1cc. Which of the following is a valid Feynman diagram for the beta decay of a charm quark?(a) ...(b) ...(c) ...(d) ... Get solution
1mcq. According to the text, the de Broglie wavelength, λ, of a 5-MeV alpha particle is 6.4 fm, and the closest distance, rmin, to the gold nucleus this alpha particle can get is 45.5 fm (calculated in Example 39.1). Based on the fact that λ rmin, one can conclude that, for this Rutherford scattering experiment, it is adequate to treat the alpha particle as aa) particle.b) wave.Example 39.1 Backward Scattering of Alpha Particles... Get solution
2cc. The Planck mass is approximately the same as the mass of aa) Z boson.b) gold atom.c) leg of a fruit fly.d) baseball.e) aircraft carrier. Get solution
2mcq. Which of the following is a composite particle? (select all that apply)a) electronb) neutrinoc) protond) muon Get solution
3cc. From Figure 39.33, the isospin projections, tz, of the anti-up quark ... and the anti-down quark ... area) ....b) ....c) ....d) ....e) ....Figure 39.33 Quark composition of the two meson nonets.... Get solution
3mcq. Which of the following formed latest in the universe?a) quarksb) protons and neutronsc) hydrogen atomsd) helium nucleie) gluons Get solution
4mcq. An exchange particle for the weak force is thea) photon.b) meson.c) W boson.d) graviton.e) gluon. Get solution
5mcq. Which of the following particles does not have an integer spin?a) photonb) ω mesonc) π mesond) ve lepton Get solution
6mcq. At about what kinetic energy is the length scale probed by an α particle no longer calculated by the classical formula but rather by the relativistic formula?a) 0.3 GeVb) 0.03 GeVc) 3 GeVd) 30 GeV Get solution
7mcq. Which of the following experiments proved the existence of the nucleus?a) the photoelectric effectb) the Millikan oil-drop experimentc) the Rutherford scattering experimentd) the Stern-Gerlach experiment Get solution
8cq. Which of the following reactions cannot occur, and why?a) p → π+ + π0b) pπ0 → n + e+c) ... (1116) → p + K–π+d) ... (1450) → p + K– + π+ Get solution
10cq. Consider a hypothetical force mediated by the exchange of bosons that have the same mass as protons. Approximately what would be the maximum range of such a force? You may assume that the total energy of these particles is simply the rest-mass energy and that they travel close to the speed of light. If you do not make these assumptions and instead use the relativistic expression for total energy, what happens to your estimate of the maximum range of the force? Get solution
11cq. Looking at Table 39.3, do the constituent quarks uniquely define the type of meson?Table 39.3 The Most Important Mesons, Including Their Masses, Lifetimes, Quantum Numbers, and Quark Composition... Get solution
12cq. A free neutron decays into a proton and an electron (and an antineutrino). A free proton has never been observed to decay. Why then do we consider the neutron to be as “fundamental” (at the nuclear level) a particle as the proton? Why do we not consider a neutron to be a proton-electron composite? Get solution
13cq. In a positron annihilation experiment, positrons are directed toward a metal. What are we likely to observe in such an experiment, and how might it provide information about the momentum of electrons in the metal? Get solution
14cq. If the energy of the virtual photon mediating an electron-proton scattering, e– + p → e‑ + p, is E, what is the range of this electromagnetic interaction in terms of E? Get solution
15cq. Describe the physical processes that the following Feynman diagrams represent:(a) ...(b) ...(c) ... Get solution
16cq. Figure 39.34 shows a Feynman diagram for the fundamental process involved in the decay of a free neutron: One of the neutron’s down quarks converts to an up quark, emitting a virtual W‑ boson, which decays into an electron and an anti-electron-neutrino (the only decay energetically possible). Sketch the basic Feynman diagram for the fundamental process involved in each of the following decays:a) ...b) ...c) ...d) ...e) ...Figure 39.34 Feynman diagram for the beta decay of the neutron.... Get solution
17cq. Does the decay process n → p + π– violate any conservation rules? Get solution
18cq. Consider the decay process .... Can this decay occur? Get solution
19cq. Can the reaction ... occur? Get solution
20cq. How do we know for certain that the scattering process ... proceeds through an intermediate Z boson and cannot proceed through an intermediate charged W boson, while both options are possible for ... Get solution
21cq. What baryons have the quark composition uds? What is the mass of these baryons? Get solution
22cq. In the following Feynman diagram for proton-neutron scattering, what is the virtual particle?... Get solution
23. A 4.50-MeV alpha particle is incident on a platinum nucleus (Z = 78). What is the minimum distance of approach, rmin? Get solution
24. A 6.50-MeV alpha particle is incident on a lead nucleus. Because of the Coulomb force between them, the alpha particle will approach the nucleus to a minimum distance, rmin.a) Determine rmin.b) If the kinetic energy of the alpha particle is increased, will the particle’s distance of approach increase, decrease, or remain the same? Explain. Get solution
25. A 6.50-MeV alpha particle scatters at a 60.0° angle off a lead nucleus. Determine the differential cross section of the alpha particle. Get solution
26. Protons with a kinetic energy of 2.00 MeV scatter off gold nuclei in a foil target. Each gold nucleus contains 79 protons. If both the incoming protons and the gold nuclei can be treated as point objects, what is the differential cross section that will cause the protons to scatter off the gold nuclei at an angle of 30.0° from their initial trajectory? Get solution
27. The de Broglie wavelength, λ, of a 5.00-MeV alpha particle is 6.40 fm, and the closest distance, rmin, to the gold nucleus this alpha particle can get is 45.5 fm (calculated in Example 39.1). How does the ratio rminλ vary with the kinetic energy of the alpha particle?Example 39.1 Backward Scattering of Alpha Particles... Get solution
28. An experiment similar to the Geiger-Marsden experiment is done by bombarding a 1.00-μm-thick gold foil with 8.00-MeV alpha particles. Calculate the fraction of particles scattered at an anglea) between 5.00° and 6.00° andb) between 30.0° and 31.0°.(The atomic mass number of gold is 197, and its density is 19.3 g/cm3.) Get solution
29. The differential cross section that will cause particles to scatter at an angle 55° off a target is 4.0 · 10‑ m2/sr. A detector with an area of 1.0 cm2 is placed 1.0 m away from the target in order to detect particles that have been scattered at 55°. If 3.0 · 1017 particles hit the 1.0-mm2-area target every second, how many will strike the detector every second?... Get solution
30. Some particle detectors measure the total number of particles integrated over part of a sphere of radius R, where the target is at the center of the sphere. Assuming symmetry about the axis of the incoming particle beam, use the Rutherford scattering formula to obtain the total number of particles detected in an an interval of width d θ as a function of the scattering angle, θ. Get solution
31. Evaluate the form factor and the differential cross section, dσ/dΩ, for a beam of electrons scattering off a uniform-density charged sphere of total charge Ze and radius R. Describe the scattering pattern. Get solution
32. A proton is made of two up quarks and a down quark (uud). Calculate its charge. Get solution
33. Use the fact that the observed magnetic moment of a proton is 1.4 · 10–26 A m2 to estimate the speed of its quarks. For this estimate, assume that the quarks move in circular orbits of radius 0.80 fm and that they all move at the same speed and direction. Ignore any relativistic effects. Get solution
34. Determine the approximate probing distance of a photon with an energy of 2.0 keV. Get solution
35. Draw a Feynman diagram for an electron-proton scattering, e– + p → e– + p, mediated by photon exchange. Get solution
36. Based on the information in Table 39.2, what is the approximate upper bound on the range of a reaction mediated by the Higgs boson? Get solution
37. Draw Feynman diagrams for the following phenomena:a) protons scattering off each otherb) a neutron beta decays to a proton: .... Get solution
38. A proton and a neutron interact via the strong nuclear force. Their interaction is mediated by a meson, much like the interaction between charged particles is mediated by photons—the particles of the electromagnetic field.a) Perform a rough estimate of the mass of the meson from the uncertainty principle and the known dimensions of a nucleus (~10–15 m). Assume that the meson travels at relativistic speed.b) Use a line of reasoning similar to that in part (a) to prove that the theoretically expected rest mass of the photon is zero. Get solution
39. How many fundamental fermions are there in a carbon dioxide molecule (CO2)? Get solution
40. Suppose a neutral pion at rest decays into two identical photons.a) What is the energy of each photon?b) What is the frequency of each photon?c) To what part of the electromagnetic spectrum do the photons correspond? Get solution
41. Draw a quark-level Feynman diagram for the decay of a neutral kaon into two charged pions: K0 → π+ + π–. Get solution
42. During the radiation-dominated era of the universe, the temperature was falling gradually according to equation 39.17. Using Stefan’s Law, find the time dependence of background-radiation intensity during that era.... Get solution
43. Use equation 39.17 to estimate the age of the universe when protons and neutrons began to form.... Get solution
44. Three hundred thousand years after the Big Bang, the average temperature of the universe was about 3000 K.a) At what wavelength would the blackbody spectrum peak for this temperature?b) In what portion of the electromagnetic spectrum is this wavelength found? Get solution
45. At about 10–6 s after the Big Bang, the universe had cooled to a temperature of approximately 1013 K.a) Calculate the thermal energy kBT of the universe at that temperature.b) Explain what happened to most of the hadrons—protons and neutrons—at that time.c) Explain what happened to electrons and positrons in terms of temperature and time. Get solution
46. Three hundred thousand years after the Big Bang, the temperature of the universe was 3000 K. Because of expansion, the temperature of the universe is now 2.75 K. Modeling the universe as an ideal gas and assuming that the expansion is adiabatic, calculate how much the volume of the universe has changed. If the process is irreversible, estimate the change in the entropy of the universe based on the change in volume. Get solution
47. The fundamental observation underlying the Big Bang theory of cosmology is Edwin Hubble’s 1929 discovery that the arrangement of galaxies throughout space is expanding. Like the photons of the cosmic microwave background, the light from distant galaxies is stretched to longer wavelengths by the expansion of the universe. This is not a Doppler shift: Except for their local motions around each other, the galaxies are essentially at rest in space; it is space itself that expands. The ratio of the wavelength of light received at Earth from a galaxy, λrec, to its wavelength at emission, λemit, is equal to the ratio of the scale factor (radius of curvature) a of the universe at reception to its value at emission. The redshift, z, of the light—which is what Hubble could measure—is defined by 1 + z = λrec/λemit = arec/aemit.a) Hubble’s Law states that the redshift, z, of light from a galaxy is proportional to the galaxy’s distance from Earth (for reasonably nearby galaxies): ..., where c is the vacuum speed of light, H is the Hubble constant, and ∆s is the distance of the galaxy from Earth. Derive this law from the relationships described in the problem statement, and determine the Hubble constant in terms of the scale-factor function a(t).b) If the Hubble constant currently has the value H0 = 72 (km/s)/Mpc, how far away is a galaxy whose light has the redshift z = 0.10? (The megaparsec (Mpc) is a unit of length equal to 3.26 · 106 light-years. For comparison, the Great Nebula in Andromeda is approximately 0.60 Mpc from Earth.) Get solution
48. What is the minimum energy of a photon capable of producing an electron-positron pair? What is the wavelength of this photon? Get solution
49. a) Calculate the kinetic energy of a neutron that has a de Broglie wavelength of 0.15 nm. Compare this with the energy of an X-ray photon that has the same wavelength.b) Comment on how this energy difference is relevant to using neutrons or X-rays for investigating biological samples. Get solution
50. A photon can interact with matter by producing a proton-antiproton pair. What is the minimum energy the photon must have? Get solution
51. Suppose you had been doing an experiment to probe structure on a scale for which you needed electrons with 100. eV of kinetic energy. Then a neutron beam became available for the experiment. What energy would the neutrons need to have to give you the same resolution? Get solution
52. What is the de Broglie wavelength of an alpha particle that has a kinetic energy of 100. MeV? According to Figure 39.13, how does this wavelength compare to the size of structure that can be probed with this alpha particle?Figure 39.13 Minimum kinetic energy required to probe a structure of a given size for electrons (red), photons (blue), and alpha particles (green).... Get solution
53. One of the elementary bosons that can mediate electroweak interactions is the Z0 boson, having the mass of 91.1876 GeV/c2. Find the order of magnitude of the range of the electroweak interaction. Get solution
54. What are the wavelengths of the two photons produced when a proton and an antiproton at rest annihilate? Get solution
55. Estimate the cross section of a Λ0 particle decay (into p + π–, n + π0) if the time it takes for this electroweak interaction to occur is ~10–10 s. Get solution
56. Determine the classical differential cross section for Rutherford scattering of alpha particles of energy 5.00 MeV projected at uranium atoms and scattered at an angle of 35.0° from the initial trajectory. Assume that both the target and the projectile atoms are pointlike. Get solution
57. The Geiger-Marsden experiment successfully demonstrated the existence of the nucleus and put limits on its size using the scattering of alpha particles from gold foils. Assume that the alpha particles were fired with a speed about 5.00% of the speed of light.a) Derive the upper bound of the radius of the nucleus in terms of the speed of the alpha particle that is scattered in the backward direction.b) Calculate the approximate radius of the gold nucleus using the result from part (a). Get solution
58. An electron-positron pair, traveling toward each other with a speed of 0.99c with respect to their center of mass, collide and annihilate according to e– + e+ → λ + λ. Assuming that the observer is at rest with respect to the center of mass of the electron-positron pair, what is the wavelength of the emitted photons? Get solution
59. Electron and positron beams are collided, and pairs of tau leptons are produced. If the angular distribution of the tau leptons varies as (1 + cos2θ), what fraction of the tau lepton pairs will be captured in a detector that covers only the angles from 60° to 120°? Get solution
60. On July 4, 2012, the discovery of the Higgs boson at the Large Hadron Collider was announced. During the data-taking run, the LHC reached a peak luminosity of 4.00 · 1033 cm–2 s–1 (this means that in an area of 1 square centimeter, 4.00 · 1033 protons collided every second). Assume that the cross section for the production of the Higgs boson in these proton-proton collisions is 1.00 pb (picobarn). If the LHC accelerator ran without interruption for 1.00 yr at this luminosity, how many Higgs bosons would be produced? Get solution
61. Evaluate the form factor and the differential cross section, dσ/dΩ, for a beam of electrons scattering off a thin spherical shell of total charge Ze and radius a. Could this scattering experiment distinguish between thin-shell and solid-sphere charge distributions? Explain Get solution
62. A neutrino beam with E = 337 GeV is passed through a 68.5-cm-thick slab of aluminum-27 (with 27 nucleons in each nucleus). What fraction of the neutrinos will scatter off a nucleon if the cross section is given by σ(E) = (0.68 · 10–38 cm2 GeV–1)E? (Aluminum has a density of 2.77 g/cm3.) Get solution
63. A neutrino beam with E = 143 GeV is passed through a slab of aluminum-27 (with 27 nucleons in each nucleus). The probability that a neutrino in the beam will scatter off a nucleon in the aluminum slab is 4.19 · 10–12. The scattering cross section is given by σ(E) = (0.68 · 10–38 cm2 GeV–1)E, and aluminum has a density of 2.77 g/cm3. How thick is the slab? Get solution
64. A high-energy neutrino beam is passed through a slab of aluminum-27 (with 27 nucleons in each nucleus) of thickness 71.1 cm. The probability that a neutrino in the beam will scatter off a nucleon in the aluminum slab is 6.00 · 10–12. The scattering cross section is given by σ(E) = (0.68 · 10–38 cm2 GeV–1)E, and aluminum has a density of 2.77 g/cm3. What is the energy (in GeV) of the neutrino beam? Get solution
65. A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of I(94.9°) = 853 counts/s at a scattering angle of 94.9°±0.7°. What is the intensity (in counts/s) at a scattering angle of 60.5°±0.7° if the scattering obeys the Rutherford formula? Get solution
66. A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of I(95.1°) = 1129 counts/s at a scattering angle of 95.1°±0.4°. At a second scattering angle, the intensity is measured to be 4840 counts/s. Assuming that the scattering obeys the Rutherford formula, what is that second angle (in degrees, to the same uncertainty)? Get solution
67. A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, is set up with two detectors at θ1 = 85.1°±0.9° and θ2 = 62.9°±0.9°. Assuming that the scattering obeys the Rutherford formula, what is the ratio of the measured intensities, I1/I2? Get solution
1mcq. According to the text, the de Broglie wavelength, λ, of a 5-MeV alpha particle is 6.4 fm, and the closest distance, rmin, to the gold nucleus this alpha particle can get is 45.5 fm (calculated in Example 39.1). Based on the fact that λ rmin, one can conclude that, for this Rutherford scattering experiment, it is adequate to treat the alpha particle as aa) particle.b) wave.Example 39.1 Backward Scattering of Alpha Particles... Get solution
2cc. The Planck mass is approximately the same as the mass of aa) Z boson.b) gold atom.c) leg of a fruit fly.d) baseball.e) aircraft carrier. Get solution
2mcq. Which of the following is a composite particle? (select all that apply)a) electronb) neutrinoc) protond) muon Get solution
3cc. From Figure 39.33, the isospin projections, tz, of the anti-up quark ... and the anti-down quark ... area) ....b) ....c) ....d) ....e) ....Figure 39.33 Quark composition of the two meson nonets.... Get solution
3mcq. Which of the following formed latest in the universe?a) quarksb) protons and neutronsc) hydrogen atomsd) helium nucleie) gluons Get solution
4mcq. An exchange particle for the weak force is thea) photon.b) meson.c) W boson.d) graviton.e) gluon. Get solution
5mcq. Which of the following particles does not have an integer spin?a) photonb) ω mesonc) π mesond) ve lepton Get solution
6mcq. At about what kinetic energy is the length scale probed by an α particle no longer calculated by the classical formula but rather by the relativistic formula?a) 0.3 GeVb) 0.03 GeVc) 3 GeVd) 30 GeV Get solution
7mcq. Which of the following experiments proved the existence of the nucleus?a) the photoelectric effectb) the Millikan oil-drop experimentc) the Rutherford scattering experimentd) the Stern-Gerlach experiment Get solution
8cq. Which of the following reactions cannot occur, and why?a) p → π+ + π0b) pπ0 → n + e+c) ... (1116) → p + K–π+d) ... (1450) → p + K– + π+ Get solution
10cq. Consider a hypothetical force mediated by the exchange of bosons that have the same mass as protons. Approximately what would be the maximum range of such a force? You may assume that the total energy of these particles is simply the rest-mass energy and that they travel close to the speed of light. If you do not make these assumptions and instead use the relativistic expression for total energy, what happens to your estimate of the maximum range of the force? Get solution
11cq. Looking at Table 39.3, do the constituent quarks uniquely define the type of meson?Table 39.3 The Most Important Mesons, Including Their Masses, Lifetimes, Quantum Numbers, and Quark Composition... Get solution
12cq. A free neutron decays into a proton and an electron (and an antineutrino). A free proton has never been observed to decay. Why then do we consider the neutron to be as “fundamental” (at the nuclear level) a particle as the proton? Why do we not consider a neutron to be a proton-electron composite? Get solution
13cq. In a positron annihilation experiment, positrons are directed toward a metal. What are we likely to observe in such an experiment, and how might it provide information about the momentum of electrons in the metal? Get solution
14cq. If the energy of the virtual photon mediating an electron-proton scattering, e– + p → e‑ + p, is E, what is the range of this electromagnetic interaction in terms of E? Get solution
15cq. Describe the physical processes that the following Feynman diagrams represent:(a) ...(b) ...(c) ... Get solution
16cq. Figure 39.34 shows a Feynman diagram for the fundamental process involved in the decay of a free neutron: One of the neutron’s down quarks converts to an up quark, emitting a virtual W‑ boson, which decays into an electron and an anti-electron-neutrino (the only decay energetically possible). Sketch the basic Feynman diagram for the fundamental process involved in each of the following decays:a) ...b) ...c) ...d) ...e) ...Figure 39.34 Feynman diagram for the beta decay of the neutron.... Get solution
17cq. Does the decay process n → p + π– violate any conservation rules? Get solution
18cq. Consider the decay process .... Can this decay occur? Get solution
19cq. Can the reaction ... occur? Get solution
20cq. How do we know for certain that the scattering process ... proceeds through an intermediate Z boson and cannot proceed through an intermediate charged W boson, while both options are possible for ... Get solution
21cq. What baryons have the quark composition uds? What is the mass of these baryons? Get solution
22cq. In the following Feynman diagram for proton-neutron scattering, what is the virtual particle?... Get solution
23. A 4.50-MeV alpha particle is incident on a platinum nucleus (Z = 78). What is the minimum distance of approach, rmin? Get solution
24. A 6.50-MeV alpha particle is incident on a lead nucleus. Because of the Coulomb force between them, the alpha particle will approach the nucleus to a minimum distance, rmin.a) Determine rmin.b) If the kinetic energy of the alpha particle is increased, will the particle’s distance of approach increase, decrease, or remain the same? Explain. Get solution
25. A 6.50-MeV alpha particle scatters at a 60.0° angle off a lead nucleus. Determine the differential cross section of the alpha particle. Get solution
26. Protons with a kinetic energy of 2.00 MeV scatter off gold nuclei in a foil target. Each gold nucleus contains 79 protons. If both the incoming protons and the gold nuclei can be treated as point objects, what is the differential cross section that will cause the protons to scatter off the gold nuclei at an angle of 30.0° from their initial trajectory? Get solution
27. The de Broglie wavelength, λ, of a 5.00-MeV alpha particle is 6.40 fm, and the closest distance, rmin, to the gold nucleus this alpha particle can get is 45.5 fm (calculated in Example 39.1). How does the ratio rminλ vary with the kinetic energy of the alpha particle?Example 39.1 Backward Scattering of Alpha Particles... Get solution
28. An experiment similar to the Geiger-Marsden experiment is done by bombarding a 1.00-μm-thick gold foil with 8.00-MeV alpha particles. Calculate the fraction of particles scattered at an anglea) between 5.00° and 6.00° andb) between 30.0° and 31.0°.(The atomic mass number of gold is 197, and its density is 19.3 g/cm3.) Get solution
29. The differential cross section that will cause particles to scatter at an angle 55° off a target is 4.0 · 10‑ m2/sr. A detector with an area of 1.0 cm2 is placed 1.0 m away from the target in order to detect particles that have been scattered at 55°. If 3.0 · 1017 particles hit the 1.0-mm2-area target every second, how many will strike the detector every second?... Get solution
30. Some particle detectors measure the total number of particles integrated over part of a sphere of radius R, where the target is at the center of the sphere. Assuming symmetry about the axis of the incoming particle beam, use the Rutherford scattering formula to obtain the total number of particles detected in an an interval of width d θ as a function of the scattering angle, θ. Get solution
31. Evaluate the form factor and the differential cross section, dσ/dΩ, for a beam of electrons scattering off a uniform-density charged sphere of total charge Ze and radius R. Describe the scattering pattern. Get solution
32. A proton is made of two up quarks and a down quark (uud). Calculate its charge. Get solution
33. Use the fact that the observed magnetic moment of a proton is 1.4 · 10–26 A m2 to estimate the speed of its quarks. For this estimate, assume that the quarks move in circular orbits of radius 0.80 fm and that they all move at the same speed and direction. Ignore any relativistic effects. Get solution
34. Determine the approximate probing distance of a photon with an energy of 2.0 keV. Get solution
35. Draw a Feynman diagram for an electron-proton scattering, e– + p → e– + p, mediated by photon exchange. Get solution
36. Based on the information in Table 39.2, what is the approximate upper bound on the range of a reaction mediated by the Higgs boson? Get solution
37. Draw Feynman diagrams for the following phenomena:a) protons scattering off each otherb) a neutron beta decays to a proton: .... Get solution
38. A proton and a neutron interact via the strong nuclear force. Their interaction is mediated by a meson, much like the interaction between charged particles is mediated by photons—the particles of the electromagnetic field.a) Perform a rough estimate of the mass of the meson from the uncertainty principle and the known dimensions of a nucleus (~10–15 m). Assume that the meson travels at relativistic speed.b) Use a line of reasoning similar to that in part (a) to prove that the theoretically expected rest mass of the photon is zero. Get solution
39. How many fundamental fermions are there in a carbon dioxide molecule (CO2)? Get solution
40. Suppose a neutral pion at rest decays into two identical photons.a) What is the energy of each photon?b) What is the frequency of each photon?c) To what part of the electromagnetic spectrum do the photons correspond? Get solution
41. Draw a quark-level Feynman diagram for the decay of a neutral kaon into two charged pions: K0 → π+ + π–. Get solution
42. During the radiation-dominated era of the universe, the temperature was falling gradually according to equation 39.17. Using Stefan’s Law, find the time dependence of background-radiation intensity during that era.... Get solution
43. Use equation 39.17 to estimate the age of the universe when protons and neutrons began to form.... Get solution
44. Three hundred thousand years after the Big Bang, the average temperature of the universe was about 3000 K.a) At what wavelength would the blackbody spectrum peak for this temperature?b) In what portion of the electromagnetic spectrum is this wavelength found? Get solution
45. At about 10–6 s after the Big Bang, the universe had cooled to a temperature of approximately 1013 K.a) Calculate the thermal energy kBT of the universe at that temperature.b) Explain what happened to most of the hadrons—protons and neutrons—at that time.c) Explain what happened to electrons and positrons in terms of temperature and time. Get solution
46. Three hundred thousand years after the Big Bang, the temperature of the universe was 3000 K. Because of expansion, the temperature of the universe is now 2.75 K. Modeling the universe as an ideal gas and assuming that the expansion is adiabatic, calculate how much the volume of the universe has changed. If the process is irreversible, estimate the change in the entropy of the universe based on the change in volume. Get solution
47. The fundamental observation underlying the Big Bang theory of cosmology is Edwin Hubble’s 1929 discovery that the arrangement of galaxies throughout space is expanding. Like the photons of the cosmic microwave background, the light from distant galaxies is stretched to longer wavelengths by the expansion of the universe. This is not a Doppler shift: Except for their local motions around each other, the galaxies are essentially at rest in space; it is space itself that expands. The ratio of the wavelength of light received at Earth from a galaxy, λrec, to its wavelength at emission, λemit, is equal to the ratio of the scale factor (radius of curvature) a of the universe at reception to its value at emission. The redshift, z, of the light—which is what Hubble could measure—is defined by 1 + z = λrec/λemit = arec/aemit.a) Hubble’s Law states that the redshift, z, of light from a galaxy is proportional to the galaxy’s distance from Earth (for reasonably nearby galaxies): ..., where c is the vacuum speed of light, H is the Hubble constant, and ∆s is the distance of the galaxy from Earth. Derive this law from the relationships described in the problem statement, and determine the Hubble constant in terms of the scale-factor function a(t).b) If the Hubble constant currently has the value H0 = 72 (km/s)/Mpc, how far away is a galaxy whose light has the redshift z = 0.10? (The megaparsec (Mpc) is a unit of length equal to 3.26 · 106 light-years. For comparison, the Great Nebula in Andromeda is approximately 0.60 Mpc from Earth.) Get solution
48. What is the minimum energy of a photon capable of producing an electron-positron pair? What is the wavelength of this photon? Get solution
49. a) Calculate the kinetic energy of a neutron that has a de Broglie wavelength of 0.15 nm. Compare this with the energy of an X-ray photon that has the same wavelength.b) Comment on how this energy difference is relevant to using neutrons or X-rays for investigating biological samples. Get solution
50. A photon can interact with matter by producing a proton-antiproton pair. What is the minimum energy the photon must have? Get solution
51. Suppose you had been doing an experiment to probe structure on a scale for which you needed electrons with 100. eV of kinetic energy. Then a neutron beam became available for the experiment. What energy would the neutrons need to have to give you the same resolution? Get solution
52. What is the de Broglie wavelength of an alpha particle that has a kinetic energy of 100. MeV? According to Figure 39.13, how does this wavelength compare to the size of structure that can be probed with this alpha particle?Figure 39.13 Minimum kinetic energy required to probe a structure of a given size for electrons (red), photons (blue), and alpha particles (green).... Get solution
53. One of the elementary bosons that can mediate electroweak interactions is the Z0 boson, having the mass of 91.1876 GeV/c2. Find the order of magnitude of the range of the electroweak interaction. Get solution
54. What are the wavelengths of the two photons produced when a proton and an antiproton at rest annihilate? Get solution
55. Estimate the cross section of a Λ0 particle decay (into p + π–, n + π0) if the time it takes for this electroweak interaction to occur is ~10–10 s. Get solution
56. Determine the classical differential cross section for Rutherford scattering of alpha particles of energy 5.00 MeV projected at uranium atoms and scattered at an angle of 35.0° from the initial trajectory. Assume that both the target and the projectile atoms are pointlike. Get solution
57. The Geiger-Marsden experiment successfully demonstrated the existence of the nucleus and put limits on its size using the scattering of alpha particles from gold foils. Assume that the alpha particles were fired with a speed about 5.00% of the speed of light.a) Derive the upper bound of the radius of the nucleus in terms of the speed of the alpha particle that is scattered in the backward direction.b) Calculate the approximate radius of the gold nucleus using the result from part (a). Get solution
58. An electron-positron pair, traveling toward each other with a speed of 0.99c with respect to their center of mass, collide and annihilate according to e– + e+ → λ + λ. Assuming that the observer is at rest with respect to the center of mass of the electron-positron pair, what is the wavelength of the emitted photons? Get solution
59. Electron and positron beams are collided, and pairs of tau leptons are produced. If the angular distribution of the tau leptons varies as (1 + cos2θ), what fraction of the tau lepton pairs will be captured in a detector that covers only the angles from 60° to 120°? Get solution
60. On July 4, 2012, the discovery of the Higgs boson at the Large Hadron Collider was announced. During the data-taking run, the LHC reached a peak luminosity of 4.00 · 1033 cm–2 s–1 (this means that in an area of 1 square centimeter, 4.00 · 1033 protons collided every second). Assume that the cross section for the production of the Higgs boson in these proton-proton collisions is 1.00 pb (picobarn). If the LHC accelerator ran without interruption for 1.00 yr at this luminosity, how many Higgs bosons would be produced? Get solution
61. Evaluate the form factor and the differential cross section, dσ/dΩ, for a beam of electrons scattering off a thin spherical shell of total charge Ze and radius a. Could this scattering experiment distinguish between thin-shell and solid-sphere charge distributions? Explain Get solution
62. A neutrino beam with E = 337 GeV is passed through a 68.5-cm-thick slab of aluminum-27 (with 27 nucleons in each nucleus). What fraction of the neutrinos will scatter off a nucleon if the cross section is given by σ(E) = (0.68 · 10–38 cm2 GeV–1)E? (Aluminum has a density of 2.77 g/cm3.) Get solution
63. A neutrino beam with E = 143 GeV is passed through a slab of aluminum-27 (with 27 nucleons in each nucleus). The probability that a neutrino in the beam will scatter off a nucleon in the aluminum slab is 4.19 · 10–12. The scattering cross section is given by σ(E) = (0.68 · 10–38 cm2 GeV–1)E, and aluminum has a density of 2.77 g/cm3. How thick is the slab? Get solution
64. A high-energy neutrino beam is passed through a slab of aluminum-27 (with 27 nucleons in each nucleus) of thickness 71.1 cm. The probability that a neutrino in the beam will scatter off a nucleon in the aluminum slab is 6.00 · 10–12. The scattering cross section is given by σ(E) = (0.68 · 10–38 cm2 GeV–1)E, and aluminum has a density of 2.77 g/cm3. What is the energy (in GeV) of the neutrino beam? Get solution
65. A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of I(94.9°) = 853 counts/s at a scattering angle of 94.9°±0.7°. What is the intensity (in counts/s) at a scattering angle of 60.5°±0.7° if the scattering obeys the Rutherford formula? Get solution
66. A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of I(95.1°) = 1129 counts/s at a scattering angle of 95.1°±0.4°. At a second scattering angle, the intensity is measured to be 4840 counts/s. Assuming that the scattering obeys the Rutherford formula, what is that second angle (in degrees, to the same uncertainty)? Get solution
67. A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, is set up with two detectors at θ1 = 85.1°±0.9° and θ2 = 62.9°±0.9°. Assuming that the scattering obeys the Rutherford formula, what is the ratio of the measured intensities, I1/I2? Get solution
