1. Describe the design features of an apparatus that will produce the correct magnetic field needed in Figure 3.2. ... Get solution
1q. How did the ionization of gas by cathode rays prevent H. Hertz from discovering the true character of electrons? Get solution
2. For an electric field of 2.5 × 105 V/m, what is the strength of the magnetic field needed to pass an electron of speed 2.2 × 106 m/s with no deflection? Draw the mutually perpendicular ...and ...directions that allow this to occur. Get solution
2q. Women in the late 1890s were terrified about the possible misuse of the new Röntgen x rays. What use do you think they envisioned? Get solution
3. Across what potential difference does an electron have to be accelerated to reach the speed v = 1.8 × 107 m/s? Work the problem both nonrelativistically and relativistically and compare the results. Get solution
3q. Women in the late 1890s were terrified about the possible misuse of the new Röntgen x rays. What use do you think they envisioned? Get solution
4. An electron entering Thomson’s e/m apparatus (Figures 3.2 and 3.3) has an initial velocity (in horizontal direction only) of 4.0 × 106 m/s. In the lab is a permanent horseshoe magnet of strength 12 mT, which you would like to use. (a) What electric field will you need in order to produce zero deflection of the electrons as they travel through the apparatus? (b) The length of nonzero ...fields is 2.0 cm. When the magnetic field is turned off, but the same electric field remains, how far in the vertical direction will the electron beam be deflected over this length? Get solution
4q. In the late 1890s many people had x rays taken of their body. X-ray machines were common in shoe stores in the late 1940s and early 1950s for people to examine how their shoes fi t; customers enjoyed seeing pictures of their bones. Discuss the safety of these undertakings. Get solution
5. Consider the following possible forces on an oil drop in Millikan’s experiment: gravitational, electrical, frictional, and buoyant. Draw a diagram indicating the forces on the oil drop (a) when the electric field is turned off and the droplet is falling freely and (b) when the electric field causes the droplet to rise. Get solution
5q. Parents tell their children not to sit close to the television screen. Can x rays be produced in old, cathoderaytype televisions? Explain. Get solution
6. Neglect the buoyancy force on an oil droplet and show that the terminal speed of the droplet is vt = mg/b, where b is the coefficient of friction when the droplet is in free fall. (Remember that the frictional force ...is given by ...where velocity is a vector.) Get solution
6q. In Example 3.2, why would you be concerned about observing a cluster of several balls in the Millikan electron charge experiment? ... ... Get solution
7. Stokes’s law relates the coefficient of friction b to the radius r of the oil drop and the viscosity ηof the medium the droplet is passing through .... Show that the radius of the oil drop is given in terms of the terminal velocity vt (see Problem 6), η, g, and the density of the oil ... Get solution
7q. In Figure 3.5, why are the histogram peaks more difficult to identify as the charge increases? ... Get solution
8q. How is it possible for the plastic balls in Example 3.2 to have both positive and negative charges? What is happening? How is it possible for the plastic balls in Example 3.2 to have both positive and negative charges? What is happening? Example 3.2 ... ... Get solution
9. What is the series limit (that is, the smallest wavelength) for (a) the Lyman series and (b) the Balmer series? Get solution
9q. Why do you suppose Millikan tried several kinds of oil, as well as H2O and Hg, for his oil-drop experiment? Get solution
10. Light from a slit passes through a transmission diffraction grating of 400 lines/mm, which is located 3.0 m from a screen. What are the distances on the screen (from the unscattered slit image) of the three brightest visible (first-order) hydrogen lines? Get solution
10q. In the experiment of Example 3.2, how could you explain an experimental value of q = 0.8 × 10-19 C? Example 3.2 ... ... Get solution
11. A transmission diffraction grating with 420 lines/mm is used to study the light intensity of different orders (n). A screen is located 2.8 m from the grating. What are the positions on the screen of the three brightest red lines for a hydrogen source? Get solution
11q. Why do you suppose scientists worked so hard to develop better diffraction gratings? Get solution
12. Calculate the four largest wavelengths for the Brackett and Pfund series for hydrogen. Get solution
12q. Why was helium discovered in the sun’s spectrum before being observed on Earth? Why was hydrogen observed on Earth first? Get solution
13. Josef von Fraunhofer made the first diffraction grating in 1821 and used it to measure the wavelengths of specific colors as well as the dark lines in the solar spectrum. His first diffraction grating consisted of 262 parallel wires. Assume that the wires were 0.20 mm apart and that Fraunhofer could resolve two spectral lines that were deflected at angles 0.50 min of arc apart. Using this grating, what is the minimum separation (in wavelength) that can be resolved of two first order spectral lines near a wavelength of 400 nm? Get solution
13q. Do you believe there is any relation between the wavelengths of the Paschen (1908) and Pfund (1924) series and the respective dates they were discovered? Explain. Get solution
14. Suppose that a detector in the Hubble Space Telescope was capable of detecting visible light in the wavelength range of 400 to 700 nm. (a) List all the wavelengths for the hydrogen atom that are in this range and their series name. (b) The detector measures visible wavelengths of 537.5 nm, 480.1 nm, and 453.4 nm that researchers believe are due to the hydrogen atom. Why are all the known visible hydrogen lines not detected? (c) Use these data to calculate the speed of the stellar object that emitted the spectra. Assume that the object is not rotating. Why might rotation be an issue? Get solution
14q. It is said that no two snowflakes look exactly alike, but we know that snowflakes have a quite regular, although complex, crystal structure. Discuss how this could be due to quantized behavior. Get solution
15. The Spitzer Space Telescope was launched in 2003 to detect infrared radiation. Suppose a particular detector on the telescope is sensitive over part of the near-infrared region of wavelengths 980 to 1920 nm. Astronomers want to detect the radiation being emitted from a red giant star and decide to concentrate on wavelengths from the Paschen series of the hydrogen atom. (a) What are the known wavelengths in this wavelength region? (b) The detector measures wavelengths of 1334.5, 1138.9, and 1046.1 nm believed to be from the Paschen series. Why are these wavelengths different from those found in part (a)? (c) How fast is the star moving with respect to us? Get solution
15q. Why do we say that the elementary units of matter or “building blocks” must be some basic unit of massenergy rather than only of mass? Get solution
16. Quarks have charges ±e/3 and ±2e/3. What combination of three quarks could yield (a) a proton, (b) a neutron? Get solution
16q. Why is a red-hot object cooler than a white-hot one of the same material? Get solution
17. Calculate λmax for blackbody radiation for (a) liquid helium (4.2 K), (b) room temperature (293 K), (c) a steel furnace (2500 K), and (d) a blue star (9000 K). Get solution
17q. Why did scientists choose to study blackbody radiation from something as complicated as a hollow container rather than the radiation from something simple, such as a thin, solid cylinder (such as a dime)? Get solution
18. Calculate the temperature of a blackbody if the spectral distribution peaks at (a) gamma rays, λ = 1.50 × 10-14 m; (b) x rays, 1.50 nm; (c) red light, 640 nm; (d) broadcast television waves, λ = 1.00 m; and (e) AM radio waves, λ = 204 m. Get solution
18q. Why does the sun’s radiation output match that of a blackbody? Get solution
19. (a) A blackbody’s temperature is increased from 900 K to 2300 K. By what factor does the total power radiated per unit area increase? (b) If the original temperature is again 900 K, what final temperature is required to double the power output? Get solution
19q. Astronomers determine the surface temperature of a star by measuring its brightness at different frequencies. Explain how they can then use the Planck radiation law to obtain the surface temperature. Get solution
20. (a) At what wavelength will the human body radiate the maximum radiation? (b) Estimate the total power radiated by a person of medium build (assume an area given by a cylinder of 175-cm height and 13-cm radius). (c) Using your answer to (b), compare the energy radiated by a person in one day with the energy intake of a 2000-kcal diet. Get solution
20q. In a typical photoelectric effect experiment, consider replacing the metal photocathode with a gas. What difference would you expect? Get solution
21. White dwarf stars have been observed with a surface temperature as hot as 200,000°C. What is the wavelength of the maximum intensity produced by this star? Get solution
21q. What do the work functions of Table 3.3 tell us about the properties of particular metals? Which have the most tightly and least tightly bound electrons? ... Get solution
22. For a temperature of 5800 K (the sun’s surface temperature), find the wavelength for which the spectral distribution calculated by the Planck and Rayleigh- Jeans results differ by 5%. Get solution
22q. Why is it important to produce x-ray tubes with high accelerating voltages that are also able to withstand electron currents? Get solution
23. A tungsten fi lament of a typical incandescent lightbulb operates at a temperature near 3000 K. At what wavelength is the intensity at its maximum? Get solution
23q. For a given beam current and target thickness, why would you expect a tungsten target to produce a higher x-ray intensity than targets of molybdenum or chromium? Get solution
24. Use a computer to calculate Planck’s radiation law for a temperature of 3000 K, which is the temperature of a typical tungsten fi lament in an incandescent lightbulb. Plot the intensity versus wavelength. (a) How much of the power is in the visible region (400–700 nm) compared with the ultraviolet and infrared? (b) What is the ratio of the intensity at 400 nm and 700 nm to the wavelength with maximum intensity? Get solution
24q. List all possible known interactions between photons and electrons discussed in this chapter. Can you think of any more? Get solution
25. Show that the ultraviolet catastrophe is avoided for short wavelengths ...with Planck’s radiation law by calculating the limiting intensity ... as .... Get solution
25q. Discuss why it is difficult to see the Compton effect using visible light. Get solution
26. Estimate the power radiated by (a) a basketball at 20°C and (b) the human body (assume a temperature of 37°C). Get solution
26q. What do you believe to be an optimum lifetime for a positron-emitting radioactive nuclide used in brain tumor diagnostics? Explain. Get solution
27. At what wavelength is the radiation emitted by the human body at its maximum? Assume a temperature of 37°C. Get solution
28. If we have waves in a one-dimensional box, such that the wave displacement _(x, t) _ 0 for x _ 0 and x _ L, where L is the length of the box, and ... show that the solutions are of the from ... and a(t) satisfies the (harmonic-oscillator) equation ... where ...is the angular frequency 2 πf. Get solution
29. If the angular frequencies of waves in a three-dimensional box of sides L generalize to ... where all n are integers, show that the number of distinct states in the frequency interval f(=ω/2 π) to f + Δf is given by (where f is large) ... Get solution
30. Let the energy density in the frequency interval f to f + df within a blackbody at temperature T be dU(f, T). Show that the power emitted through a small hole of area ΔA in the container is ... Get solution
31. Derive the Planck radiation law emitted by a blackbody. Remember that light has two directions of polarization and treat the waves as an ensemble of harmonic oscillators. Get solution
32. An FM radio station of frequency 98.1 MHz puts out a signal of 50,000 W. How many photons/s are emitted? Get solution
33. How many photons/s are contained in a beam of electromagnetic radiation of total power 180 W if the source is (a) an AM radio station of 1100 kHz, (b) 8.0-nm x rays, and (c) 4.0-MeV gamma rays? Get solution
34. What is the threshold frequency for the photoelectric effect on lithium (Ø = 2.93 eV)? What is the stopping potential if the wavelength of the incident light is 380 nm? Get solution
35. What is the maximum wavelength of incident light that can produce photoelectrons from silver (Ø = 4.64 eV)? What will be the maximum kinetic energy of the photoelectrons if the wavelength is halved? Get solution
36. A 2.0-mW green laser (λ = 532 nm) shines on a cesium photocathode (φ = 1.95 eV). Assume an efficiency of 10-5 for producing photoelectrons (that is, one photoelectron produced for every 105 incident photons) and determine the photoelectric current. Get solution
37. An experimenter fi nds that no photoelectrons are emitted from tungsten unless the wavelength of light is less than 270 nm. Her experiment will require photoelectrons of maximum kinetic energy 2.0 eV. What frequency of light should be used to illuminate the tungsten? Get solution
38. The human eye is sensitive to a pulse of light containing as few as 100 photons. For orange light of wavelength 610 nm, how much energy is contained in the pulse? Get solution
39. In a photoelectric experiment it is found that a stopping potential of 1.00 V is needed to stop all the electrons when incident light of wavelength 260 nm is used and 2.30 V is needed for light of wavelength 207 nm. From these data determine Planck’s constant and the work function of the metal. Get solution
40. Find the wavelength of light incident on a tungsten target that will release electrons with a maximum speed of 1.4 × 106 m/s. Get solution
41. What is the minimum x-ray wavelength produced for a dental x-ray machine operated at 30 kV? Get solution
42. The Stanford Linear Accelerator can accelerate electrons to 50 GeV (50 × 109 eV). What is the minimum wavelength of photon it can produce by bremsstrahlung? Is this photon still called an x ray? Get solution
43. A cathode-ray tube in a scanning electron microscope operates at 25 keV. What is λmin for the continuous x-ray spectrum produced when the electrons hit the target? Get solution
44. Calculate λmin for all three elements shown in Figure 3.19. Use the value of the work function for tungsten in Table 3.3 and calculate the percentage error in neglecting the work function for the Duane-Hunt rule using the data of Figure 3.19. ... ... Get solution
45. The two peaks for the molybdenum spectra of Figure 3.19 are characteristic spectral lines for the molybdenum element. What is the minimum potential difference needed to accelerate electrons in an x-ray tube to produce both of these lines? ... Get solution
46. Calculate the maximum Δ λ/ λ of Compton scattering for blue light (λ = 480 nm). Could this be easily observed? Get solution
47. A photon having 40 keV scatters from a free electron at rest. What is the maximum energy that the electron can obtain? Get solution
48. If a 7.0-keV photon scatters from a free proton at rest, what is the change in the photon’s wavelength if the photon recoils at 90°? Get solution
49. Is it possible to have a scattering similar to Compton scattering from a proton in H2 gas? What would be the Compton wavelength for a proton? What energy photon would have this wavelength? Get solution
50. An instrument has resolution Δ λ/ λ = 0.40%. What wavelength of incident photons should be used in order to resolve the modified and unmodified scattered photons for scattering angles of (a) 30°, (b) 90°, and (c) 170°? Get solution
51. Derive the relation for the recoil kinetic energy of the electron and its recoil angle f in Compton scattering. Show that ... Get solution
52. A 650-keV gamma ray Compton-scatters from an electron. Find the energy of the photon scattered at 110°, the kinetic energy of the scattered electron, and the recoil angle of the electron. Get solution
53. A photon of wavelength 2.0 nm Compton-scatters from an electron at an angle of 90°. What is the modified wavelength and the fractional change, Δλ/ λ? Get solution
54. How much photon energy is required to produce a proton-antiproton pair? Where could such a high-energy photon come from? Get solution
55. What is the minimum photon energy needed to create an e- - e- pair when a photon collides (a) with a free electron at rest and (b) with a free proton at rest? Get solution
56g. What wavelength photons are needed to produce 30.0-keV electrons in Compton scattering? Get solution
57g. A typical person can detect light with a minimum intensity of 4.0 × 10-11 W/m2. For light of this intensity and λ = 550 nm, how many photons enter the eye each second if the pupil is open wide with a diameter of 9.0 mm? Get solution
58g. A copper wire carrying a high current glows “red hot” just before the wire melts at a temperature of 1085°C. (a) What is the peak wavelength of the emitted radiation? (b) Given your answer to part (a), how can the wire be “red hot”? Get solution
59g. The gravitational energy of Earth is approximately 0.5(GM 2 E /RE ) where ME is the mass of Earth. This is approximately the energy needed to blow the planet into small fragments (the size of asteroids). How large would an antimatter meteorite the density of nickeliron (ρ = 5 × 103 kg/m3) have to be in order to blow up Earth when it strikes? Compute the energy involved in the particle-antiparticle annihilation and compare it with the total energy in all the nuclear arsenals of the world [~5000 megatons (MT), where 1 MT = 4.2 × 1015 J]. Get solution
60g. Show that the maximum kinetic energy of the recoil electron in Compton scattering is given by ... At what angles θ and Ø does this occur? If we detect a scattered electron at Ø = 0° of 100 keV, what energy photon was scattered? Get solution
61g. Use the Wien displacement law to make a log-log plot of λmax (from 10-8 m to 10-2 m) versus temperature (from 100 K to 105 K). Mark on the plot the regions of visible, ultraviolet, infrared, and microwave wavelengths. Put the following points on the line: sun (5800 K), furnace (1900 K), room temperature (300 K), and the background radiation of the universe (2.7 K). Discuss the electromagnetic radiation that is emitted from each of these sources. Does it make sense? Get solution
62g. (a) What is the maximum possible energy for a Compton-backscattered x ray (θ = 180°)? Express your answer in terms of λ, the wavelength of the incoming photon. (b) Evaluate numerically when the incoming photon’s energy is 100 keV. Get solution
63g. The naked eye can detect a stellar object of sixth magnitude in the night sky. With binoculars, we can see an object of the ninth magnitude. The sun’s brightness at Earth is 1400 W/m2. The Hubble Space Telescope can detect an object of the 30th magnitude, which amounts to a brightness of about 2 × 10-20 W/m2. (a) Consider a detector in the Hubble Space Tele-scope with a collection area of 0.30 m2. If you assume hydrogen light of frequency 486 nm (blue-green), how many photons/s enter the telescope from a 30thmagnitude star? (b) An increase of magnitude one represents a decrease in brightness by a factor of 1001/5. Estimate how many photons/s from a sixth-magnitude star would enter your eye if the diameter of your pupil is 6.5 mm. Get solution
64g. Original data from Millikan’s pivotal photoelectric experiment that confirmed Einstein’s quantum explanation is shown in Figure 3.16 [from R. A. Millikan, Physical Review 7, 362 (1916)]. Sodium was the photocathode. Use the data to find the work function for sodium and Planck’s constant. Get solution
65g. A prototype laser weapon tested in 2010 used a laser with an infrared wavelength of 1.06 m, because the atmosphere is fairly transparent at that wavelength. The laser’s continuous output was 25 kW. How many photons per second were produced? Get solution
66g. A typical chemical reaction such as an explosive combustion releases about 5 MJ of energy per kg fuel used. At the sun’s current rate of energy production, how much time would the sun last at that rate? Compare your answer with the sun’s estimated lifetime of 10 billion years. Get solution
67g. The bright star Sirius A has a diameter 1.6 times the sun’s and surface temperature 9600 K. (a) What is the peak wavelength of radiation emitted from the surface? (Note: Sirius has a distinctive blue tint when viewed with the naked eye.) (b) Find the net power output from the surface of Sirius A and compare with that from the sun. Get solution
68g. In developing Equation (3.36), we argued that the recoiling nucleus could be ignored. Consider again the x-ray tube described in Example 3.15 with 35-keV electrons striking a tungsten target. Suppose an electron is deflected through a negligible angle and its kinetic energy drops to 30 keV in a scattering event with a nucleus. Assuming that the nucleus was initially at rest, use conservation of momentum to find the kinetic energy of the recoiling nucleus and comment on the result. ... Get solution
69g. The Fermi Gamma-ray Space Telescope, launched in 2008, can detect gamma rays with energies ranging from 10 keV to 300 MeV. For each of those energy extremes, fi nd the resulting kinetic energy and speed of an electron created by the gamma ray as part of an electron-positron pair. Assume that the electron has half of the gamma ray’s energy. Get solution
70g. Gamma-ray detectors like the one described in the preceding problem often use calorimetry to determine gamma-ray energies. Suppose a beam of 100-MeV gamma rays strikes a target with a mass of 2.5 kg and specific heat 430 J/(kg . K). How many gamma rays are needed to raise the target’s temperature by 10 mK? Get solution
1q. How did the ionization of gas by cathode rays prevent H. Hertz from discovering the true character of electrons? Get solution
2. For an electric field of 2.5 × 105 V/m, what is the strength of the magnetic field needed to pass an electron of speed 2.2 × 106 m/s with no deflection? Draw the mutually perpendicular ...and ...directions that allow this to occur. Get solution
2q. Women in the late 1890s were terrified about the possible misuse of the new Röntgen x rays. What use do you think they envisioned? Get solution
3. Across what potential difference does an electron have to be accelerated to reach the speed v = 1.8 × 107 m/s? Work the problem both nonrelativistically and relativistically and compare the results. Get solution
3q. Women in the late 1890s were terrified about the possible misuse of the new Röntgen x rays. What use do you think they envisioned? Get solution
4. An electron entering Thomson’s e/m apparatus (Figures 3.2 and 3.3) has an initial velocity (in horizontal direction only) of 4.0 × 106 m/s. In the lab is a permanent horseshoe magnet of strength 12 mT, which you would like to use. (a) What electric field will you need in order to produce zero deflection of the electrons as they travel through the apparatus? (b) The length of nonzero ...fields is 2.0 cm. When the magnetic field is turned off, but the same electric field remains, how far in the vertical direction will the electron beam be deflected over this length? Get solution
4q. In the late 1890s many people had x rays taken of their body. X-ray machines were common in shoe stores in the late 1940s and early 1950s for people to examine how their shoes fi t; customers enjoyed seeing pictures of their bones. Discuss the safety of these undertakings. Get solution
5. Consider the following possible forces on an oil drop in Millikan’s experiment: gravitational, electrical, frictional, and buoyant. Draw a diagram indicating the forces on the oil drop (a) when the electric field is turned off and the droplet is falling freely and (b) when the electric field causes the droplet to rise. Get solution
5q. Parents tell their children not to sit close to the television screen. Can x rays be produced in old, cathoderaytype televisions? Explain. Get solution
6. Neglect the buoyancy force on an oil droplet and show that the terminal speed of the droplet is vt = mg/b, where b is the coefficient of friction when the droplet is in free fall. (Remember that the frictional force ...is given by ...where velocity is a vector.) Get solution
6q. In Example 3.2, why would you be concerned about observing a cluster of several balls in the Millikan electron charge experiment? ... ... Get solution
7. Stokes’s law relates the coefficient of friction b to the radius r of the oil drop and the viscosity ηof the medium the droplet is passing through .... Show that the radius of the oil drop is given in terms of the terminal velocity vt (see Problem 6), η, g, and the density of the oil ... Get solution
7q. In Figure 3.5, why are the histogram peaks more difficult to identify as the charge increases? ... Get solution
8q. How is it possible for the plastic balls in Example 3.2 to have both positive and negative charges? What is happening? How is it possible for the plastic balls in Example 3.2 to have both positive and negative charges? What is happening? Example 3.2 ... ... Get solution
9. What is the series limit (that is, the smallest wavelength) for (a) the Lyman series and (b) the Balmer series? Get solution
9q. Why do you suppose Millikan tried several kinds of oil, as well as H2O and Hg, for his oil-drop experiment? Get solution
10. Light from a slit passes through a transmission diffraction grating of 400 lines/mm, which is located 3.0 m from a screen. What are the distances on the screen (from the unscattered slit image) of the three brightest visible (first-order) hydrogen lines? Get solution
10q. In the experiment of Example 3.2, how could you explain an experimental value of q = 0.8 × 10-19 C? Example 3.2 ... ... Get solution
11. A transmission diffraction grating with 420 lines/mm is used to study the light intensity of different orders (n). A screen is located 2.8 m from the grating. What are the positions on the screen of the three brightest red lines for a hydrogen source? Get solution
11q. Why do you suppose scientists worked so hard to develop better diffraction gratings? Get solution
12. Calculate the four largest wavelengths for the Brackett and Pfund series for hydrogen. Get solution
12q. Why was helium discovered in the sun’s spectrum before being observed on Earth? Why was hydrogen observed on Earth first? Get solution
13. Josef von Fraunhofer made the first diffraction grating in 1821 and used it to measure the wavelengths of specific colors as well as the dark lines in the solar spectrum. His first diffraction grating consisted of 262 parallel wires. Assume that the wires were 0.20 mm apart and that Fraunhofer could resolve two spectral lines that were deflected at angles 0.50 min of arc apart. Using this grating, what is the minimum separation (in wavelength) that can be resolved of two first order spectral lines near a wavelength of 400 nm? Get solution
13q. Do you believe there is any relation between the wavelengths of the Paschen (1908) and Pfund (1924) series and the respective dates they were discovered? Explain. Get solution
14. Suppose that a detector in the Hubble Space Telescope was capable of detecting visible light in the wavelength range of 400 to 700 nm. (a) List all the wavelengths for the hydrogen atom that are in this range and their series name. (b) The detector measures visible wavelengths of 537.5 nm, 480.1 nm, and 453.4 nm that researchers believe are due to the hydrogen atom. Why are all the known visible hydrogen lines not detected? (c) Use these data to calculate the speed of the stellar object that emitted the spectra. Assume that the object is not rotating. Why might rotation be an issue? Get solution
14q. It is said that no two snowflakes look exactly alike, but we know that snowflakes have a quite regular, although complex, crystal structure. Discuss how this could be due to quantized behavior. Get solution
15. The Spitzer Space Telescope was launched in 2003 to detect infrared radiation. Suppose a particular detector on the telescope is sensitive over part of the near-infrared region of wavelengths 980 to 1920 nm. Astronomers want to detect the radiation being emitted from a red giant star and decide to concentrate on wavelengths from the Paschen series of the hydrogen atom. (a) What are the known wavelengths in this wavelength region? (b) The detector measures wavelengths of 1334.5, 1138.9, and 1046.1 nm believed to be from the Paschen series. Why are these wavelengths different from those found in part (a)? (c) How fast is the star moving with respect to us? Get solution
15q. Why do we say that the elementary units of matter or “building blocks” must be some basic unit of massenergy rather than only of mass? Get solution
16. Quarks have charges ±e/3 and ±2e/3. What combination of three quarks could yield (a) a proton, (b) a neutron? Get solution
16q. Why is a red-hot object cooler than a white-hot one of the same material? Get solution
17. Calculate λmax for blackbody radiation for (a) liquid helium (4.2 K), (b) room temperature (293 K), (c) a steel furnace (2500 K), and (d) a blue star (9000 K). Get solution
17q. Why did scientists choose to study blackbody radiation from something as complicated as a hollow container rather than the radiation from something simple, such as a thin, solid cylinder (such as a dime)? Get solution
18. Calculate the temperature of a blackbody if the spectral distribution peaks at (a) gamma rays, λ = 1.50 × 10-14 m; (b) x rays, 1.50 nm; (c) red light, 640 nm; (d) broadcast television waves, λ = 1.00 m; and (e) AM radio waves, λ = 204 m. Get solution
18q. Why does the sun’s radiation output match that of a blackbody? Get solution
19. (a) A blackbody’s temperature is increased from 900 K to 2300 K. By what factor does the total power radiated per unit area increase? (b) If the original temperature is again 900 K, what final temperature is required to double the power output? Get solution
19q. Astronomers determine the surface temperature of a star by measuring its brightness at different frequencies. Explain how they can then use the Planck radiation law to obtain the surface temperature. Get solution
20. (a) At what wavelength will the human body radiate the maximum radiation? (b) Estimate the total power radiated by a person of medium build (assume an area given by a cylinder of 175-cm height and 13-cm radius). (c) Using your answer to (b), compare the energy radiated by a person in one day with the energy intake of a 2000-kcal diet. Get solution
20q. In a typical photoelectric effect experiment, consider replacing the metal photocathode with a gas. What difference would you expect? Get solution
21. White dwarf stars have been observed with a surface temperature as hot as 200,000°C. What is the wavelength of the maximum intensity produced by this star? Get solution
21q. What do the work functions of Table 3.3 tell us about the properties of particular metals? Which have the most tightly and least tightly bound electrons? ... Get solution
22. For a temperature of 5800 K (the sun’s surface temperature), find the wavelength for which the spectral distribution calculated by the Planck and Rayleigh- Jeans results differ by 5%. Get solution
22q. Why is it important to produce x-ray tubes with high accelerating voltages that are also able to withstand electron currents? Get solution
23. A tungsten fi lament of a typical incandescent lightbulb operates at a temperature near 3000 K. At what wavelength is the intensity at its maximum? Get solution
23q. For a given beam current and target thickness, why would you expect a tungsten target to produce a higher x-ray intensity than targets of molybdenum or chromium? Get solution
24. Use a computer to calculate Planck’s radiation law for a temperature of 3000 K, which is the temperature of a typical tungsten fi lament in an incandescent lightbulb. Plot the intensity versus wavelength. (a) How much of the power is in the visible region (400–700 nm) compared with the ultraviolet and infrared? (b) What is the ratio of the intensity at 400 nm and 700 nm to the wavelength with maximum intensity? Get solution
24q. List all possible known interactions between photons and electrons discussed in this chapter. Can you think of any more? Get solution
25. Show that the ultraviolet catastrophe is avoided for short wavelengths ...with Planck’s radiation law by calculating the limiting intensity ... as .... Get solution
25q. Discuss why it is difficult to see the Compton effect using visible light. Get solution
26. Estimate the power radiated by (a) a basketball at 20°C and (b) the human body (assume a temperature of 37°C). Get solution
26q. What do you believe to be an optimum lifetime for a positron-emitting radioactive nuclide used in brain tumor diagnostics? Explain. Get solution
27. At what wavelength is the radiation emitted by the human body at its maximum? Assume a temperature of 37°C. Get solution
28. If we have waves in a one-dimensional box, such that the wave displacement _(x, t) _ 0 for x _ 0 and x _ L, where L is the length of the box, and ... show that the solutions are of the from ... and a(t) satisfies the (harmonic-oscillator) equation ... where ...is the angular frequency 2 πf. Get solution
29. If the angular frequencies of waves in a three-dimensional box of sides L generalize to ... where all n are integers, show that the number of distinct states in the frequency interval f(=ω/2 π) to f + Δf is given by (where f is large) ... Get solution
30. Let the energy density in the frequency interval f to f + df within a blackbody at temperature T be dU(f, T). Show that the power emitted through a small hole of area ΔA in the container is ... Get solution
31. Derive the Planck radiation law emitted by a blackbody. Remember that light has two directions of polarization and treat the waves as an ensemble of harmonic oscillators. Get solution
32. An FM radio station of frequency 98.1 MHz puts out a signal of 50,000 W. How many photons/s are emitted? Get solution
33. How many photons/s are contained in a beam of electromagnetic radiation of total power 180 W if the source is (a) an AM radio station of 1100 kHz, (b) 8.0-nm x rays, and (c) 4.0-MeV gamma rays? Get solution
34. What is the threshold frequency for the photoelectric effect on lithium (Ø = 2.93 eV)? What is the stopping potential if the wavelength of the incident light is 380 nm? Get solution
35. What is the maximum wavelength of incident light that can produce photoelectrons from silver (Ø = 4.64 eV)? What will be the maximum kinetic energy of the photoelectrons if the wavelength is halved? Get solution
36. A 2.0-mW green laser (λ = 532 nm) shines on a cesium photocathode (φ = 1.95 eV). Assume an efficiency of 10-5 for producing photoelectrons (that is, one photoelectron produced for every 105 incident photons) and determine the photoelectric current. Get solution
37. An experimenter fi nds that no photoelectrons are emitted from tungsten unless the wavelength of light is less than 270 nm. Her experiment will require photoelectrons of maximum kinetic energy 2.0 eV. What frequency of light should be used to illuminate the tungsten? Get solution
38. The human eye is sensitive to a pulse of light containing as few as 100 photons. For orange light of wavelength 610 nm, how much energy is contained in the pulse? Get solution
39. In a photoelectric experiment it is found that a stopping potential of 1.00 V is needed to stop all the electrons when incident light of wavelength 260 nm is used and 2.30 V is needed for light of wavelength 207 nm. From these data determine Planck’s constant and the work function of the metal. Get solution
40. Find the wavelength of light incident on a tungsten target that will release electrons with a maximum speed of 1.4 × 106 m/s. Get solution
41. What is the minimum x-ray wavelength produced for a dental x-ray machine operated at 30 kV? Get solution
42. The Stanford Linear Accelerator can accelerate electrons to 50 GeV (50 × 109 eV). What is the minimum wavelength of photon it can produce by bremsstrahlung? Is this photon still called an x ray? Get solution
43. A cathode-ray tube in a scanning electron microscope operates at 25 keV. What is λmin for the continuous x-ray spectrum produced when the electrons hit the target? Get solution
44. Calculate λmin for all three elements shown in Figure 3.19. Use the value of the work function for tungsten in Table 3.3 and calculate the percentage error in neglecting the work function for the Duane-Hunt rule using the data of Figure 3.19. ... ... Get solution
45. The two peaks for the molybdenum spectra of Figure 3.19 are characteristic spectral lines for the molybdenum element. What is the minimum potential difference needed to accelerate electrons in an x-ray tube to produce both of these lines? ... Get solution
46. Calculate the maximum Δ λ/ λ of Compton scattering for blue light (λ = 480 nm). Could this be easily observed? Get solution
47. A photon having 40 keV scatters from a free electron at rest. What is the maximum energy that the electron can obtain? Get solution
48. If a 7.0-keV photon scatters from a free proton at rest, what is the change in the photon’s wavelength if the photon recoils at 90°? Get solution
49. Is it possible to have a scattering similar to Compton scattering from a proton in H2 gas? What would be the Compton wavelength for a proton? What energy photon would have this wavelength? Get solution
50. An instrument has resolution Δ λ/ λ = 0.40%. What wavelength of incident photons should be used in order to resolve the modified and unmodified scattered photons for scattering angles of (a) 30°, (b) 90°, and (c) 170°? Get solution
51. Derive the relation for the recoil kinetic energy of the electron and its recoil angle f in Compton scattering. Show that ... Get solution
52. A 650-keV gamma ray Compton-scatters from an electron. Find the energy of the photon scattered at 110°, the kinetic energy of the scattered electron, and the recoil angle of the electron. Get solution
53. A photon of wavelength 2.0 nm Compton-scatters from an electron at an angle of 90°. What is the modified wavelength and the fractional change, Δλ/ λ? Get solution
54. How much photon energy is required to produce a proton-antiproton pair? Where could such a high-energy photon come from? Get solution
55. What is the minimum photon energy needed to create an e- - e- pair when a photon collides (a) with a free electron at rest and (b) with a free proton at rest? Get solution
56g. What wavelength photons are needed to produce 30.0-keV electrons in Compton scattering? Get solution
57g. A typical person can detect light with a minimum intensity of 4.0 × 10-11 W/m2. For light of this intensity and λ = 550 nm, how many photons enter the eye each second if the pupil is open wide with a diameter of 9.0 mm? Get solution
58g. A copper wire carrying a high current glows “red hot” just before the wire melts at a temperature of 1085°C. (a) What is the peak wavelength of the emitted radiation? (b) Given your answer to part (a), how can the wire be “red hot”? Get solution
59g. The gravitational energy of Earth is approximately 0.5(GM 2 E /RE ) where ME is the mass of Earth. This is approximately the energy needed to blow the planet into small fragments (the size of asteroids). How large would an antimatter meteorite the density of nickeliron (ρ = 5 × 103 kg/m3) have to be in order to blow up Earth when it strikes? Compute the energy involved in the particle-antiparticle annihilation and compare it with the total energy in all the nuclear arsenals of the world [~5000 megatons (MT), where 1 MT = 4.2 × 1015 J]. Get solution
60g. Show that the maximum kinetic energy of the recoil electron in Compton scattering is given by ... At what angles θ and Ø does this occur? If we detect a scattered electron at Ø = 0° of 100 keV, what energy photon was scattered? Get solution
61g. Use the Wien displacement law to make a log-log plot of λmax (from 10-8 m to 10-2 m) versus temperature (from 100 K to 105 K). Mark on the plot the regions of visible, ultraviolet, infrared, and microwave wavelengths. Put the following points on the line: sun (5800 K), furnace (1900 K), room temperature (300 K), and the background radiation of the universe (2.7 K). Discuss the electromagnetic radiation that is emitted from each of these sources. Does it make sense? Get solution
62g. (a) What is the maximum possible energy for a Compton-backscattered x ray (θ = 180°)? Express your answer in terms of λ, the wavelength of the incoming photon. (b) Evaluate numerically when the incoming photon’s energy is 100 keV. Get solution
63g. The naked eye can detect a stellar object of sixth magnitude in the night sky. With binoculars, we can see an object of the ninth magnitude. The sun’s brightness at Earth is 1400 W/m2. The Hubble Space Telescope can detect an object of the 30th magnitude, which amounts to a brightness of about 2 × 10-20 W/m2. (a) Consider a detector in the Hubble Space Tele-scope with a collection area of 0.30 m2. If you assume hydrogen light of frequency 486 nm (blue-green), how many photons/s enter the telescope from a 30thmagnitude star? (b) An increase of magnitude one represents a decrease in brightness by a factor of 1001/5. Estimate how many photons/s from a sixth-magnitude star would enter your eye if the diameter of your pupil is 6.5 mm. Get solution
64g. Original data from Millikan’s pivotal photoelectric experiment that confirmed Einstein’s quantum explanation is shown in Figure 3.16 [from R. A. Millikan, Physical Review 7, 362 (1916)]. Sodium was the photocathode. Use the data to find the work function for sodium and Planck’s constant. Get solution
65g. A prototype laser weapon tested in 2010 used a laser with an infrared wavelength of 1.06 m, because the atmosphere is fairly transparent at that wavelength. The laser’s continuous output was 25 kW. How many photons per second were produced? Get solution
66g. A typical chemical reaction such as an explosive combustion releases about 5 MJ of energy per kg fuel used. At the sun’s current rate of energy production, how much time would the sun last at that rate? Compare your answer with the sun’s estimated lifetime of 10 billion years. Get solution
67g. The bright star Sirius A has a diameter 1.6 times the sun’s and surface temperature 9600 K. (a) What is the peak wavelength of radiation emitted from the surface? (Note: Sirius has a distinctive blue tint when viewed with the naked eye.) (b) Find the net power output from the surface of Sirius A and compare with that from the sun. Get solution
68g. In developing Equation (3.36), we argued that the recoiling nucleus could be ignored. Consider again the x-ray tube described in Example 3.15 with 35-keV electrons striking a tungsten target. Suppose an electron is deflected through a negligible angle and its kinetic energy drops to 30 keV in a scattering event with a nucleus. Assuming that the nucleus was initially at rest, use conservation of momentum to find the kinetic energy of the recoiling nucleus and comment on the result. ... Get solution
69g. The Fermi Gamma-ray Space Telescope, launched in 2008, can detect gamma rays with energies ranging from 10 keV to 300 MeV. For each of those energy extremes, fi nd the resulting kinetic energy and speed of an electron created by the gamma ray as part of an electron-positron pair. Assume that the electron has half of the gamma ray’s energy. Get solution
70g. Gamma-ray detectors like the one described in the preceding problem often use calorimetry to determine gamma-ray energies. Suppose a beam of 100-MeV gamma rays strikes a target with a mass of 2.5 kg and specific heat 430 J/(kg . K). How many gamma rays are needed to raise the target’s temperature by 10 mK? Get solution
