Ch 27 Answers

CHAPTER27 Quantum Theory KE ϭ ϪqV0 ϭ Ϫ(Ϫ1.60ϫ10Ϫ19 C)(3.2 J/C) ϭ 5.1ϫ10Ϫ19 J page 732 6. The threshold wavelength of zinc is 310 nm. Find the threshold frequency, in Hz, and the work function, in eV, of zinc. 3.00ϫ108 m/s c f0 ϭ ᎏᎏ ϭ ᎏᎏ ϭ 9.7ϫ1014 Hz Ϫ9 ␭0 310ϫ10 m Practice Problems 27.1 A Particle Model of Waves pages 723–734 page 730 1. An electron has an energy of 2.3 eV. What is the energy of the electron in joules? (2.3 eV)΂ᎏᎏ΃ ϭ 3.7ϫ10Ϫ19 J 2. What is the energy in eV of an electron with a velocity of 6.2ϫ106 m/s? 1 KE ϭ ᎏ mv 2 2 1 ϭ ΂ ᎏ ΃(9.11ϫ10Ϫ31 kg)(6.2ϫ106 m/s)2 2 1.60ϫ10Ϫ19 J 1 eV W ϭ hf0 ϭ (6.63ϫ10Ϫ34 J/Hz) (9.7ϫ1014 Hz)΂ ᎏᎏ Ϫ19 ΃ 1 eV 1.60ϫ10 J ϭ 4.0 eV 7. The work function for cesium is 1.96 eV. What is the kinetic energy, in eV, of photoelectrons ejected when 425-nm violet light falls on the cesium? 1240 eVиnm KEmax ϭ ᎏᎏ Ϫ hf0 ␭ 1240 eVиnm ϭ ᎏᎏ Ϫ 1.96 eV 425 nm ϭ (1.75ϫ10Ϫ17 J)΂ ᎏᎏ Ϫ19 ΃ 1 eV 1.60ϫ10 J ϭ 1.1ϫ102 eV 3. What is the velocity of the electron in problem 1? Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1 m ϭ 9.11ϫ10Ϫ31 kg, KE ϭ ᎏ mv 2 2 vϭ ϭ Ί๶ Ί๶๶ 2KE ᎏᎏ ϭ m (2)(3.7ϫ10Ϫ19 J) ᎏᎏ 9.11ϫ10Ϫ31 kg ϭ 0.960 eV 8. When a metal is illuminated with 193-nm ultraviolet radiation, electrons with energies of 3.5 eV are emitted. What is the work function of the metal? KE ϭ hf Ϫ hf0 hc hf0 ϭ hf Ϫ KE ϭ ᎏᎏ Ϫ KE ␭ 1240 eVиnm ϭ ᎏᎏ Ϫ KE ␭ 1240 eVиnm ϭ ᎏᎏ Ϫ 3.5 eV 193 nm 9.0ϫ105 m/s 4. The stopping potential for a photoelectric cell is 5.7 V. Calculate the maximum kinetic energy of the emitted photoelectrons in eV. KE ϭ ϪqV0 ϭ Ϫ(Ϫ1.60ϫ10Ϫ19 C)(5.7 J/C) ΂ 1 eV ᎏᎏ 1.60ϫ10Ϫ19 J ΃ ϭ 5.7 eV 5. The stopping potential required to prevent current through a photocell is 3.2 V. Calculate the maximum kinetic energy in joules of the photoelectrons as they are emitted. Physics: Principles and Problems ϭ 2.9 eV Solutions Manual 531 causing electrons to be ejected. Inc. If the incident photon does not have sufficient energy.50 eV. hc 1240 eVиnm E ϭ ᎏᎏ ϭ ᎏᎏ ϭ 6ϫ104 eV ␭ 0. A metal has a work function of 4.9 eV ␭ 650 nm Copyright © Glencoe/McGraw-Hill. emerges from the target. Explain whether this event is a result of the photoelectric effect or the Compton effect. The photoelectric effect is the emission of electrons from a metal sample when radiation of sufficient energy is incident on it.89 eV 15. Each incident photon interacts with a single electron.60ϫ10Ϫ19 C) (1. Photoelectric Effect Why is high-intensity. but no other radiation. highfrequency light can? Explain. and is scattered. a form of electromagnetic radiation.1 A Particle Model of Waves pages 723–734 page 734 10.50 eV 13. 12. which is the capture of a photon by an electron in matter and the transfer of the photon’s energy to the electron. whereas the total energy increases as T 4. Light. a division of The McGraw-Hill Companies. it cannot eject an electron.44 eV W ϭ Egreen light Ϫ KEejected electron ϭ 2. of the electron. in eV. estimate the energy.33 eV ␭ 532 nm Section Review 27. An electron. whereas high frequency light does. ␭0 ϭ ᎏᎏ ϭ 276 nm 4. 532 Solutions Manual KEejected electron ϭ ϪqV ϭ Ϫ(Ϫ1. Energy of a Photon What is the energy.Chapter 27 continued 9. whereas low-intensity. Because energy is directly related to frequency. If the X ray has a wavelength of approximately 0.50 eV.33 eV Ϫ 1. of the photons produced by a laser pointer having a 650-nm wavelength? hc 1240 eVиnm E ϭ ᎏᎏ ϭ ᎏᎏ ϭ 1. in eV.44 eV ϭ 0. yet it does have kinetic energy. Photoelectric and Compton Effects Distinguish the photoelectric effect from the Compton effect. of the metal? hc 1240 eVиnm Egreen light ϭ ᎏᎏ ϭ ᎏᎏ ϭ 2. is quantized and massless. collides with an electron. The ejected electrons can be stopped by a potential of 1.60ϫ10Ϫ19 J ΃ ϭ 1. Frequency and Energy of Hot-Body Radiation As the temperature of a body is increased. low frequency light does not have sufficient energy to eject an electron. Photoelectric Effect An X ray is absorbed in a bone and releases an electron. Compton Effect An X ray strikes a bone.44 V. What is the longest-wavelength radiation that will cause it to emit photoelectrons? hc hf0 ϭ 4. How does the wavelength of the scattered X ray compare to the wavelength of the incoming X ray? Physics: Principles and Problems . Photoelectric Effect Green light (␭ ϭ 532 nm) strikes an unknown metal. low-frequency light unable to eject electrons from a metal. Photoelectric and Compton Effects An experimenter sends an X ray into a target.02 nm 17.44 J/C) 1 eV ΂ ᎏᎏ 1. in eV. It is a result of the photoelectric effect. resulting in a photon of lower energy and momentum. 16. What is the work function. The peak frequency increases as T. 11. so ᎏᎏ ϭ 4. The Compton effect is the scattering of a photon by matter. 14. how does the frequency of peak intensity change? How does the total amount of radiated energy change? Both frequency of peak intensity and total energy radiated increase.50 eV ␭0 1240 eVиnm Thus.02 nm. 60 ϫ10Ϫ19 J ΃ Ϫ34 ϭ 1. in eV.5 eV. 22.2ϫ10Ϫ2 eV Section Review 27. Inc. Would this proton gain as much energy from the collision as the electron does? Would the photon lose as much energy as it does when it collides with the electron? The answer to both questions is no.5 V.125-nm wavelength? h h ␭ ϭ ᎏᎏ. vϭ (2)(1. What is the kinetic energy.0 kg)(8. causing the electrons to form a diffraction pattern. 18.125ϫ10Ϫ9 m ΃ ᎏᎏ (2)(9. so it would have to be accelerated through 96. A 7. 20. is h 1 1 h KE ϭ ᎏᎏmv 2 ϭ ᎏᎏm΂ᎏᎏ΃ ϭ ᎏ 2 2 2 m␭ 2m␭ 2 Practice Problems 27.5 m/s) Jиs) (6. The electron in Example Problem 3 has a de Broglie wavelength of 0. a.Chapter 27 continued The scattered X ray has a longer wavelength than the incoming X ray. so 2 ϭ 4.7ϫ10Ϫ11 m Physics: Principles and Problems Solutions Manual 533 .63ϫ10 ϭ ᎏᎏᎏᎏᎏ Ϫ27 Ϫ9 2 (2)(1. Wavelike Properties Describe the experiment that confirmed that particles have wavelike properties.63ϫ10Ϫ34 Jиs ␭ ϭ ᎏ ϭ ᎏᎏ mv (7.14 nm.60ϫ10Ϫ19 J ΃ ϭ 96. What is the de Broglie wavelength of the bowling ball? Copyright © Glencoe/McGraw-Hill. of a proton (m ϭ 1. What is the de Broglie wavelength and speed of an electron accelerated by a potential difference of 250 V? 1 ᎏᎏmv 2 ϭ qV.67ϫ10 kg)(0.67ϫ10Ϫ27 kg) with the same wavelength? The de Broglie wavelength is ␭ ϭ ᎏᎏ so the velocity is v ϭ ᎏᎏ The kinetic energy.14ϫ10 m) 1 eV ᎏᎏ ΂ 1. a division of The McGraw-Hill Companies.11ϫ10Ϫ31 kg) Ϫ34 h 2 ᎏᎏ 1 eV ϭ (1.4ϫ106 m/s h ␭ ϭ ᎏᎏ mv 6. the crystal acted like a diffraction grating.2 Matter Waves pages 735–737 page 736 19. 21.4ϫ10 m/s) Ϫ34 ϭ 7. then.11ϫ10 kg m Ϫ19 Ϫ31 ϭ 9. Critical Thinking Imagine that the collision of two billiard balls models the interaction of a photon and an electron during the Compton effect. The diffraction of the electrons (particles) is similar to the diffraction of light (waves) through a grating.63ϫ10 Jиs ϭ ᎏᎏᎏᎏ Ϫ31 6 (9. Suppose the electron is replaced by a much more massive proton.1ϫ10Ϫ35 m b. A tennis ball can transfer more kinetic energy to a softball than it can to a bowling ball. h m␭ 2 h mv 2 h 6.544ϫ10Ϫ17 J)΂ ᎏᎏ 1. so p ϭ ᎏᎏ p ␭ ΂␭΃ p2 1 KE ϭ ᎏᎏmv 2 ϭ ᎏ ϭ ᎏ 2m 2m 2 ϭ 6. When a beam of electrons was aimed at a crystal. Why does the bowling ball exhibit no observable wave behavior? The wavelength is too small to show observable effects.0-kg bowling ball rolls with a velocity of 8.60ϫ10 C)(250 J/C) 2qV ᎏᎏᎏᎏ ᎏ ϭ Ί๶๶ Ίᎏ ๶ 9.11ϫ10 kg)(9.2 Matter Waves pages 735–737 page 737 23. What voltage is needed to accelerate an electron so it has a 0.63ϫ10 Jиs ᎏ ΂ᎏ 0.5 m/s. Incandescent Light An incandescent lightbulb is controlled by a dimmer. ␭ ϭ d sin ␪. If we assume sin ␪ is around 0. you cannot be sure which of the slits 534 Solutions Manual Chapter Assessment Concept Mapping page 742 29.1. Atoms passing through the grating produce an interference pattern.04ϫ10Ϫ24 kgиm/s h 6. 25. resulting in the distribution of photons or atoms seen in the interference pattern. Because of the unknown momentum. Copyright © Glencoe/McGraw-Hill. Wave Nature Explain why the wave nature of matter is not obvious. Complete the following concept map using these terms: dual nature. mass. momentum.04ϫ10 kgиm/s Ϫ34 ϭ 1.63ϫ106 m/s p ϭ mv ϭ (9. Wavelengths of Matter and Radiation When an electron collides with a massive particle. dual nature wave properties particle properties interference diffraction mass momentum Mastering Concepts page 742 30. then the de Broglie wavelength is a few tens of nanometers. Note.1) The light becomes redder. Heisenberg Uncertainty Principle When light or a beam of atoms passes through a double slit. The wavelengths of most objects are much too small to be detected. the electron’s velocity and wavelength decrease.11ϫ10 kg Ϫ19 Ϫ31 the beam passed through.Chapter 27 continued 24. diffraction. then. The photon still travels at c. How does the Heisenberg uncertainty principle explain this? The Heisenberg uncertainty principle states that you cannot simultaneously know the precise position and momentum of a particle. How is it possible to increase the wavelength of a photon? If the photon undergoes Compton scattering with a fixed target.11ϫ10Ϫ31 kg)(6.63ϫ10 Jиs ␭ ϭ ᎏ ϭ ᎏᎏᎏ Ϫ24 p 6. The de Broglie wavelength. Both results occur even when atoms or photons pass through the slits one at a time. an interference pattern forms. however. and ␪ is the angular separation between consecutive peaks.63ϫ106 m/s) ϭ 6. Critical Thinking Physicists recently made a diffraction grating of standing waves of light. what was the approximate de Broglie wavelength of the atoms? For diffraction gratings. if you know the precise position of a photon or an atom as it passes through the slit. 28. you cannot know its precise momentum. where d is the spacing of the slits. that the photon’s speed is not changed. De Broglie Wavelength What is the de Broglie wavelength of an electron accelerated through a potential difference of 125 V? vϭ Ϫ2qV ᎏ Ίᎏ ๶ m C)(125 V) Ϫ2(Ϫ1. a division of The McGraw-Hill Companies. 27.10ϫ10Ϫ10 m ϭ 0. is ␭ ϭ (250 nm) sin ␪. What happens to the color of the light given off by the bulb as the dimmer control is turned down? (27. Physics: Principles and Problems .110 nm 26. Thus. Inc.60ϫ10 ᎏᎏᎏᎏ ϭ Ί๶๶ 9. If the spacing of the slits in the grating were ᎏᎏ␭ (about 250 nm). 1 2 ϭ 6. wave properties. the wavelength of the photon will increase. 2) a. This result is incorrect because massless photons have nonzero momenta. c. wavelength Scatter electrons off a crystal and measure the angles of diffraction. mass Balance the force of an electric field against that of a magnetic field to find m/q. wavelength Measure the angle of diffraction when light passes through two slits Solutions Manual Copyright © Glencoe/McGraw-Hill. (27. 32. Light with greater intensity contains more photons per second.1) Red photons do not have enough energy to cause the chemical reaction that exposes film. 535 . the photons are still unable to eject an electron. 40.2) No. The momentum. a division of The McGraw-Hill Companies. 35. (27.1) a photon 34. Explain this on the basis of the photon theory of light.Chapter 27 continued 31. What is quantized in Max Planck’s interpretation of the radiation of incandescent bodies? (27. using the equation yields a photon momentum of zero because photons are massless. If the intensity of the light increases. Inc. thus. Explain how each of the following electron properties could be measured. c. 33. (27. b. 39. Explain how Einstein’s theory accounts for the fact that light below the threshold frequency of a metal produces no photoelectrons. 36. or measure the KE of the electrons ejected from a known metal at only one wavelength.1) Quantized energy means that energy can exist only in multiples of some minimum value. charge Balance the force of gravity against the force of an electric field on the charge. momentum Measure the change in wavelength of X rays scattered by matter. How does the Compton effect demonstrate that photons have momentum as well as energy? (27. Physics: Principles and Problems 37.2) a. Light above the threshold frequency shines on the metal cathode in a photocell. Explain how each of the following photon properties could be measured. b. of a particle of matter is given by p ϭ mv. (27. it causes the ejection of more photoelectrons per second. they can be developed in a darkroom that is illuminated by red light. regardless of the intensity of the light.1) The vibrational energy of the incandescent atoms is quantized.1) Elastic collisions transfer both momentum and energy. Only if photons have momentum can the equations be satisfied. then use the measured value of q. Photographic Film Because certain types of black-and-white film are not sensitive to red light. Can you calculate the momentum of a photon using the same equation? Explain. What is a quantum of light called? (27. Explain the concept of quantized energy.1) Each photon ejects a photoelectron. the number of photons increases but their energy does not. (27. (27. the current of photoelectrons increases? (27. p. energy Measure the KE of the electrons ejected from a metal for at least two different wavelengths.1) Photons below the threshold frequency do not have sufficient energy to eject an electron. 38. How does Einstein’s photoelectric effect theory explain the fact that as the light intensity increases. One glows dark red. how does the frequency of vibration of an atom change if it gives off 5. Inc. tungsten has the higher threshold frequency. whereas tungsten emits photoelectrons when struck by ultraviolet radiation. so 5.2. or measure the angle the light is bent when it passes through a prism. assuming that both frequencies are above the threshold frequency? Not necessarily.44ϫ10 J E f ϭ ᎏᎏ ϭ ᎏᎏᎏ Ϫ34 nh (1)(6. Which bar is hotter? the rod glowing bright orange b. 5800 K: ~3. 8000 K: ~4. an increase by a factor of slightly greater than 18.8ϫ10Ϫ19 J? Physics: Principles and Problems . Thus.5 to 9. whereas the de Broglie wavelength is 10–34 m. a.1 A Particle Model of Waves page 742–743 Level 1 46. a division of The McGraw-Hill Companies. Mastering Problems 27.6ϫ1014 Hz b.21ϫ1014 Hz 47.63ϫ10 Jиs) Ϫ19 ϭ 8. a.10 m.5ϫ1014 Hz. 44. What potential difference is needed to stop electrons with a maximum kinetic energy of 4. the number of ejected electrons is proportional to the number 536 Solutions Manual 0. Potassium emits photoelectrons when struck by blue light.10 m 21 m/s ■ Figure 27-11 Copyright © Glencoe/McGraw-Hill. of incident photons or the brightness of the light. Will high-frequency light eject a greater number of electrons from a photosensitive surface than low-frequency light. By what factor does the intensity of the red light given off change as the body’s temperature increases from 4000 K to 8000 K? The intensity in the red portion of the spectrum increases from approximately 0.44ϫ10Ϫ19 J while changing its value of n by 1? E ϭ nhf . Which bar is radiating more energy? the rod glowing bright orange 43. a. while the other glows bright orange. Two iron bars are held in a fire. Use the emission spectrum of an incandescent body at three different temperatures shown in Figure 27-1 on page 724 to answer the following questions.Chapter 27 continued or a diffraction grating. 42. Which metal has a larger work function? tungsten 45. the baseball is about 1033 times larger than the wavelength. The diameter of the baseball is about 0. Applying Concepts page 742 41. not the frequency of the light. Compare the de Broglie wavelength of the baseball shown in Figure 27-11 with the diameter of the baseball.5ϫ1014 Hz. measure the width of a single-slit diffraction pattern. What can you conclude about the relationship between the frequency of peak radiation emission intensity and temperature for an incandescent body? The frequency of the peak intensity increases with increasing temperature. At what frequency does the peak emission intensity occur for each of the three temperatures? 4000 K: ~2. According to Planck’s theory. c. b. Which metal has a higher threshold frequency? Blue light has a lower frequency and energy than UV light. how large an area of converters would produce the energy needed by the home? Solutions Manual ϭ (6. a.4ϫ1014 Hz) ϭ 2. In many parts of the United States.0 V V0 ϭ ᎏᎏ ϭ ᎏᎏᎏ Ϫ19 Ϫq Ϫ(Ϫ1. Inc.00ϫ1014 Hz΃ ΂ ᎏᎏ 6.7ϫ10Ϫ27 kgиm/s Level 2 49.0 eV 1. What is the maximum kinetic energy of the photoelectrons in the following units? Cathode Anode ؉ ■ 5. Solar Energy A home uses about 4ϫ1011 J of energy each year.4ϫ1014 Hz.63ϫ10Ϫ34 J/Hz)(4.07ϫ10Ϫ19 J Physics: Principles and Problems 537 . The stopping potential of a certain metal is shown in Figure 27-12.9ϫ10Ϫ19 J 52.00ϫ1015 Hz Ϫ 4.63ϫ10Ϫ34 Jиs) 3. so C 4. so E ϭ (1000 J/m2иs)΂ ᎏ ΃΂ ᎏ ΃ 3600 s h 3000 h y ϭ 8.0 V ؊ Figure 27-12 a.8ϫ10 KE ϭ 3. If light with a frequency of 1.Chapter 27 continued KE ϭ ϪqV0. How much energy from the Sun falls on one square meter each year? Earth receives about 1000 J/m2 each second.0 eV b.50ϫ10Ϫ7 m 8 ϭ 1.0ϫ102 nm? 6.0ϫ10 Ϫ19 J 50.60ϫ10 J ᎏ ᎏ ᎏ΃ ΂ᎏ 1 ΃΂ 1 eV Ϫ19 ϭ 1. What is the momentum of a photon of violet light that has a wavelength of 4. joules 5.63ϫ10Ϫ34 Jиs h p ϭ ᎏᎏ ϭ ᎏᎏ 4. KE ϭ ϪqV0 ϭ Ϫ(Ϫ1 elementary charge)(5.4ϫ1014 Hz) ϭ 3.8 eV 54.60ϫ10 C) Ϫ19 51.00ϫ1014 Hz. The threshold frequency of sodium is 4. there are about 3000 h of sunlight each year. What should be the work function of the cathode if the photocell is to be sensitive to red light (␭ ϭ 680 nm) as well as to the other colors of light? 1240 eVиnm 1240 eVиnm W ϭ ᎏᎏ ϭ ᎏᎏ ␭0 680 nm 48. What is the maximum kinetic energy of an ejected photoelectron if the metal is illuminated by light with a wavelength of 6. what is the maximum kinetic energy of the photoelectrons? KE ϭ hf Ϫ hf0 ϭ h(f Ϫ f0) ϭ (6.0ϫ10Ϫ7 m ␭ ϭ 1. Light Meter A photographer’s light meter uses a photocell to measure the light falling on the subject to be photographed.00ϫ10 m/s Ϫ 3.0 V) ϭ 5.00ϫ1015 Hz falls on the sodium in the previous problem.50ϫ102 nm? KE ϭ hf Ϫ hf0 ϭ h ΂ᎏᎏ Ϫ f0΃ ␭ c ϭ 1ϫ1010 J/m2 per year b. If this solar energy can be converted to useful energy with an efficiency of 20 percent. a division of The McGraw-Hill Companies. electron volts Copyright © Glencoe/McGraw-Hill.63ϫ10Ϫ34 J/Hz) (1. The threshold frequency of a certain metal is 3. How much work must be done to free an electron from the surface of sodium? Work ϭ hf0 ϭ (6.7ϫ10Ϫ19 J Level 3 53. 8ϫ10Ϫ10 m 59.63ϫ10 Jиs ϭ ᎏᎏᎏᎏ Ϫ27 3 (1. What is the velocity of the electron? 1 ᎏᎏmv 2 ϭ qV 2 1 KE ϭ ᎏ mv 2 2 vϭ ϭ 2KE ᎏ Ίᎏ ๶ m JրeV) (2)(13.0ϫ10Ϫ21 J 1 ϭ ᎏ mv 2 2 1. a division of The McGraw-Hill Companies. The kinetic energy of a hydrogen atom’s electron is 13.0ϫ106 m/s? h ␭ϭ ᎏ mv 6.4ϫ10Ϫ10 m ϭ 0.2 Matter Waves page 743 Level 1 55. What is the wavelength associated with the electron? h ␭ϭ ᎏ mv ϭ 0.60ϫ10 ᎏᎏᎏᎏ Ί๶๶๶ 9. a. What is the de Broglie wavelength of an electron moving at 3.0ϫ10Ϫ10 m? h ␭ ϭ ᎏᎏ mv h v ϭ ᎏᎏ m␭ J/Hz 6.0ϫ10 m) Ϫ34 (2)(4. ϭ 2.11ϫ10 kg)(4. A cathode-ray tube accelerates an electron from rest across a potential difference of 5. C ϭ 2␲r 538 Solutions Manual Physics: Principles and Problems .67ϫ10 Ϫ34 kg)(2.0ϫ106 m/s) ϭ 1. Calculate the electron’s de Broglie wavelength.11ϫ10 kg)(2.65 eV)(1.19ϫ10 m/s) Ϫ34 vϭ ᎏ Ί๶ qV 1 ᎏ ᎏm 2 vϭ ᎏ ᎏ ᎏ ᎏ Ί๶๶ ΂ ΃ (1.67ϫ10 kg Ϫ21 Ϫ27 ϭ 2.24 nm 56.60ϫ10Ϫ19 C)(5. h ␭ϭ ᎏ mv 6.65 eV. Find the velocity of the electron.2ϫ10 m/s) Ϫ34 ϭ 2ϫ102 m2 27.19ϫ106 m/s b.519 nm.Chapter 27 continued 4ϫ10 J Area ϭ ᎏᎏᎏ 10 2 (0.332 nm c.63ϫ10 ϭ ᎏᎏᎏᎏ Ϫ31 7 (9.7ϫ10Ϫ11 m ϭ 0.017 nm 58.11ϫ10 kg Ϫ19 Ϫ31 ϭ 2.2ϫ103 m/s b. a.63ϫ10Ϫ34 Jиs ϭ ᎏᎏᎏᎏ (9.0ϫ103 V.11ϫ10 kg)(3.63ϫ10 kgиm/s ϭ ᎏᎏᎏᎏ Ϫ31 6 (9. What is the velocity of the neutron? KE ϭ (0. h ␭ϭ ᎏ mv 6. Find the de Broglie wavelength of the neutron. calculate the circumference of a hydrogen atom and compare it with the de Broglie wavelength for the atom’s electron. Inc. Copyright © Glencoe/McGraw-Hill.025 eV.11ϫ10Ϫ31 kg)(3.11ϫ10Ϫ31 kg) 2 ϭ 4.2ϫ10 m/s) ϭ 1.0ϫ103 V) 1 ᎏᎏ (9.2)(1ϫ10 J/m ) 11 J/Hz 6.2ϫ107 m/s b. Given that a hydrogen atom’s radius is 0. What velocity would an electron need to have a de Broglie wavelength of 3.4ϫ106 m/s Level 2 57. A neutron is held in a trap with a kinetic energy of only 0. a.0ϫ10 J) 2KE ᎏϭ ᎏᎏ Ίᎏ ๶ Ί๶๶ m 1.025 eV)΂ ᎏᎏ ΃ ϭ 4.60ϫ10Ϫ19 J eV vϭ ϭ 2.63ϫ10 ϭ ᎏᎏᎏᎏ Ϫ31 Ϫ10 (9. the kinetic energy is KE ϭ qV. If a proton has a de Broglie wavelength of 0.63ϫ10 Jиs) ϭ ᎏᎏᎏᎏᎏᎏ Ϫ31 Ϫ19 Ϫ9 (2)(9.519 nm) ϭ 3.8 V? KE ϭ ϪqV0 ϭ Ϫ(Ϫ1 elementary charge)(3.26 nm The circumference is approximately equal to ten complete wavelengths.18 nm.63ϫ10Ϫ34 J/Hz)(8. Inc.60ϫ10 C)(0.67ϫ10 kg)(1. Combining these and solving for voltage. An electron has a de Broglie wavelength of 0. h Vϭ ᎏ 2 2mq␭ (6.18ϫ10 Ϫ34 2 2 ϭ 47 V b. What is the maximum kinetic energy of photoelectrons ejected from a metal that has a stopping potential of 3. the voltage is h Vϭ ᎏ 2 2mq␭ (6. m␭ The kinetic energy. Level 3 60. is 1 KE ϭ ᎏ mv 2 2 1 h ϭ ᎏ m΂ᎏᎏ΃ 2 m␭ h ϭ ᎏ 2 2m␭ 2 2 In terms of voltage.63ϫ10 Jиs) ϭ ᎏᎏᎏᎏᎏᎏ Ϫ27 Ϫ19 Ϫ9 2 (2)(1.0ϫ1014 Hz) ϭ 5.0ϫ1014 Hz.18ϫ10 m) Ϫ34 2 2 ϭ 0. a division of The McGraw-Hill Companies.11ϫ10 kg)(1.8 eV 62. Using the same derivation as before.60ϫ10 C)(0. The threshold frequency of a certain metal is 8. mv h which gives a velocity of v ϭ ᎏ .3ϫ10Ϫ19 J Physics: Principles and Problems Solutions Manual 539 .025 V Mixed Review page 743–744 Level 1 61.Chapter 27 continued ϭ (2␲)(0. then. a. What is the work function of the metal? W ϭ hf0 ϭ (6.8 V) ϭ 3. how large is the potential difference that it experienced if it started from rest? Copyright © Glencoe/McGraw-Hill. How large a potential difference did it experience if it started from rest? h The de Broglie wavelength is ␭ ϭ ᎏ .18 nm. 3ϫ10Ϫ19 J 64.6 eV 66. so ␭0 hc ␭0 ϭ ᎏ 2.6ϫ1015 Hz falls on the metal in the previous problem.3ϫ10Ϫ27 kg that moves with a speed of 2. h ␭ϭ ᎏ mv 6.0ϫ10 m) Ϫ34 h mv ϭ 1.7 eV ␭ ␭0 150 nm ϭ 3.7 eV.01ϫ10Ϫ7 m ϭ 501 nm 67. a.82ϫ103 m/s ϭ 8. The work function of iron is 4. a division of The McGraw-Hill Companies.3ϫ10 kg)(2.0 nm? h The de Broglie wavelength is ␭ ϭ ᎏᎏ.43ϫ10Ϫ6 eV 68.0ϫ10Ϫ12 m b.60ϫ10Ϫ19 J (2. If light with a frequency of 1.48 eV ϭ hf0 ϭ ᎏᎏ. What is the longest wavelength of light that will cause electrons to be emitted from barium? hc Work function ϭ 2.48 eV. what is the maximum kinetic energy of the photoelectrons? KE ϭ hf Ϫ hf0 ϭ (6.3ϫ10Ϫ19 J ϭ 5. What energy in eV has to be given to an electron for it to have a de Broglie wavelength of 20.Chapter 27 continued 63.11ϫ10 kg)(400.5ϫ10 m/s) Ϫ34 ϭ ᎏᎏᎏ 1.48 eV The kinetic energy. An electron has a de Broglie wavelength of 400.60ϫ10Ϫ19 J ΃ ϭ 9.00ϫ108 m/s) ϭ 5.11ϫ10 kg)(20. 1 KE ϭ ᎏᎏmv 2 2 Level 2 65. What is the threshold wavelength of iron? hc 1240 eVиnm W ϭ ᎏᎏ ϭ ᎏᎏ ␭0 ␭0 1240 eVиnm 1240 eVиnm ␭0 ϭ ᎏᎏ ϭ ᎏᎏ W 4.77ϫ10Ϫ3 eV 540 Solutions Manual Physics: Principles and Problems . then.48 eV)΂ᎏ ᎏ΃ 1 eV (6. What is the maximum kinetic energy of the ejected electrons in eV? hc hc 1240 eVиnm KE ϭ ᎏᎏ Ϫ ᎏᎏ ϭ ᎏᎏ Ϫ 4. Find the velocity of the electron.63ϫ10Ϫ34 Jиs)2 (2)(9.0ϫ10 ϭ 3. the shortest wavelength of visible light.63ϫ10Ϫ34 J/Hz)(1.5ϫ104 m/s.82ϫ103 m/s)2 1 2 eV ΂ ᎏᎏ 1.63ϫ10Ϫ34 Jиs)(3. Iron is exposed to radiation of wavelength 150 nm. Calculate the energy of the electron in eV. is KE ϭ ᎏᎏmv 2 ϭ ᎏᎏm΂ᎏᎏ΃ 1 2 h ϭ ᎏ 2 2m␭ 2 1 2 h 2 m␭ ϭ ΂ ᎏᎏᎏᎏᎏ Ϫ31 Ϫ9 2΃ m) 1 eV ΂ ᎏᎏ 1.63ϫ10 Jиs ϭ ᎏᎏᎏᎏ Ϫ27 4 (3.11ϫ10Ϫ31 kg)(1.6ϫ102 nm b. h which gives a velocity of v ϭ ᎏᎏ.0 nm.7 eV ϭ ΂ᎏᎏ΃(9. Barium has a work function of 2.6ϫ1015 Hz) Ϫ 5. Inc. m␭ mv Copyright © Glencoe/McGraw-Hill. Find the de Broglie wavelength of a deuteron (nucleus of 2H isotope) of mass 3. a.60ϫ10Ϫ19 J ΃ (6. Electron Microscope An electron microscope is useful because the de Broglie wavelengths of electrons can be made smaller than the wavelength of visible light.63ϫ10 ϭ ᎏᎏᎏᎏ Ϫ31 Ϫ9 (9. ␭ ϭ ᎏᎏ h v ϭ ᎏᎏ m␭ J/Hz 6. ϭ 2. 2ϫ10 Hz b. Cathode Anode Thinking Critically page 744 70.14ϫ10Ϫ19 J b.5 mW (equivalent to 5ϫ10Ϫ4 J/s). How many photons are emitted each second by the laser? P 5ϫ10 J/s n ϭ ᎏᎏ ϭ ᎏᎏᎏ Ϫ19 E 3. A typical small laser has a power of 0. Apply Concepts A helium-neon laser emits photons with a wavelength of 632. that enters the person’s eye? Power ϭ (intensity)(area) ϭ (intensity)(␲r 2) ϭ (1.00ϫ108 m/s c ϭ 2.5ϫ10Ϫ7 m ␭ ϭ ᎏᎏ ϭ ᎏᎏ 15 f 1. Each photon has energy hc E ϭ ᎏᎏ ␭ ␭ ϭ 167 nm (6.63ϫ10 ϭ ᎏᎏᎏᎏ Ϫ Ϫ9 167ϫ10 m Ϫ34 8 ϭ 2ϫ1015 photons/s 71.60ϫ10 Figure 27-14 a.0ϫ10Ϫ19 J c.5ϫ10Ϫ11 W/m2) (␲ (3. What is the threshold wavelength of tin? c ϭ ␭f 3. What is the work function of tin? W ϭ hf0 ϭ (6.2ϫ1015 Hz) ϭ 8. as shown in Figure 27-14. What is the kinetic energy of the ejected electrons in eV? hc KEmax ϭ ᎏᎏ Ϫ hf0 ␭ J/Hz)(3.Chapter 27 continued Level 3 69. Apply Concepts Just barely visible light with an intensity of 1.63ϫ10 Jиs)(3.9ϫ10Ϫ19 J)΂ ᎏᎏ Ϫ19 ΃ ϭ 2.5ϫ10Ϫ11 W/m2 enters a person’s eye.2ϫ1015 Hz. in joules.4 eV 1 eV 1.9ϫ10Ϫ19 J J Pupil (diameter ϭ 7.00ϫ10 m/s) (6. Find the energy. a. of each photon emitted by the laser.0 mm) ■ (3. Inc. If this light shines into the person’s eye and passes through the person’s pupil. Incident radiation falls on tin. ␭ ϭ 550 nm Lens 8. a division of The McGraw-Hill Companies. in watts. what is the power. The threshold frequency of tin is 1. as shown in Figure 27-13.63ϫ10Ϫ34 J/Hz)(1.14ϫ10 J/photon Ϫ4 Figure 27-13 a.0ϫ10Ϫ19 J ϭ 3.8ϫ10 m ؊ Ϫ34 8 ؉ ■ ϭ 3.8 nm.5ϫ10Ϫ3 m)2) ϭ 5. The incident electromagnetic radiation has a wavelength of 167 nm.00ϫ10 m/s) ϭ ᎏᎏᎏᎏ Ϫ9 632.8ϫ10Ϫ16 W Physics: Principles and Problems Solutions Manual 541 . Cornea Copyright © Glencoe/McGraw-Hill. 0ϫ10Ϫ7 C experiences a force of 9. From the slope and intercept of the line. ϭ 1600 photons/s 72. Plot the data (stopping potential versus frequency) and use your calculator to draw the best-fit straight line (regression line).63ϫ10Ϫ34 J/Hz) h ᎏ ϭ ᎏᎏᎏ (1.18ϫ10Ϫ15 V/Hz ϭ 4.60ϫ10Ϫ19 C) e q q d ϭ 4. What is the magnitude of the second charge? (Chapter 20) A B FϭKᎏ 2 Convert wavelength to frequency and plot.15 m Copyright © Glencoe/McGraw-Hill. find the work function. which gives a c threshold wavelength of ␭0 ϭ ᎏ ᎏ ϭ f0 3.18ϫ10Ϫ15 J/HzиC The accepted value is (6. a division of The McGraw-Hill Companies. the lower the speed of sound and the flatter the pitch of the sound produced. as shown in Table 27-1. the threshold frequency is f0 ϭ 4.99ϫ1014 Hz function of W ϭ hf0 ϭ (6. Table 27-1 Stopping Potential v.31ϫ10Ϫ19 J ϭ 3. the threshold wavelength. Energy per photon hc Eϭ ᎏ ␭ (6.20 2. Wavelength ␭ (nm) 200 300 400 500 600 V0 (eV) 4. Why? (Chapter 15) Answer: The pitch of a wind instrument depends on the speed of sound in the air within it. Nano-formed metallic grids were used as a diffraction grating.99ϫ1014 Hz. As of 2003. The spring in a pogo stick is compressed 15 cm when a child who weighs 400.03 Cumulative Review page 744 74.8ϫ10Ϫ16 J/s n ϭ ᎏ ϭ ᎏᎏᎏ E 3. the largest is a buckyball. A charge of 8. Determine the best straight line through the data. ϭ 3ϫ103 N/m 75. Inc. Research the most massive particle for which interference effects have been seen.02 m from a second charge. Slope ϭ 4. Use the given wavelength of the incident light and information provided in Figure 27-14 to calculate the number of photons per second entering the eye.41 0.63ϫ10Ϫ34 J/Hz)(4. The photocell had a sodium cathode. 76. and the value of h/q from this experiment. Describe the experiment and how the interference was created.06 1.0 N when placed 0.14ϫ10Ϫ15 J/HzиC 542 Solutions Manual qB ϭ ᎏᎏ Physics: Principles and Problems Fd 2 KqA .05 0. A marching band sounds flat as it plays on a very cold day.Chapter 27 continued b.00ϫ108 m/s ᎏᎏ ϭ 601 nm and a work 4. What is the spring constant of the spring? (Chapter 14) F ϭ kx 400 N F k ϭ ᎏ ᎏ ϭ ᎏᎏ x 0. a C60 molecule.63ϫ10 Jиs)(3.00ϫ10 m/s) ϭ ᎏᎏᎏᎏ Ϫ9 550ϫ10 m Ϫ34 8 From the graph. Compare the value of h/q to the accepted value.99ϫ1014 Hz) ϭ 3.62ϫ10Ϫ19 J/photon Writing in Physics page 744 73.0 N stands on it.62ϫ10Ϫ19 J P 5. Make and Use Graphs A student completed a photoelectric-effect experiment and recorded the stopping potential as a function of wavelength. The colder the air. 5ϫ10Ϫ7 J 2. Mass ϭ 5.6ϫ1011 steps 3. where the energy of the vibrations is given by the equation E ϭ nhf.3ϫ10Ϫ19 J 3.2-m wire is 1. Each light set has 24 bulbs connected in series. A homeowner buys a dozen identical 120-V light sets. a division of The McGraw-Hill Companies.0 g Maximum velocity ϭ 1.0ϫ1014 Hz) ϭ 3.0 cm/s. How much current is in the wire? (Chapter 24) F ϭ BIL 1.3ϫ10Ϫ19 J/step ΂ ΃ ϭ 1.63ϫ10Ϫ34 J/Hz)(5.1ϫ10Ϫ3 N.0 N)(0. The force on a 1.0ϫ101 A 78.5ϫ10Ϫ7 J ᎏᎏᎏ ϭ 7.0 cm/s Physics: Principles and Problems Solutions Manual 543 .Chapter 27 continued (9.0 ⍀) ϭ 2. Find the maximum kinetic energy of the vibrating object.0 ⍀.0ϫ1014 Hz. Calculate the total load in amperes if the homeowner operates all the sets from a single exterior outlet. Determine the number of equally sized energy-step reductions that the object would have to make in order to lose all of its energy. Challenge Problem page 731 Suppose a nickel with a mass of 5.1ϫ10 N F I ϭ ᎏᎏ ϭ ᎏᎏᎏ ϭ 2ϫ101 A Ϫ5 BL (5ϫ10 T)(1. (Chapter 23) Itotal ϭ 12Iset ϭ (12)΂ ᎏ ΃ V 24R 120 V ϭ (12) ᎏᎏ (24)(6. The maximum velocity of the nickel during the oscillations is 1. If the energy is emitted in a single step.0ϫ10Ϫ3 kg)(1. The vibrating object emits energy in the form of light with a frequency of 5. The wire is perpendicular to Earth’s magnetic field. E ϭ hf ϭ (6.0ϫ10Ϫ2 m/s)2 2 ϭ 5ϫ10Ϫ7 C 77. Assume that the vibrating nickel models the quantum vibrations of the electrons within an atom. 2. 1 KE ϭ ᎏ mv 2 2 1 ϭ ΂ ᎏ ΃(5.0 g vibrates up and down while it is connected to a spring.0ϫ10 C) 2 1.2 m) 3 Copyright © Glencoe/McGraw-Hill.0ϫ10 Nиm րC )(8. find the energy lost by the object.02 m) ϭ ᎏᎏᎏᎏ Ϫ7 9 2 2 (9. and the resistance of each bulb is 6. Inc.