium isotopes with respect to their value of N. The German physicists Maria Goeppert- Mayer and J. Hans D. Jensen won the Nobel Prize in Physics in 1963 for their discoveries concerning the nuclear shell model. Get solution

63g. Use the nuclear shell model of the previous problem to list five stable nuclides that have magic numbers for both Z and N. Get solution