Chapter #40 Solutions - University Physics with Modern Physics Volume 2 (Chapters 21-40) - Gary Westfall, Wolfgang Bauer - 2nd Edition

1cc. Which isotope X is needed to complete the reaction ...a) ...b) ...c) ...d) ...e) ... Get solution

1mcq. Radium-226 decays by emitting an alpha particle. What is the daughter nucleus?a) Rdb) Rnc) Bid) Pb Get solution

2cc. The isotopes ..., and ... have masses of 81.9134836 u, 81.9182086 u, and 81.91840164 u, respectively. For which of the β+ decays of ... and ... is positron emission possible?a) for neitherb) only for the ... decayc) only for the ... decayd) for both Get solution

2mcq. Which of the following decay modes involves a transition between states of the same nucleus?a) alpha decayb) beta decayc) gamma decayd) none of the above Get solution

3cc. Which of the following types of nuclear decays are possible for the isotope ...? (Hint: The mass of ... is 81.925 u, the mass of ... is 81.930 u, the mass of ... is 81.917 u, the mass of ... is 77.932 u, and the mass of ... is 4.0026u.)a) alpha decayb) beta decayc) positron emissiond) electron capturee) gamma decay Get solution

3mcq. In neutron stars, which are roughly 90% neutrons and are held together almost entirely by nuclear forces, which of the following terms become(s) relatively dominant for the binding energy, compared to that energy in an ordinary nucleus?a) the Coulomb termb) the asymmetry termc) the pairing termd) all of the abovee) none of the above Get solution

4cc. Which of the following isotopes has the largest fissionability?a) ...b) ...c) ...d) ... Get solution

4mcq. When a target nucleus is bombarded by a beam of the appropriate particles, it is possible to producea) a less massive nucleus, but not a more massive one.b) a more massive nucleus, but not a less massive one.c) a nucleus with a smaller charge number, but not one with a larger charge number.d) a nucleus with a larger charge number, but not one with a smaller charge number.e) a nucleus with either a larger or smaller charge number. Get solution

5cc. With that much hydrogen being converted into helium, how much longer can the Sun keep shining at the current burn rate? (Hint: The mass of the Sun is 1.99 · 1030 kg, the core contains approximately 10% of that mass, and approximately half of the core mass is currently still hydrogen.)a) 30,000 yearsb) 2 million yearsc) 100 million yearsd) 5 billion yearse) 3.3 · 1018 years Get solution

5mcq. The strong forcea) is only attractive.b) does not act on electrons.c) only acts over distances of a few femtometers.d) All of the above are true.e) None of the above are true. Get solution

6mcq. Cobalt has a stable isotope, ..., and 22 radioactive isotopes. The most stable radioactive isotope is .... What is the dominant decay mode of this isotope?a) β +b) β–c) proton emissiond) neutron emission Get solution

7mcq. The mass of an atom (atomic mass) is equal toa) the sum of the masses of the protons.b) the sum of the masses of protons and neutrons.c) the sum of the masses of protons, neutrons, and electrons.d) the sum of the masses of protons, neutrons, and electrons minus theatom’s binding energy. Get solution

9cq. Apart from fatigue, what is another reason the Federal Aviation Administration limits the number of hours that commercial jet pilots can fly each year? Get solution

10cq. Why are there magic numbers in the nuclear shell model? Get solution

11cq. The binding energy of ... is lower than that of .... Provide a plausible explanation, taking into consideration the Coulomb interaction between two protons in .... Get solution

12cq. Which of the following quantities is conserved during a nuclear reaction, and how?a) chargeb) the number of nucleons, Ac) mass-energyd) linear momentume) angular momentum Get solution

13cq. Some food is treated with gamma radiation to kill bacteria. Why is it not a concern that people who eat such food are ingesting gamma radiation? Get solution

14cq. The subsection “Terrestrial Fusion” in Section 40.4 discussed how achieving controlled fusion would be the solution to the world’s energy problems and how difficult it is to do this. Why is it so hard? The Sun does it all the time (see the subsection “Stellar Fusion”). Do we need to understand better how the Sun works to build a nuclear fusion reactor? Get solution

15cq. Why are atomic nuclei more or less limited in size and in neutron-proton ratio? That is, why are there no stable nuclei with 10 times as many neutrons as protons, and why are there no atomic nuclei the size of marbles? Get solution

16cq. A nuclear reaction of the kind ... is called a pick-up reaction.a) Why does it have this name, that is, what is picked up, what picked it up, and where did it come from?b) What is the resulting nucleus, X?c) What is the Q-value of this reaction?d) Is this reaction endothermic or exothermic? Get solution

17cq. Isospin, or isotopic spin, is a quantum variable describing the relationship between protons and neutrons in nuclear and particle physics. (Strictly, it describes the relationship between up and down quarks, as described in Chapter 39, but it was introduced before the advent of the quark model.) It has the same algebraic properties as quantum angular momentum: A proton and a neutron form an iso-doublet of states, with total isospin quantum number ...; the proton is in the tz = + ... state, and the neutron is in the tz = – ... state, where z refers to a direction in an abstract isospin space.a) What isospin states can be constructed from two nucleons, that is, two particles with t = ... ? To what nuclei do these states correspond?b) What isospin states can be constructed from three nucleons? To what nuclei do these correspond? Get solution

18cq. Before looking it up, predict intrinsic spin (i.e., actual angular momentum) of the deuteron, .... Explain your reasoning. (Hint: Nucleons are fermions.) Get solution

19cq. 18 39Ar is an isotope with a half-life of 269 yr. If it decays through β– decay, what isotope will result? Get solution

20cq. A neutron star is essentially a gigantic nucleus with mass 1.35 times that of the Sun, or a mass number of order 1057. It consists of approximately 99% neutrons, the rest being protons and an equal number of electrons. Explain the physics that determines these features. Get solution

21cq. What is the nuclear configuration of the daughter nucleus associated with the alpha decay of Hf (A = 157, Z = 72)? Get solution

22. Estimate the volume of the uranium-235 nucleus. Get solution

23. Calculate the binding energies of the following nuclei.a) ... b) ...c) ...d) ... Get solution

24. Give the numbers of protons, nucleons, neutrons, and electrons in an atom of .... Get solution

25. Using the Fermi function, determine the relative change in density, (dn(r)/dr)/n0, at the nuclear surface, r = R(A). Get solution

26. Calculate the binding energy for the following two uranium isotopes (where u = 1.66 · 10–27 kg):a) ..., which consists of 92 protons, 92 electrons, and 146 neutrons, with a total mass of 238.0507826 ub) ..., which consists of 92 protons, 92 electrons, and 143 neutrons, with a total mass of 235.0439299 uWhich isotope is more stable (or less unstable)? Get solution

27. Write equations for the β– decay of the following isotopes:a) ...b) ...c) ... Get solution

28. Write equations for the alpha decay of the following isotopes:a) ...b) ... Get solution

29. How much energy is released in the beta decay of ...? Get solution

30. A certain radioactive isotope decays to one-eighth of its original amount in 5.0 h.a) What is its half-life?b) What is its mean lifetime? Get solution

31. A certain radioactive isotope decays to one-eighth of its original amount in 5.00 h. How long would it take for 10.0% of it to decay? Get solution

32. Determine the decay constant of radium-226, which has a half-life of 1600 yr. Get solution

33. A 1.00-g sample of radioactive thorium-228 decays via β– decay, and 75 counts are recorded in one day by a detector that has 10.0% efficiency (that is, 10.0% of all events that occur are recorded by the detector). What is the lifetime of this isotope? Get solution

35. The specific activity of a radioactive material is the number of disintegrations per second per gram of radioactive atoms.a) Given the half-life of ... of 5730 yr, calculate the specific activity of .... Express your result in disintegrations per second per gram, becquerel per gram, and curie per gram.b) Calculate the initial activity of a 5.00-g piece of wood.c) How many ... disintegrations have occurred in a 5.00-g piece of wood that was cut from a tree on January 1, 1700? Get solution

36. During a trip to an excavation site, an archeologist found a piece of charcoal. Analysis of the charcoal found the activity of ... in the sample to be 0.42 Bq. If the mass of the charcoal is 7.2 g, estimate the approximate age of the site. Get solution

37. In 2008, crime scene investigators discover the bones of a person who appeared to have been the victim of a brutal attack that occurred a long time ago. They would like to know the year when the person was murdered. Using carbon dating, they determine that the rate of change of the ... is 0.268 Bq per gram of carbon. The rate of change of ... in the bones of a person who had just died is 0.270 Bq per gram of carbon. What year was the victim killed? The half-life of ... is 5.73 · 103 yr. Get solution

38. Physicists blow stuff up better than anyone else. The measure for gauging the usefulness of blowing something up is the fraction of initial rest mass converted into energy in the process. Looking up the necessary data, calculate this fraction for the following processes:a) chemical combustion of hydrogen: 2H2 + O2 → 2H2Ob) nuclear fission: ...c) thermonuclear fusion: ...d) decay of free neutron: ...e) decay of muon: ...f) electron-positron annihilation: e– + e+→ 2γ Get solution

39. An unstable nucleus A decays to an unstable nucleus B, which in turn decays to a stable nucleus. If at t = 0 s there are NA0 and NB0 nuclei present, derive an expression for NB, the number of B nuclei present, as a function of time. Get solution

40. In a simple case of chain radioactive decay, a parent radioactive nucleus, A, decays with a decay constant λ1 into a daughter radioactive nucleus, B, which then decays with a decay constant λ2 to a stable nucleus, C.a) Write the equations describing the number of nuclei of each of the three types as a function of time, and derive expressions for the number of daughter nuclei, N2, as a function of time and for the activity of the daughter nuclei, A2, as a function of time.b) Discuss the results in the case when λ2 > λ1 (λ2 ≈ 10 λ1) and when λ2 >> λ1 (λ2 ≈100 λ1). Get solution

41. Show that for the case of nuclei with odd mass number, A, the Bethe-Weizsäcker formula can be written as a quadratic in Z—and thus, for any given A, the binding energies of the isotopes having that A take a quadratic form, B = a + bZ + cZ2. Use your result to find the most strongly bound isotope (the most stable one) having A = 117. Get solution

42. The neutron drip line is defined to be the point at which the neutron separation energy for any isotope of an element is negative. That is, the neutron is unbound. Using the Bethe-Weizsäcker formula, find the neutron drip line for the element Sn. Find this value using Sn and S2n. Plot both Sn and S2n/2 as a function of neutron number. Get solution

43. A nuclear fission power plant produces about 1.50 GW of electrical power. Assume that the plant has an overall efficiency of 35.0% and that each fission event produces 200. MeV of energy. Calculate the mass of ... consumed each day. Get solution

44. a) What is the energy released in the fusion reaction ...?b) The Earth’s oceans have a total mass of water of 1.50 · 1016 kg, and 0.0300% of this quantity is deuterium, .... If all the deuterium in the oceans were fused by controlled fusion into ..., how many joules of energy would be released?c) World power consumption is about 1.00 · 1013 W. If consumption stayed constant and all problems arising from ocean water consumption (including those of political, meteorological, and ecological nature) could be avoided, how many years would the energy calculated in part (b) last? Get solution

45. The Sun radiates energy at the rate of 3.85 · 1026 W.a) At what rate, in kilograms per second, is the Sun’s mass converted into energy?b) Why is this result different from the rate calculated in Example 40.6: 6.02 · 1011 kg of protons being converted into helium each second?c) Assuming that the current mass of the Sun is 1.99 · 1030 kg and that it has radiated at the same rate for its entire lifetime of 4.50 · 109 yr, what percentage of the Sun’s mass has been converted into energy during its entire lifetime? Get solution

46. Consider the following fusion reaction, through which stars produce progressively heavier elements: .... The mass of ... is 3.016029 u, the mass of ... is 4.002603 u, and the mass of ... is 7.0169298 u. The atomic mass unit is 1 u = 1.66 · 10–27 kg. Assuming that the Be atom is at rest after the reaction and neglecting any potential energy between the atoms and the kinetic energy of the He nuclei, calculate the minimum possible energy and maximum possible wavelength of the photon, γ, that is emitted in this reaction. Get solution

47. Estimate the temperature that would be needed to initiate the fusion reaction ... Get solution

48. Consider a hypothetical fission process in which a ... nucleus splits into two identical ... nuclei without producing any other particles or radiation. The mass of ... is 119.904040 u, and the mass of ... is 59.934078 u. At the moment when the two iron nuclei form, but before they start moving away due to Coulomb repulsion, how far apart are the two nuclei? Get solution

49. The mass excess of a nucleus is defined as the difference between the atomic mass (in atomic mass units, u), and the mass number of the nucleus, A. Using the mass-energy conversion 1 u = 931.49 MeV/c2, this mass excess is usually expressed in kilo-electron-volts (keV). The table below presents the mass excess for several nuclei (from the Berkeley National Lab NuBase database):...a) Calculate the atomic mass (in atomic mass units) for each of the nuclei in the table. For reference, the atomic mass of the neutron is given.b) Using your results from part (a), determine the mass-energy difference between the initial and final states for the following possible fission reactions:...c) Will these reactions occur spontaneously? Get solution

50. Neutron stars are sometimes approximated to be nothing more than large atomic nuclei (but with many more neutrons). Assuming that a neutron star is as dense as an atomic nucleus, estimate the number of nucleons in a 10.0-km-diameter star. Get solution

51. What is the average kinetic energy of protons at the center of a star, where the temperature is 1.00 · 107 K? What is the average velocity of those protons? Get solution

52. Billions of years ago, the Solar System was created out of the remnants of a supernova explosion. Nuclear scientists believe that two isotopes of uranium, ... and ..., were created in equal amounts at that time. However, today 99.28% of uranium is in the form of ... and only 0.72% is in the form of .... Assuming a simplified model in which all of the matter in the Solar System originated in a single exploding star, estimate the approximate time of this explosion. Get solution

53. A drug containing ... (t1/2 = 6.05 h) with an activity of 1.50 μCi is to be injected into a patient at 9.30 a.m. You are to prepare the drug 2.50 h before the injection (at 7:00 a.m.). What activity should the drug have at the preparation time (7:00 a.m.)? Get solution

54. A 42.58-MHz photon is needed to produce nuclear magnetic resonance in free protons in a magnetic field of 1.000 T. What is the wavelength of the photon, its energy, and the region of the spectrum in which it lies? Could it be harmful to the human body? Get solution

55. The radon isotope ..., which has a half-life of 3.825 days, is used for medical purposes such as radiotherapy. How long does it take until ... decays to 10.00% of its initial quantity? Get solution

56. Radiation therapy is one of the techniques used for cancer treatment. Based on the approximate mass of a tumor, oncologists can calculate the radiation dose necessary to treat a patient. Suppose a patient has a 50.0-g tumor and needs to receive 0.180 J of energy to kill the cancer cells. What radiation absorbed dose should the patient receive? Get solution

57. The atom of sodium-22 ... has a mass of 21.994435 u. How much work would be needed to take this nucleus completely apart into its constituent pieces (protons, neutrons, and electrons)? Get solution

58. A Geiger counter initially records 7210 counts/s from a sample of radioactive material. After 45 min, it records 4585 counts/s. Ignore any uncertainty in the counts and find the half-life of the material. Get solution

59. How close can a 5.00-MeV alpha particle get to a uranium-238 nucleus, assuming that the only interaction is Coulomb? Get solution

60. ... decays with a half-life of 24,100 yr via emission of a 5.25-MeV alpha particle. If you have a 1.00 kg spherical sample of 2..., find the initial activity in becquerels. Get solution

62. Assuming that carbon makes up 14% of the mass of a human body, calculate the activity of a 75-kg person considering only the beta decays of carbon-14. Get solution

63. ... is an isotope that has a lifetime of less than a second. Its mass is 8.022485 u. Calculate its binding energy in MeV. Get solution

64. What is the total energy released in the decay ... Get solution

65. A gallon of regular gasoline (density of 737 kg/m3) contains about 131 MJ of chemical energy. How much energy is contained in the rest mass of this gallon? Get solution

66. If 1030 atoms of a radioactive sample remain after 10 half-lives, how many atoms remain after 20 half-lives? Get solution

67. Calculate the binding energy per nucleon ofa) ....b) ....c) ...d) ... Get solution

68. The mean lifetime for a radioactive nucleus is 4300 s. What is its half-life? Get solution

69. ... has a half-life of 26.8 min. How many minutes must elapse for 90.0% of a given sample of ... atoms to decay? Get solution

70. The most common isotope of uranium, ..., produces radon, ..., through the following sequence of decays:...A sample of ... will build up equilibrium concentrations of its daughter nuclei down to ...; the concentrations of each are such that each daughter is produced as fast as it decays. The ... decays to ..., which escapes as a gas. (The alpha particles also escape, as helium; this is a source of much of the helium found on Earth.) Radon is a health hazard when it occurs in high concentrations in buildings built on soil or foundations containing uranium ores, as it can be inhaled.a) Look up the necessary data, and calculate the rate at which 1.00 kg of an equilibrium mixture of ... and its first five daughters produces ... (mass per unit time).b) What activity (in curies per unit time) of radon does this represent? Get solution

71. After a tree has been chopped down and burned to ash, the carbon isotopes in the ash are found to have a ... to ... ratio of 1.300 · 10–12. Experimental tests on the ... atoms reveal that ... is a beta emitter with a half-life of 5730 yr. At an archeological excavation, a skeleton is found next to some wood ash from a campfire. If 50.0 g of carbon from the ash emits electrons at a rate of 20.0 per hour, how long ago did the campfire burn? Get solution

72. If your mass is 70.0 kg and you have a lifetime of 70.0 yr, how many proton decays will occur in your body during your life (assuming that your body is entirely composed of water)? Use a half-life of 1.00 · 1030 yr. Get solution

73. You have developed a grand unified theory that predicts the following things about the decay of protons: (1) protons never get any older, in the sense that their probability of decay per unit time never changes, and (2) half the protons in any given collection of protons will have decayed in 1.80 · 1029 yr. You are given experimental facilities to test your theory: a tank containing 1.00 · 104 metric tons of water and sensors to record proton decays. You will be allowed access to this facility for 2 years. How many proton decays will occur in this period if your theory is correct? Get solution

74. The precession frequency of the protons in a laboratory NMR spectrometer is 15.35850 MHz. The magnetic dipole moment of the proton is 1.410608 · 10–26 J/T, while its spin angular momentum is 0.5272863 · 10–34 J s. Calculate the magnitude of the magnetic field in which the protons are immersed. Get solution

75. Two species of radioactive nuclei, A and B, each with an initial population N0, start decaying. After a time of 100. s, it is observed that NA = 100NB. If ..., find the value of .... Get solution

76. A 12.43-g fragment of charcoal is to be carbon dated. Measurements show that it has an activity of 105 decays/ min. How many years ago did the tree from which the charcoal was produced die? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution

77. A fragment of charcoal has been determined by carbon dating to be 4384 years old. Measurements show that it has an activity of 107 decays/ min. What is the mass of the charcoal fragment? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution

78. A 13.83-g fragment of charcoal has been determined by carbon dating to be 4814 years old. How many decays per minute were measured in the carbon dating process? (Hint: The half-life of ... is 5730 yr, and the ... ratio in living organic matter is 1.20 · 10–12.) Get solution

Chapter #39 Solutions - University Physics with Modern Physics Volume 2 (Chapters 21-40) - Gary Westfall, Wolfgang Bauer - 2nd Edition

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

Chapter #38 Solutions - University Physics with Modern Physics Volume 2 (Chapters 21-40) - Gary Westfall, Wolfgang Bauer - 2nd Edition

1cc. The number of lines in the Brackett series that have wavelengths greater than the maximum wavelength in the Paschen series isa) 1.b) 2.c) 4.d) 8.e) ∞. Get solution

1mcq. The wavelength of the fourth line in the Lyman series of the hydrogen spectrum isa) 80.0 nm.b) 85.0 nm.c) 90.2 nm.d) 94.9 nm. Get solution

2cc. How many wave functions are possible in the n = 5 shell?a) 9b) 14c) 16d) 21e) 25 Get solution

2mcq. The electron in a certain hydrogen atom is in the n = 5 state. Which of the following could be the EBμ and m values for the electron?a) 5, –3b) 4, –5c) 3, –2d) 4, –6 Get solution

3cc. Element 111 was discovered in 1994 and named roentgenium in 2004. It exists for only a few seconds before it decays. The electron configuration of roentgenium has not been determined yet. What would you predict it to be?a) [Xe]4f145d106s26p6b) [Rn]4f145d106s26p6c) [Rn]5f146d97s2d) [Xe]5f146d97s2 Get solution

3mcq. A muon has the same charge as an electron but a mass that is 207 times greater. The negatively charged muon can bind to a proton to form a new type of hydrogen atom. How does the binding energy, EBμ, of the muon in the ground state of a muonic hydrogen atom compare with the binding energy, EBe, of an electron in the ground state of a conventional hydrogen atom?a) |EBμ| ≈ |EBe|b) |EBμ| ≈ 100 |EBe|c) |EBμ| ≈ |EBe|/100d) |EBμ| ≈ 200 |EBe|e) |EBμ| ≈ |EBe|/200 Get solution

4cc. Element 118 was discovered in 2006 and exists for approximately 1 millisecond before it decays. Only a few atoms of this element have been produced. The ionization energy for element 118 has not been measured yet. What would you predict it to be?a) approximately 0 eV (the atom is unstable)b) approximately 2 eVc) approximately 5 eVd) approximately 10 eVe) approximately 20 eV Get solution

4mcq. Which of the following can be used to explain why you can’t walk through walls?a) Coulomb repulsive forceb) the strong nuclear forcec) gravityd) Pauli Exclusion Principlee) none of the above Get solution

5cc. In the X-ray spectrum in Figure 38.22, suppose one of the peaks corresponds to a K-shell transition and the other to an L-shell transition. Which of the following is true?a) The peak with the higher photon energy corresponds to the K-shell transition.b) The peak with the higher photon energy corresponds to the L-shell transition.c) Either peak could correspond to either transition, depending on the electrostatic potential difference applied in the X-ray tube.d) The peaks cannot be identified, without knowing what material was used for the anode.Figure 38.22 Sketch of an X-ray spectrum with a bremsstrahlung continuum plus sharp peaks due to electron transitions between atomic shells.... Get solution

5mcq. How many antinodes are there in a system with the quantum number n = 6?a) 12b) 6c) 3d) 5 Get solution

6cc. What is the population ratio of the 5s state relative to the 3p state at a temperature of 5000 K?a) 1.2·10–33b) 4.3·10–23c) 0.011d) 0.51e) 2.4 Get solution

6mcq. Transition metals can be defined as the elements in which the d subshells go from empty to full. How many transition metals are there in each period?a) 2b) 6c) 10d) 14 Get solution

7mcq. What is the shortest wavelength photon that can be emitted by singly ionized helium (He+)?a) 0.00 nmb) 22.8 nmc) 46.0 nmd) 91.0 nme) 365 nm Get solution

9cq. The common depiction of an atom, with electrons tracing elliptical orbits centered on the nucleus, is an icon of the Atomic Age. Given what you know of the physics of atoms, what’s wrong with this picture? Get solution

10cq. Given that the hydrogen atom has an infinite number of energy levels, why can’t a hydrogen atom in the ground state absorb all possible wavelengths of light? Get solution

12cq. What would happen to the energy levels of a hydrogen atom if the Coulomb force doubled in strength? What would happen to the sizes of atoms? Get solution

13cq. Which model of the hydrogen atom—the Bohr model or the quantum mechanical model—predicts that the electron spends more time near the nucleus? Get solution

14cq. For ... > 4, which values of ... and m correspond to wave functions that have their maximum probability in the xy-plane? Get solution

15cq. Hund’s rule, a component of the Aufbauprinzip (construction principle), states that as one moves across the periodic table, with increasing atomic number, the available subshells are filled successively with one electron in each orbital, their spins all parallel; only when all orbitals in a subshell contain one electron are second electrons, with spins opposite to the first, placed in the orbitals. Explain why the ground-state electron configurations of successive elements should follow this pattern. Get solution

16cq. The energy-level diagram for a four-level laser is presented in the figure, which includes information about the relative times required for the various transitions involved in the operation of such a laser. Explain why the nonradiative transitions have to be fast (higher rate of transitions per second) compared to the slower laser transition.... Get solution

17cq. The hydrogen atom wave function ψ200 is zero when r = 2a0. Does this mean that the electron in that state can never be observed at a distance of 2a0 from the nucleus or that the electron can never be observed passing through the spherical surface defined by r = 2a0? Is there a difference between those two descriptions? Get solution

18cq. A 10-eV electron collides with (but is not captured by) a hydrogen atom in its ground state. Calculate the wavelengths of all photons that might be emitted. Get solution

19. What is the shortest wavelength of light that a hydrogen atom will emit? Get solution

20. Determine the wavelength of the second line in the Paschen series. Get solution

21. The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen atom to/from the n = 5 energy level from/to higher energy levels. What are the shortest and longest wavelengths of lines in the Pfund series? Are any of these in the visible portion of the electromagnetic spectrum? Get solution

22. An electron in the second excited state of a hydrogen atom jumps to the ground state. What are the possible colors and wavelengths of the light emitted as a result of the jump? Get solution

23. Calculate the energy of the fifth excited state of a hydrogen atom. Get solution

24. Hydrogen atoms are bombarded with 13.1-eV electrons. Determine the shortest wavelength of light the atoms will emit. Get solution

25. The Rydberg constant with a finite mass of the nucleus is given by Rmodified = RH/(1+m/M), where m and M are the masses of an electron and a nucleus, respectively. Calculate the modified value of the Rydberg constant fora) a hydrogen atom, andb) a positronium (in a positronium, the “nucleus” is a positron, which has the same mass as an electron). Get solution

26. A muon is a particle very similar to an electron. It has the same charge but its mass is 1.88·10–28 kg.a) Calculate the reduced mass for a hydrogen-like muonic atom consisting of a single proton and a muon.b) Calculate the ionization energy for such an atom, assuming that the muon is initially in its ground state. Get solution

27. An excited hydrogen atom emits a photon with an energy of 1.133 eV. What were the initial and final states of the hydrogen atom before and after emitting the photon? Get solution

28. An 8.00-eV photon is absorbed by an electron in the n = 2 state of a hydrogen atom. Calculate the final speed of the electron. Get solution

29. Assume that Bohr’s quantized energy levels apply to planetary orbits. Derive an equation similar to equation 38.6 that gives the allowed radii of those orbits, and estimate the principal quantum number for the Earth’s orbit. Get solution

30. Prove that the period of an electron in the nth Bohr orbit is given by T = n3/(2cRH), with n = 1,2,3, ... . Get solution

31. What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell? Get solution

32. Electrons with the same value of the quantum number n are said to occupy the same electron shell, K, L, M, N, or higher. Calculate the maximum allowed number of electrons for thea) κ shell,b) L shell, andc) M shell. Get solution

33. What is the angle between the total angular momentum vector and the z-axis for a hydrogen atom in the stationary state (3, 2, 1)? Get solution

34. A hydrogen atom is in its fifth excited state, with principal quantum number n = 6. The atom emits a photon with a wavelength of 410 nm. Determine the maximum possible orbital angular momentum of the electron after emission. Get solution

35. The radial wave function for hydrogen in the 1s state is given by R1s = A1e–r/a0 where the normalization constant, A1, was found in Example 38.2.a) Calculate the probability density at r = a0/2.b) The 1s wave function has a maximum at r = 0 but the 1s radial probability density peaks at r = a0. Explain this difference.Example 38.2 Normalization of the Hydrogen Wave Function... Get solution

36. For the wave function ψ100(r) in equation 38.30, find the value of r for which the function P(r) = 4πr2|ψ100(r)|2 is a maximum. Get solution

37. An electron in a hydrogen atom is in the 2s state. Calculate the probability of finding the electron within a Bohr radius (a0 = 0.05295 nm) of the proton. The 2s wave function for hydrogen is...Evaluating the integral is a bit tedious, so you may want to consider using a program such as Mathcad or Mathematica or finding the integral online at http://integrals.wolfram.com/index.jsp. Get solution

38. Calculate the energy needed to change a single ionized helium atom into a double ionized helium atom (that is, change it from He+ into He2+). Compare it to the energy needed to ionize the hydrogen atom. Assume that both atoms are in their ground state. Get solution

39. A He+ ion consists of a nucleus (containing two protons and two neutrons) and a single electron. Find the Bohr radius for this system. Get solution

40. Find the wavelengths of the three lowest-energy lines in the Paschen series of the spectrum of the He+ ion. Get solution

41. The binding energy of an extra electron added when As atoms are used to dope a Si crystal may be approximately calculated by considering the Bohr model of a hydrogen atom.a) Express the ground energy of the hydrogen-like atoms in terms of the dielectric constant, the effective mass of an extra electron, and the ground-state energy of a hydrogen atom.b) Calculate the binding energy of the extra electron in a Si crystal. The dielectric constant of Si is about 10.0, and the effective mass of extra electrons in a Si crystal is about 20.0% of that of free electrons. Get solution

42. What is the wavelength of the first visible line in the spectrum of doubly ionized lithium? Begin by writing the formula for the energy levels of the electron in doubly ionized lithium—then consider energy-level differences that give energies in the appropriate (visible) range. Express the answer as “the transition from state n to state n' produces the first visible line, with wavelength X.” Get solution

43. Following the steps used in the text for the hydrogen atom, apply the Bohr model of the atom to derive an expression fora) the radius of the nth orbit,b) the speed of the electron in the nth orbit, andc) the energy levels in a hydrogen-like ionized atom with charge number Z that has lost all of its electrons except for one. Compare the results with the corresponding ones for the hydrogen atom. Get solution

44. Apply the results of Problem 38.43 to determine the maximum and minimum wavelengths of the spectral lines in the Lyman, Balmer, and Paschen series for a singly ionized helium atom (He+). Get solution

45. Consider an electron in a hydrogen atom. If you are able to excite the electron from the n = 1 shell to the n = 2 shell with laser light of a given wavelength, what wavelength of laser light will excite that electron again from the n = 2 to the n = 3 shell? Explain. Get solution

46. A low-power laser has a power of 0.50 mW and a beam diameter of 3.0 mm.a) Calculate the average light intensity of the laser beam.b) Compare the value from part (a) to the intensity of light from a 100-W light bulb viewed from 2.0 m. Get solution

47. A ruby in a laser consists mostly of alumina (Al2O3) and a small amount of chromium ions, responsible for its red color. A 3.00-kW ruby laser emits light pulses of duration 10.0 ns and wavelength 694 nm.a) What is the energy of each of the photons in a pulse?b) Determine the number of chromium atoms undergoing stimulated emission to produce a pulse. Get solution

48. You have both a green, 543-nm, 5.00-mW laser and a red, 633-nm, 4.00-mW laser. Which one will produce more photons per second, and why? Get solution

49. What is the shortest possible wavelength in the Lyman series in hydrogen? Get solution

50. How much energy is required to ionize a hydrogen atom when the electron is in the nth level? Get solution

51. By what percentage is the mass of the electron changed by using the reduced mass for the hydrogen atom? What would the reduced mass be if the proton had the same mass as the electron? Get solution

53. Section 38.2 established that an electron, if observed in the ground state of hydrogen, is expected to have a speed of 0.0073c. For what nuclear charge Z would an innermost electron have a speed of approximately 0.500c, when considered classically? Get solution

54. A collection of hydrogen atoms have all been placed into the n = 4 excited state. What wavelengths of photons will be emitted by the hydrogen atoms as they transition back to the ground state? Get solution

55. Consider a muonic hydrogen atom, in which the electron is replaced by a muon of mass 105.66 MeV/c2 that orbits the proton. What are the first three energy levels of the muon in this type of atom? Get solution

56. What is the ionization energy of a hydrogen atom excited to the n = 2 state? Get solution

57. He+ is a helium atom with one electron missing. Treating this ion like a hydrogen atom, what are its first three energy levels? Get solution

58. What is the energy of a transition capable of producing light of wavelength 10.6 μm? (This is the wavelength of light associated with a commonly available infrared laser.) Get solution

59. What is the energy of the orbiting electron in a hydrogen atom with a radial quantum number of 45? Get solution

60. Find the energy difference between the ground state of hydrogen and the ground state of deuterium (hydrogen with an extra neutron in the nucleus). Get solution

61. An excited hydrogen atom, whose electron is in the n = 4 state, is motionless. When the electron drops to the ground state, does it set the atom in motion? If so, with what speed? Get solution

62. The radius of the n = 1 orbit in the hydrogen atom is a0 = 0.053 nm.a) Compute the radius of the n = 6 orbit. How many times larger is this than the n = 1 radius?b) If an electron in the n = 6 orbit drops to the n = 1 orbit (ground state), what are the frequency and the wavelength of the emitted radiation? What kind of radiation is emitted (visible, infrared, etc.)?c) How would your answer to part (a) change if the atom was a singly ionized helium atom (He+) instead? Get solution

63. An electron in a hydrogen atom is in the ground state (1s). Calculate the probability of finding the electron within a Bohr radius (a0 = 0.05295 nm) of the proton. The ground-state wave function for hydrogen is... Get solution

65. A beam of electrons with a speed of 676.01 km/s is incident on a system of excited hydrogen atoms. If an electron hits a hydrogen atom in the n = 3 state, what is the highest level n, to which this hydrogen atom can be excited in this collision? (In the collision of the electron with the hydrogen atom, you may neglect the recoil energy of the hydrogen atom, because it has a mass much greater than that of the electron.) Get solution

66. A beam of electrons with a speed of 378.92 km/s is incident on a system of excited hydrogen atoms. If an electron hits a hydrogen atom and excites it to the n = 10 state, what is the lowest level n in which this hydrogen atom could have been before the collision? (In the collision of the electron with the hydrogen atom, you may neglect the recoil energy of the hydrogen atom, because it has a mass much greater than that of the electron.)... Get solution

67. Find the ratio of the number of hydrogen atoms in the n = 3 state to the number of hydrogen atoms in the n = 7 state at a temperature of 528.3 K. Get solution

68. At what temperature is the ratio of the number of hydrogen atoms in the n = 3 state to the number of hydrogen atoms in the n = 8 state equal to 5.1383·105? Get solution