1cc. The visible spectrum of light extends from approximately 380 nm
(violetblue) to 780 nm (red). What is the corresponding range of photon
energies in units of electron-volts?a) 1.59 eV to 3.26 eVb) 2.54 ·
10–19 eV to 5.23 · 10–19 eVc) 0.38 · 1015 eV to 0.78 · 1015 eVd) 190 eV
to 390 eV Get solution
1mcq. Ultraviolet light of wavelength 350 nm is incident on a material with a stopping potential of 0.25 V. The work function of the material isa) 4.0 eV.b) 3.3 eV.c) 2.3 eV.d) 5.2 eV. Get solution
2cc. You have a source of light with a given intensity and wavelength. You reduce the wavelength while leaving the intensity the same. Which of the following statements is true?a) More photons per second will be emitted from the light source.b) Fewer photons per second will be emitted from the light source.c) The number of photons emitted per second will remain the same, but the energy of each one will be reduced.d) The number of photons emitted per second will remain the same, but the energy of each one will be increased.e) The number of photons emitted per second will remain the same, but each one will move slower. Get solution
2mcq. The existence of a cutoff frequency in the photoelectric effecta) cannot be explained using classical physics.b) shows that the model provided by classical physics is not correct in this case.c) shows that a photon model of light should be used in this case.d) shows that the energy of the photon is proportional to its frequency.e) All of the above are true. Get solution
3cc. Which of the following statements is true?a) More massive and faster objects have bigger de Broglie wavelengths than less massive and slower ones.b) Less massive and faster objects have bigger de Broglie wavelengths than more massive and slower ones.c) More massive and slower objects have bigger de Broglie wavelengths than less massive and faster ones.d) Less massive and slower objects have bigger de Broglie wavelengths than more massive and faster ones. Get solution
3mcq. To have a larger photocurrent, which of the following should occur? (Select all the changes that apply.)a) brighter lightb) dimmer lightc) higher frequencyd) lower frequency Get solution
4cc. Can you guess the outcome of measuring the current to determine which slit the electron passes through? If we measure the current representing the electron passing through the slits, which of the following will be the result?a) Exactly one-half of each individual electron passes through each of the two slits.b) Each individual electron passes through just one slit. The electrons passing through the left slit cause the left part of the interference pattern, and the electrons passing through the right slit cause the right part.c) Each individual electron passes through just one slit. The electrons passing through the left slit cause the right part of the interference pattern, and the electrons passing through the right slit cause the left part.d) Each individual electron passes through just one slit, but as we conduct measurements to try to determine this, the interference pattern on the screen is destroyed, and we observe only the central maximum on the screen. Get solution
4mcq. Which of the following has the smallest de Broglie wavelength?a) an electron traveling at 80% of the speed of lightb) a proton traveling at 20% of the speed of lightc) a carbon nucleus traveling at 70% of the speed of lightd) a helium nucleus traveling at 80% of the speed of lighte) a lithium nucleus traveling at 50% of the speed of light Get solution
5cc. In Example 36.4, if all other parameters remain the same but the mass of the car is doubled, the resulting uncertainty in the speed will bea) the same.b) half as large.c) one-quarter as large.d) twice as large.e) four times as large.Example 36.4 Trying to Get Out of a Speeding Ticket...... Get solution
5mcq. A blackbody is an ideal system thata) absorbs 100% of the light incident upon it, but cannot emit light of its own.b) radiates 100% of the power it generates, but cannot absorb radiation of its own.c) either absorbs 100% of the light incident upon it, or radiates 100% of the power it generates.d) absorbs 50% of the light incident upon it, and emits 50% of the radiation it generates.e) blackens completely any body that comes in contact with it. Get solution
6cc. Which of the following distributions are possible ways to distribute 4 energy quanta over 5 fermions with spin ... ... Get solution
6mcq. Which one of the following statements is true if the intensity of a light beam is increased while its frequency is kept the same?a) The photons gain higher speeds.b) The energy of the photons is increased.c) The number of photons per unit time is increased.d) The wavelength of the light is increased. Get solution
7mcq. Which of the following has the highest temperature?a) a white-hot objectb) a red-hot objectc) a blue-hot object Get solution
10cq. Answer in your own words the question of whether an electron is a particle or a wave. Get solution
11cq. If I look in a mirror while wearing a blue shirt, my reflection is wearing a blue shirt, not a red shirt. But according to the Compton effect, the photons that bounce off the mirror should have a lower energy and therefore a longer wavelength. Explain why my reflection shows the same color shirt as I am wearing. Get solution
12cq. Vacuum in deep space is not empty, but a boiling sea of particles and antiparticles that are constantly forming and annihilating each other. Determine the maximum lifetime for a proton-antiproton pair to form there without violating Heisenberg’s Uncertainty Relation. Get solution
13cq. Consider a universe where Planck’s constant is 5 J s. How would a game of tennis change? Consider the interactions of individual players with the ball and the interaction of the ball with the net. Get solution
14cq. In classical mechanics, what information is needed in order to predict where a particle with no net force on it will be at some later time? Why is this prediction not possible in quantum mechanics? Get solution
15cq. What would a classical physicist expect to be the result of shining an increasingly brighter UV lamp on a metal surface, in terms of the energy of emitted electrons? How does this differ from what the theory of the photoelectric effect predicts? Get solution
16cq. Which is more damaging to human tissue, a 60-W source of visible light or a 2-mW source of X-rays? Explain your choice. Get solution
17cq. Neutrons are spin- ½ fermions. An unpolarized beam of neutrons has equal numbers of neutrons in the + ½ and – ½ spin states. When a beam of unpolarized neutrons is passed through a gas of unpolarized 3He atoms, the neutrons can be absorbed by the 3He atoms to create 4He atoms. If the 3He atoms are polarized, so that the spins of the neutrons in their nuclei are all aligned, will the same number of neutrons from the unpolarized neutron beam be absorbed by the polarized 3He atoms? How well are neutrons in each of the two spin states of the unpolarized neutron beam absorbed by the 3He? Get solution
18cq. You are performing a photoelectric effect experiment. Using a photocathode made of cesium, you first illuminate it with a green laser beam (λ = 514.5 nm) of power 100 mW. Next, you double the power of the laser beam, to 200 mW. How will the energies per electron of the electrons emitted by the photocathode compare for the two cases? Get solution
19. Calculate the peak wavelengths ofa) the solar light received by Earth, andb) the light emitted by the Earth.Assume that the surface temperatures of the Sun and the Earth are 5800. K and 300. K, respectively. Get solution
21. Ultra-high-energy gamma rays with energies up to 3.5 · 1012 eV, come from the equator of the Milky Way. What is the wavelength of this radiation? How does its energy compare to the rest energy of a proton? Get solution
23. The temperature of your skin is approximately 35.0 °C.a) Assuming that your skin is a blackbody, what is the peak wavelength of the radiation it emits?b) Assuming a total surface area of 2.00 m2, what is the total power emitted by your skin?c) Given your answer to part (b), why don’t you glow as brightly as a light bulb? Get solution
22. Consider the radiation emitted by an object at room temperature (20. °C). For radiation at the peak of the spectral energy density, calculatea) the wavelength,b) the frequency, andc) the energy of one photon. Get solution
24. A pure, defect-free, semiconductor material will absorb the electromagnetic radiation incident on it only if the energy of the individual photons in the incident beam is larger than a threshold value known as the band-gap of the semiconductor. Otherwise, the material will be transparent to the photons. The known room-temperature band-gaps for germanium, silicon, and gallium-arsenide, three widely used semiconductors, are 0.66 eV,1.12 eV, and 1.42 eV, respectively.a) Determine the room-temperature transparency range of each semiconductor.b) Compare these with the transparency range of ZnSe, a semiconductor with a band-gap of 2.67 eV, and explain the yellow color observed experimentally for the ZnSe crystals.c) Which of these materials could be used to detect the 1550-nm optical communications wavelength? Get solution
25. The mass of a dime is 2.268 g, its diameter is 17.91 mm, and its thickness is 1.350 mm. Determinea) the radiant energy emitted by a dime per second at room temperature,b) the number of photons leaving the dime per second (assuming that all photons have the wavelength of the peak of the distribution for this estimate), andc) the volume of air that has an energy equal to that of 1 s of radiation from the dime. Get solution
26. The work function of a certain material is 5.8 eV. What is the photoelectric threshold frequency for this material? Get solution
27. What is the maximum kinetic energy of the electrons ejected from a sodium surface by light of wavelength 470 nm? Get solution
28. The threshold wavelength for the photoelectric effect for a specific alloy is 400. nm. What is the work function in electron-volts? Get solution
29. In a photoelectric effect experiment, a laser beam of unknown wavelength is shone on a cesium photocathode (work function of φ = 2.100 eV). It is found that a stopping potential of 0.310 V is needed to eliminate the current. Next, the same laser is shone on a photocathode made of an unknown material, and a stopping potential of 0.110 V is needed to eliminate the current.a) What is the work function for the unknown material?b) What metal is a possible candidate for the unknown material? Get solution
30. You illuminate a zinc surface with 550-nm light. How high do you have to turn up the stopping potential to eliminate the photoelectric current completely? Get solution
31. White light, λ = 400. to 750. nm, falls on barium (φ = 2.48 eV) .a) What is the maximum kinetic energy of electrons ejected from the metal?b) Would the longest-wavelength light eject electrons?c) What wavelength of light would eject electrons with zero kinetic energy? Get solution
32. To determine the work function of the material of a photodiode, you measured a maximum kinetic energy of 1.50 eV corresponding to a certain wavelength. Later, you decreased the wavelength by 50.0% and found the maximum kinetic energy of the photoelectrons to be 3.80 eV. From this information, determinea) the work function of the material, andb) the original wavelength. Get solution
33. X-rays of wavelength λ = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons deflected at a 90.0° angle relative to the incident beam? Get solution
34. A 2.0-MeV X-ray photon is scattered off a free electron at rest and deflected by an angle of 53°. What is the wavelength of the scattered photon? Get solution
35. A photon with a wavelength of 0.30 nm collides with an electron that is initially at rest. If the photon rebounds at an angle of 160°, how much energy did it lose in the collision? Get solution
36. X-rays having an energy of 400.0 keV undergo Compton scattering from a target electron. The scattered rays are detected at an angle of 25.0° relative to the incident rays. Finda) the kinetic energy of the scattered X-rays, andb) the kinetic energy of the recoiling electron. Get solution
37. Consider the case in which photons scatter off a free proton.a) If 140.-keV X-rays deflect off a proton at 90.0°, what is their fractional change in energy, (E0 – E)/E0?b) What initial energy would a photon have to have to experience a 1.00% change in energy at 90.0° scattering? Get solution
38. An X-ray photon with an energy of 50.0 keV strikes an electron that is initially at rest inside a metal. The photon is scattered at an angle of 45°. What are the kinetic energy and the momentum (magnitude and direction) of the electron after the collision? You may use the nonrelativistic relationship between the kinetic energy and the momentum of the electron. Get solution
39. Calculate the wavelength ofa) a 2.00-eV photon, andb) an electron with a kinetic energy of 2.00 eV. Get solution
40. What is the de Broglie wavelength of a 2.000 · 103-kg car moving at a speed of 100.0 km/h? Get solution
41. A nitrogen molecule of mass m = 4.648 · 10–26 kg has a speed of 300.0 m/s.a) Determine its de Broglie wavelength.b) How far apart are the double slits if a beam of nitrogen molecules creates an interference pattern with fringes 0.30 cm apart on a screen 70.0 cm in front of the slits? Get solution
42. Alpha particles are accelerated through a potential difference of 20.0 kV. What is their de Broglie wavelength? Get solution
43. Consider an electron whose de Broglie wavelength is equal to the wavelength of green light (550 nm).a) Treating the electron nonrelativistically, what is its speed?b) Does your calculation confirm that a nonrelativistic treatment is sufficient?c) Calculate the kinetic energy of the electron in electron-volts. Get solution
44. After you tell your 60.0-kg roommate about de Broglie’s hypothesis that particles of momentum p have wave characteristics with wavelength λ = h/p, he starts thinking of his fate as a wave and asks you if he could be diffracted when passing through the 90.0-cm-wide doorway of your dorm room.a) What is the maximum speed at which your roommate could pass through the doorway and be significantly diffracted?b) If it takes one step to pass through the doorway, how long should it take your roommate to make that step (assuming that the length of his step is 0.75 m) for him to be diffracted?c) What is the answer to your roommate's question? (Hint: Assume that significant diffraction occurs when the width of the diffraction aperture is less than 10.0 times the wavelength of the wave being diffracted.) Get solution
45. Consider de Broglie waves for a Newtonian particle of mass m, momentum p = mv, and energy E = p2/(2m), that is, waves with wavelength λ = h/p and frequency f = E/h.a) For these waves, calculate the dispersion relation, ω = ω (...), where ... is the wave number.b) Calculate the phase velocity (vp = ω/...) and the group velocity ... of these waves. Get solution
46. Now consider de Broglie waves for a (relativistic) particle of mass m, momentum p = mvγ, and total energy E = mc2γ, with γ = [1 – (v/c)2]–1/2. The waves have wavelength λ = h/p and frequency f = E/h as in Problem 36.45, but with the relativistic momentum and energy values.a) For these waves, calculate the dispersion relation, ω = ω (...), where ... is the wave number.b) Calculate the phase velocity (vp = ω /...) and the group velocity ... of these waves.c) Which corresponds to the classical velocity of the particle? Get solution
48. During the period of time required for light to pass through a hydrogen atom (r = 0.53 · 10–10 m), what is the least uncertainty in the atom’s energy? Express your answer in electron-volts. Get solution
50. Suppose that Fuzzy, a quantum-mechanical duck, lives in a world in which Planck’s constant is ħ = 1.00 J s. Fuzzy has a mass of 0.500 kg and initially is known to be within a 0.750-m-wide pond. What is the minimum uncertainty in Fuzzy’s speed? Assuming that this uncertainty prevails for 5.00 s, how far away could Fuzzy be from the pond after 5.00 s? Get solution
49. A free neutron (m = 1.67 · 10–27 kg) has a mean lifetime of 882 s. What is the minimum uncertainty in its mass (in kg)? Get solution
51. An electron is confined to a box with a dimension of 20.0 µm. What is the minimum speed the electron can have? Get solution
52. A dust particle of mass 1.00 · 10–16 kg and diameter 5.00 µm is confined to a box of length 15.0 µm.a) How will you know whether the particle is at rest?b) If the particle is not at rest, what will be the range of its velocity?c) At the lower limit of the velocity range, how long will it take to move a distance of 1.00 µm? Get solution
53. A quantum state of energy E can be occupied by any number n of bosons, including n = 0. At the absolute temperature T, the probability of finding n particles in the state is given by Pn = N exp(–nE/kBT), where kB is Boltzmann’s constant and N is the normalization factor determined by the requirement that all the probabilities sum to unity. Calculate the mean value of n, that is, the average occupation, of this state, given this probability distribution. Get solution
54. For the same quantum state as in Problem 36.53, with a probability distribution of the same form but with fermions, the only possible occupation values are n = 0 and n = 1. Calculate the mean occupation 〈n〉 of the state in this case. Get solution
55. Consider a system made up of N particles. The energy per particle is given by ... where Z is the partition function defined in equation 36.29. If this is a two-state system with E1 = 0 and E2 = E and g1 = g2 = 1, calculate the heat capacity of the system, defined as ... and approximate its behavior at very high and very low temperatures (that is, kBT >> 1 and kBT Get solution
56. Given that the work function of tungsten is 4.55 eV, what is the stopping potential in an experiment using tungsten cathodes at 360 nm? Get solution
58. An einstein (E) is a unit of measurement equal to Avogadro’s number (6.02 · 1023) of photons. How much energy is contained in 1 E of violet light (λ = 400. nm)? Get solution
60. What is the minimum uncertainty in the velocity of a 1.0-ng particle that is at rest on the head of a 1.0-mm-wide pin? Get solution
59. In baseball, a 100.-g ball can travel as fast as 100. mph. The Voyager spacecraft, with a mass of about 250. kg, is currently traveling at 125,000 km/h.a) What is the de Broglie wavelength of this ball?b) What is the de Broglie wavelength of Voyager? Get solution
61. A photovoltaic device uses monochromatic light of wavelength 700. nm that is incident normally on a surface of area 10.0 cm2. Calculate the photon flux rate if the light intensity is 0.300 W/cm2. Get solution
62. The solar constant measured by Earth satellites is roughly 1400. W/m2. Though the Sun emits light of different wavelengths, the peak of the wavelength spectrum is at 500. nm.a) Find the corresponding photon frequency.b) Find the corresponding photon energy.c) Find the number flux of photons (number of photons per unit area per unit time) arriving at Earth, assuming that all light emitted by the Sun has the same peak wavelength. Get solution
63. Two silver plates in vacuum are separated by 1.0 cm and have a potential difference of 5.0 V between them that opposes electron flow. What is the largest wavelength of light that can be incident on the cathode and produce a current in the anode? Get solution
64. How many photons per second must strike a surface of area 10.0 m2 to produce a force of 0.100 N on the surface, if the wavelength of the photons is 600. nm? Assume that the photons are absorbed. Get solution
65. Suppose the wave function describing an electron predicts a statistical spread of 1.00 · 10–4 m/s in the electron’s velocity. What is the corresponding statistical spread in its position? Get solution
66. What is the temperature of a blackbody whose peak emitted wavelength is in the X-ray portion of the spectrum? Get solution
67. A nocturnal bird’s eye can detect monochromatic light of frequency 5.8 · 1014 Hz with a power as small as 2.333 · 10–17 W. What is the corresponding number of photons per second that the nocturnal bird’s eye can detect? Get solution
68. A particular ultraviolet laser produces radiation of wavelength 355 nm. Suppose this is used in a photoelectric experiment with a calcium sample. What will the stopping potential be? Get solution
69. What is the wavelength of an electron that is accelerated from rest through a potential difference of 1.00 · 10–5 V? Get solution
70. Compton used photons of wavelength 0.0711 nm.a) What is the wavelength of the photons scattered at θ = 180°?b) What is energy of these photons?c) If the target were a proton and not an electron, how would your answer to part (a) change? Get solution
72. Scintillation detectors for gamma rays transfer the energy of a gamma-ray photon to an electron within a crystal, via the photoelectric effect or Compton scattering. The electron transfers its energy to atoms in the crystal, which re-emit it as a light flash detected by a photomultiplier tube. The charge pulse produced by the photomultiplier tube is proportional to the original energy in the crystal; this can be measured so that an energy spectrum can be displayed. Gamma rays absorbed in the photoelectric effect are recorded as a photopeak in the spectrum, at the full energy of the rays. The Compton-scattered electrons are also recorded, at a range of lower energies known as the Compton plateau. The highestenergy electrons form the Compton edge of the plateau. Gamma-ray photons scattered by 180° appear as a backscatter peak in the spectrum. For gamma-ray photons of energy 511 KeV, calculate the energies of the Compton edge and the backscatter peak in the spectrum. Get solution
73. A stationary free electron in a gas is struck by a 6.37-nm X-ray, which experiences an increase in wavelength of 1.13 pm. How fast is the electron moving after the interaction with the X-ray? Get solution
74. A stationary free electron in a gas is struck by an X-ray with an energy of 175.37 eV, which experiences a decrease in energy of 28.52 meV. How fast is the electron moving after the interaction with the X-ray? Get solution
75. A stationary free electron in a gas is struck by an X-ray with an energy of 159.98 eV. After the collision, the speed of the electron is measured to be 92.17 km/s. By how much did the energy of the X-ray decrease? Get solution
76. A stationary free electron in a gas is struck by an X-ray with a wavelength of 5.43 nm. After the collision, the speed of the electron is measured to be 132.7 km/s. By how much did the wavelength of the X-ray increase? Get solution
77. A stationary free electron in a gas is struck by an X-ray with a wavelength of 6.13 nm. After the collision, the speed of the electron is measured to be 118.5 km/s. By how much did the frequency of the X-ray change? Get solution
78. An accelerator boosts a proton’s kinetic energy so that its de Broglie wavelength is 3.63 · 10–15 m. What is the total energy of the proton? Get solution
79. An accelerator boosts a proton’s kinetic energy so that its de Broglie wavelength is 4.43 · 10–15 m. What is the kinetic energy of the proton? Get solution
80. An accelerator boosts a proton’s kinetic energy so that its de Broglie wavelength is 1.71 · 10–15 m. What is the speed of the proton? Get solution
1mcq. Ultraviolet light of wavelength 350 nm is incident on a material with a stopping potential of 0.25 V. The work function of the material isa) 4.0 eV.b) 3.3 eV.c) 2.3 eV.d) 5.2 eV. Get solution
2cc. You have a source of light with a given intensity and wavelength. You reduce the wavelength while leaving the intensity the same. Which of the following statements is true?a) More photons per second will be emitted from the light source.b) Fewer photons per second will be emitted from the light source.c) The number of photons emitted per second will remain the same, but the energy of each one will be reduced.d) The number of photons emitted per second will remain the same, but the energy of each one will be increased.e) The number of photons emitted per second will remain the same, but each one will move slower. Get solution
2mcq. The existence of a cutoff frequency in the photoelectric effecta) cannot be explained using classical physics.b) shows that the model provided by classical physics is not correct in this case.c) shows that a photon model of light should be used in this case.d) shows that the energy of the photon is proportional to its frequency.e) All of the above are true. Get solution
3cc. Which of the following statements is true?a) More massive and faster objects have bigger de Broglie wavelengths than less massive and slower ones.b) Less massive and faster objects have bigger de Broglie wavelengths than more massive and slower ones.c) More massive and slower objects have bigger de Broglie wavelengths than less massive and faster ones.d) Less massive and slower objects have bigger de Broglie wavelengths than more massive and faster ones. Get solution
3mcq. To have a larger photocurrent, which of the following should occur? (Select all the changes that apply.)a) brighter lightb) dimmer lightc) higher frequencyd) lower frequency Get solution
4cc. Can you guess the outcome of measuring the current to determine which slit the electron passes through? If we measure the current representing the electron passing through the slits, which of the following will be the result?a) Exactly one-half of each individual electron passes through each of the two slits.b) Each individual electron passes through just one slit. The electrons passing through the left slit cause the left part of the interference pattern, and the electrons passing through the right slit cause the right part.c) Each individual electron passes through just one slit. The electrons passing through the left slit cause the right part of the interference pattern, and the electrons passing through the right slit cause the left part.d) Each individual electron passes through just one slit, but as we conduct measurements to try to determine this, the interference pattern on the screen is destroyed, and we observe only the central maximum on the screen. Get solution
4mcq. Which of the following has the smallest de Broglie wavelength?a) an electron traveling at 80% of the speed of lightb) a proton traveling at 20% of the speed of lightc) a carbon nucleus traveling at 70% of the speed of lightd) a helium nucleus traveling at 80% of the speed of lighte) a lithium nucleus traveling at 50% of the speed of light Get solution
5cc. In Example 36.4, if all other parameters remain the same but the mass of the car is doubled, the resulting uncertainty in the speed will bea) the same.b) half as large.c) one-quarter as large.d) twice as large.e) four times as large.Example 36.4 Trying to Get Out of a Speeding Ticket...... Get solution
5mcq. A blackbody is an ideal system thata) absorbs 100% of the light incident upon it, but cannot emit light of its own.b) radiates 100% of the power it generates, but cannot absorb radiation of its own.c) either absorbs 100% of the light incident upon it, or radiates 100% of the power it generates.d) absorbs 50% of the light incident upon it, and emits 50% of the radiation it generates.e) blackens completely any body that comes in contact with it. Get solution
6cc. Which of the following distributions are possible ways to distribute 4 energy quanta over 5 fermions with spin ... ... Get solution
6mcq. Which one of the following statements is true if the intensity of a light beam is increased while its frequency is kept the same?a) The photons gain higher speeds.b) The energy of the photons is increased.c) The number of photons per unit time is increased.d) The wavelength of the light is increased. Get solution
7mcq. Which of the following has the highest temperature?a) a white-hot objectb) a red-hot objectc) a blue-hot object Get solution
10cq. Answer in your own words the question of whether an electron is a particle or a wave. Get solution
11cq. If I look in a mirror while wearing a blue shirt, my reflection is wearing a blue shirt, not a red shirt. But according to the Compton effect, the photons that bounce off the mirror should have a lower energy and therefore a longer wavelength. Explain why my reflection shows the same color shirt as I am wearing. Get solution
12cq. Vacuum in deep space is not empty, but a boiling sea of particles and antiparticles that are constantly forming and annihilating each other. Determine the maximum lifetime for a proton-antiproton pair to form there without violating Heisenberg’s Uncertainty Relation. Get solution
13cq. Consider a universe where Planck’s constant is 5 J s. How would a game of tennis change? Consider the interactions of individual players with the ball and the interaction of the ball with the net. Get solution
14cq. In classical mechanics, what information is needed in order to predict where a particle with no net force on it will be at some later time? Why is this prediction not possible in quantum mechanics? Get solution
15cq. What would a classical physicist expect to be the result of shining an increasingly brighter UV lamp on a metal surface, in terms of the energy of emitted electrons? How does this differ from what the theory of the photoelectric effect predicts? Get solution
16cq. Which is more damaging to human tissue, a 60-W source of visible light or a 2-mW source of X-rays? Explain your choice. Get solution
17cq. Neutrons are spin- ½ fermions. An unpolarized beam of neutrons has equal numbers of neutrons in the + ½ and – ½ spin states. When a beam of unpolarized neutrons is passed through a gas of unpolarized 3He atoms, the neutrons can be absorbed by the 3He atoms to create 4He atoms. If the 3He atoms are polarized, so that the spins of the neutrons in their nuclei are all aligned, will the same number of neutrons from the unpolarized neutron beam be absorbed by the polarized 3He atoms? How well are neutrons in each of the two spin states of the unpolarized neutron beam absorbed by the 3He? Get solution
18cq. You are performing a photoelectric effect experiment. Using a photocathode made of cesium, you first illuminate it with a green laser beam (λ = 514.5 nm) of power 100 mW. Next, you double the power of the laser beam, to 200 mW. How will the energies per electron of the electrons emitted by the photocathode compare for the two cases? Get solution
19. Calculate the peak wavelengths ofa) the solar light received by Earth, andb) the light emitted by the Earth.Assume that the surface temperatures of the Sun and the Earth are 5800. K and 300. K, respectively. Get solution
21. Ultra-high-energy gamma rays with energies up to 3.5 · 1012 eV, come from the equator of the Milky Way. What is the wavelength of this radiation? How does its energy compare to the rest energy of a proton? Get solution
23. The temperature of your skin is approximately 35.0 °C.a) Assuming that your skin is a blackbody, what is the peak wavelength of the radiation it emits?b) Assuming a total surface area of 2.00 m2, what is the total power emitted by your skin?c) Given your answer to part (b), why don’t you glow as brightly as a light bulb? Get solution
22. Consider the radiation emitted by an object at room temperature (20. °C). For radiation at the peak of the spectral energy density, calculatea) the wavelength,b) the frequency, andc) the energy of one photon. Get solution
24. A pure, defect-free, semiconductor material will absorb the electromagnetic radiation incident on it only if the energy of the individual photons in the incident beam is larger than a threshold value known as the band-gap of the semiconductor. Otherwise, the material will be transparent to the photons. The known room-temperature band-gaps for germanium, silicon, and gallium-arsenide, three widely used semiconductors, are 0.66 eV,1.12 eV, and 1.42 eV, respectively.a) Determine the room-temperature transparency range of each semiconductor.b) Compare these with the transparency range of ZnSe, a semiconductor with a band-gap of 2.67 eV, and explain the yellow color observed experimentally for the ZnSe crystals.c) Which of these materials could be used to detect the 1550-nm optical communications wavelength? Get solution
25. The mass of a dime is 2.268 g, its diameter is 17.91 mm, and its thickness is 1.350 mm. Determinea) the radiant energy emitted by a dime per second at room temperature,b) the number of photons leaving the dime per second (assuming that all photons have the wavelength of the peak of the distribution for this estimate), andc) the volume of air that has an energy equal to that of 1 s of radiation from the dime. Get solution
26. The work function of a certain material is 5.8 eV. What is the photoelectric threshold frequency for this material? Get solution
27. What is the maximum kinetic energy of the electrons ejected from a sodium surface by light of wavelength 470 nm? Get solution
28. The threshold wavelength for the photoelectric effect for a specific alloy is 400. nm. What is the work function in electron-volts? Get solution
29. In a photoelectric effect experiment, a laser beam of unknown wavelength is shone on a cesium photocathode (work function of φ = 2.100 eV). It is found that a stopping potential of 0.310 V is needed to eliminate the current. Next, the same laser is shone on a photocathode made of an unknown material, and a stopping potential of 0.110 V is needed to eliminate the current.a) What is the work function for the unknown material?b) What metal is a possible candidate for the unknown material? Get solution
30. You illuminate a zinc surface with 550-nm light. How high do you have to turn up the stopping potential to eliminate the photoelectric current completely? Get solution
31. White light, λ = 400. to 750. nm, falls on barium (φ = 2.48 eV) .a) What is the maximum kinetic energy of electrons ejected from the metal?b) Would the longest-wavelength light eject electrons?c) What wavelength of light would eject electrons with zero kinetic energy? Get solution
32. To determine the work function of the material of a photodiode, you measured a maximum kinetic energy of 1.50 eV corresponding to a certain wavelength. Later, you decreased the wavelength by 50.0% and found the maximum kinetic energy of the photoelectrons to be 3.80 eV. From this information, determinea) the work function of the material, andb) the original wavelength. Get solution
33. X-rays of wavelength λ = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons deflected at a 90.0° angle relative to the incident beam? Get solution
34. A 2.0-MeV X-ray photon is scattered off a free electron at rest and deflected by an angle of 53°. What is the wavelength of the scattered photon? Get solution
35. A photon with a wavelength of 0.30 nm collides with an electron that is initially at rest. If the photon rebounds at an angle of 160°, how much energy did it lose in the collision? Get solution
36. X-rays having an energy of 400.0 keV undergo Compton scattering from a target electron. The scattered rays are detected at an angle of 25.0° relative to the incident rays. Finda) the kinetic energy of the scattered X-rays, andb) the kinetic energy of the recoiling electron. Get solution
37. Consider the case in which photons scatter off a free proton.a) If 140.-keV X-rays deflect off a proton at 90.0°, what is their fractional change in energy, (E0 – E)/E0?b) What initial energy would a photon have to have to experience a 1.00% change in energy at 90.0° scattering? Get solution
38. An X-ray photon with an energy of 50.0 keV strikes an electron that is initially at rest inside a metal. The photon is scattered at an angle of 45°. What are the kinetic energy and the momentum (magnitude and direction) of the electron after the collision? You may use the nonrelativistic relationship between the kinetic energy and the momentum of the electron. Get solution
39. Calculate the wavelength ofa) a 2.00-eV photon, andb) an electron with a kinetic energy of 2.00 eV. Get solution
40. What is the de Broglie wavelength of a 2.000 · 103-kg car moving at a speed of 100.0 km/h? Get solution
41. A nitrogen molecule of mass m = 4.648 · 10–26 kg has a speed of 300.0 m/s.a) Determine its de Broglie wavelength.b) How far apart are the double slits if a beam of nitrogen molecules creates an interference pattern with fringes 0.30 cm apart on a screen 70.0 cm in front of the slits? Get solution
42. Alpha particles are accelerated through a potential difference of 20.0 kV. What is their de Broglie wavelength? Get solution
43. Consider an electron whose de Broglie wavelength is equal to the wavelength of green light (550 nm).a) Treating the electron nonrelativistically, what is its speed?b) Does your calculation confirm that a nonrelativistic treatment is sufficient?c) Calculate the kinetic energy of the electron in electron-volts. Get solution
44. After you tell your 60.0-kg roommate about de Broglie’s hypothesis that particles of momentum p have wave characteristics with wavelength λ = h/p, he starts thinking of his fate as a wave and asks you if he could be diffracted when passing through the 90.0-cm-wide doorway of your dorm room.a) What is the maximum speed at which your roommate could pass through the doorway and be significantly diffracted?b) If it takes one step to pass through the doorway, how long should it take your roommate to make that step (assuming that the length of his step is 0.75 m) for him to be diffracted?c) What is the answer to your roommate's question? (Hint: Assume that significant diffraction occurs when the width of the diffraction aperture is less than 10.0 times the wavelength of the wave being diffracted.) Get solution
45. Consider de Broglie waves for a Newtonian particle of mass m, momentum p = mv, and energy E = p2/(2m), that is, waves with wavelength λ = h/p and frequency f = E/h.a) For these waves, calculate the dispersion relation, ω = ω (...), where ... is the wave number.b) Calculate the phase velocity (vp = ω/...) and the group velocity ... of these waves. Get solution
46. Now consider de Broglie waves for a (relativistic) particle of mass m, momentum p = mvγ, and total energy E = mc2γ, with γ = [1 – (v/c)2]–1/2. The waves have wavelength λ = h/p and frequency f = E/h as in Problem 36.45, but with the relativistic momentum and energy values.a) For these waves, calculate the dispersion relation, ω = ω (...), where ... is the wave number.b) Calculate the phase velocity (vp = ω /...) and the group velocity ... of these waves.c) Which corresponds to the classical velocity of the particle? Get solution
48. During the period of time required for light to pass through a hydrogen atom (r = 0.53 · 10–10 m), what is the least uncertainty in the atom’s energy? Express your answer in electron-volts. Get solution
50. Suppose that Fuzzy, a quantum-mechanical duck, lives in a world in which Planck’s constant is ħ = 1.00 J s. Fuzzy has a mass of 0.500 kg and initially is known to be within a 0.750-m-wide pond. What is the minimum uncertainty in Fuzzy’s speed? Assuming that this uncertainty prevails for 5.00 s, how far away could Fuzzy be from the pond after 5.00 s? Get solution
49. A free neutron (m = 1.67 · 10–27 kg) has a mean lifetime of 882 s. What is the minimum uncertainty in its mass (in kg)? Get solution
51. An electron is confined to a box with a dimension of 20.0 µm. What is the minimum speed the electron can have? Get solution
52. A dust particle of mass 1.00 · 10–16 kg and diameter 5.00 µm is confined to a box of length 15.0 µm.a) How will you know whether the particle is at rest?b) If the particle is not at rest, what will be the range of its velocity?c) At the lower limit of the velocity range, how long will it take to move a distance of 1.00 µm? Get solution
53. A quantum state of energy E can be occupied by any number n of bosons, including n = 0. At the absolute temperature T, the probability of finding n particles in the state is given by Pn = N exp(–nE/kBT), where kB is Boltzmann’s constant and N is the normalization factor determined by the requirement that all the probabilities sum to unity. Calculate the mean value of n, that is, the average occupation, of this state, given this probability distribution. Get solution
54. For the same quantum state as in Problem 36.53, with a probability distribution of the same form but with fermions, the only possible occupation values are n = 0 and n = 1. Calculate the mean occupation 〈n〉 of the state in this case. Get solution
55. Consider a system made up of N particles. The energy per particle is given by ... where Z is the partition function defined in equation 36.29. If this is a two-state system with E1 = 0 and E2 = E and g1 = g2 = 1, calculate the heat capacity of the system, defined as ... and approximate its behavior at very high and very low temperatures (that is, kBT >> 1 and kBT Get solution
56. Given that the work function of tungsten is 4.55 eV, what is the stopping potential in an experiment using tungsten cathodes at 360 nm? Get solution
58. An einstein (E) is a unit of measurement equal to Avogadro’s number (6.02 · 1023) of photons. How much energy is contained in 1 E of violet light (λ = 400. nm)? Get solution
60. What is the minimum uncertainty in the velocity of a 1.0-ng particle that is at rest on the head of a 1.0-mm-wide pin? Get solution
59. In baseball, a 100.-g ball can travel as fast as 100. mph. The Voyager spacecraft, with a mass of about 250. kg, is currently traveling at 125,000 km/h.a) What is the de Broglie wavelength of this ball?b) What is the de Broglie wavelength of Voyager? Get solution
61. A photovoltaic device uses monochromatic light of wavelength 700. nm that is incident normally on a surface of area 10.0 cm2. Calculate the photon flux rate if the light intensity is 0.300 W/cm2. Get solution
62. The solar constant measured by Earth satellites is roughly 1400. W/m2. Though the Sun emits light of different wavelengths, the peak of the wavelength spectrum is at 500. nm.a) Find the corresponding photon frequency.b) Find the corresponding photon energy.c) Find the number flux of photons (number of photons per unit area per unit time) arriving at Earth, assuming that all light emitted by the Sun has the same peak wavelength. Get solution
63. Two silver plates in vacuum are separated by 1.0 cm and have a potential difference of 5.0 V between them that opposes electron flow. What is the largest wavelength of light that can be incident on the cathode and produce a current in the anode? Get solution
64. How many photons per second must strike a surface of area 10.0 m2 to produce a force of 0.100 N on the surface, if the wavelength of the photons is 600. nm? Assume that the photons are absorbed. Get solution
65. Suppose the wave function describing an electron predicts a statistical spread of 1.00 · 10–4 m/s in the electron’s velocity. What is the corresponding statistical spread in its position? Get solution
66. What is the temperature of a blackbody whose peak emitted wavelength is in the X-ray portion of the spectrum? Get solution
67. A nocturnal bird’s eye can detect monochromatic light of frequency 5.8 · 1014 Hz with a power as small as 2.333 · 10–17 W. What is the corresponding number of photons per second that the nocturnal bird’s eye can detect? Get solution
68. A particular ultraviolet laser produces radiation of wavelength 355 nm. Suppose this is used in a photoelectric experiment with a calcium sample. What will the stopping potential be? Get solution
69. What is the wavelength of an electron that is accelerated from rest through a potential difference of 1.00 · 10–5 V? Get solution
70. Compton used photons of wavelength 0.0711 nm.a) What is the wavelength of the photons scattered at θ = 180°?b) What is energy of these photons?c) If the target were a proton and not an electron, how would your answer to part (a) change? Get solution
72. Scintillation detectors for gamma rays transfer the energy of a gamma-ray photon to an electron within a crystal, via the photoelectric effect or Compton scattering. The electron transfers its energy to atoms in the crystal, which re-emit it as a light flash detected by a photomultiplier tube. The charge pulse produced by the photomultiplier tube is proportional to the original energy in the crystal; this can be measured so that an energy spectrum can be displayed. Gamma rays absorbed in the photoelectric effect are recorded as a photopeak in the spectrum, at the full energy of the rays. The Compton-scattered electrons are also recorded, at a range of lower energies known as the Compton plateau. The highestenergy electrons form the Compton edge of the plateau. Gamma-ray photons scattered by 180° appear as a backscatter peak in the spectrum. For gamma-ray photons of energy 511 KeV, calculate the energies of the Compton edge and the backscatter peak in the spectrum. Get solution
73. A stationary free electron in a gas is struck by a 6.37-nm X-ray, which experiences an increase in wavelength of 1.13 pm. How fast is the electron moving after the interaction with the X-ray? Get solution
74. A stationary free electron in a gas is struck by an X-ray with an energy of 175.37 eV, which experiences a decrease in energy of 28.52 meV. How fast is the electron moving after the interaction with the X-ray? Get solution
75. A stationary free electron in a gas is struck by an X-ray with an energy of 159.98 eV. After the collision, the speed of the electron is measured to be 92.17 km/s. By how much did the energy of the X-ray decrease? Get solution
76. A stationary free electron in a gas is struck by an X-ray with a wavelength of 5.43 nm. After the collision, the speed of the electron is measured to be 132.7 km/s. By how much did the wavelength of the X-ray increase? Get solution
77. A stationary free electron in a gas is struck by an X-ray with a wavelength of 6.13 nm. After the collision, the speed of the electron is measured to be 118.5 km/s. By how much did the frequency of the X-ray change? Get solution
78. An accelerator boosts a proton’s kinetic energy so that its de Broglie wavelength is 3.63 · 10–15 m. What is the total energy of the proton? Get solution
79. An accelerator boosts a proton’s kinetic energy so that its de Broglie wavelength is 4.43 · 10–15 m. What is the kinetic energy of the proton? Get solution
80. An accelerator boosts a proton’s kinetic energy so that its de Broglie wavelength is 1.71 · 10–15 m. What is the speed of the proton? Get solution
