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Chapter 28 Practice Problems, Review, and Assessment Section 1 Bohr's Model of the Atom: Practice Problems 1. Calculate the energies of the second, third, and fourth energy levels in the hydrogen atom. SOLUTION: 2. Calculate the energy difference between E3 and E2 in the hydrogen atom. SOLUTION: 3. Calculate the energy difference between E4 and E2 in the hydrogen atom. SOLUTION: 4. CHALLENGE The text shows the solution of the equation for n = 1, the innermost orbital radius of 2 the hydrogen atom. Note that with the exception of n , all factors in the equation are constants. The value of r1 is −11 5.3×10 m, or 0.053 nm. Use this information to calculate the radii of the second, third, and fourth energy levels in the hydrogen atom. SOLUTION: rn = n2k, where k = 5.3×10−11 m (We are using k for the combination of all the constants in the equation.) eSolutions Manual - Powered by Cognero Page 1 Chapter 28 Practice Problems, Review, and Assessment 4. CHALLENGE The text shows the solution of the equation for n = 1, the innermost orbital radius of 2 the hydrogen atom. Note that with the exception of n , all factors in the equation are constants. The value of r1 is −11 5.3×10 m, or 0.053 nm. Use this information to calculate the radii of the second, third, and fourth energy levels in the hydrogen atom. SOLUTION: rn = n2k, where k = 5.3×10−11 m (We are using k for the combination of all the constants in the equation.) 5. Find the wavelength of the light emitted in Practice Problems 2 and 3. Which lines in Figure 6 correspond to each transition? eSolutions Manual - Powered by Cognero Page 2 Chapter 28 Practice Problems, Review, and Assessment 5. Find the wavelength of the light emitted in Practice Problems 2 and 3. Which lines in Figure 6 correspond to each transition? Figure 6 SOLUTION: eSolutions Manual - Powered by Cognero 6. For a particular transition, the energy of a mercury atom drops from 8.82 eV to 6.67 eV. a. What is the energy of the photon emitted by the mercury atom? Page 3 Chapter 28 Practice Problems, Review, and Assessment 6. For a particular transition, the energy of a mercury atom drops from 8.82 eV to 6.67 eV. a. What is the energy of the photon emitted by the mercury atom? b. What is the wavelength of the photon emitted by the mercury atom? SOLUTION: a. −ΔE = 8.82 eV − 6.67 eV = 2.15 eV b. 7. CHALLENGE The ground state of a helium ion is −54.4 eV. A transition to the ground state emits a 304-nm photon. What was the energy of the excited state? SOLUTION: Therefore Eexcited = Eground + ΔE = -54.4 eV + 4.08 eV = -50.3 eV Section 1 Bohr's Model of the Atom: Review 8. MAIN IDEA Explain how energy is conserved when an atom absorbs a photon of light. SOLUTION: The initial sum of the energy of the electron in the atom plus the energy of the incident photon equals the final energy of the electron in the atom. 9. Rutherford’s Nuclear Model Summarize the structure of the atom according to Rutherford’s nuclear model. SOLUTION: In Rutherford’s nuclear model, all of an atom’s positive charge and virtually all of its mass are concentrated in a tiny, centrally located nucleus around which negatively charged electrons orbit. 10. Absorption Spectrum The absorption spectrum for a sample of hydrogen gas is shown in Figure 12. Explain how the absorption spectrum of a gas can be determined. Describe the reasons for the spectrum’s appearance. eSolutions Manual - Powered by Cognero Page 4 9. Rutherford’s Nuclear Model Summarize the structure of the atom according to Rutherford’s nuclear model. SOLUTION: Chapter 28 Practicenuclear Problems, Review, Assessment In Rutherford’s model, all ofand an atom’s positive charge and virtually all of its mass are concentrated in a tiny, centrally located nucleus around which negatively charged electrons orbit. 10. Absorption Spectrum The absorption spectrum for a sample of hydrogen gas is shown in Figure 12. Explain how the absorption spectrum of a gas can be determined. Describe the reasons for the spectrum’s appearance. SOLUTION: To obtain an absorption spectrum, white light is passed through a sample of gas and then a spectroscope. Because the gas absorbs specific wavelengths, the normally continuous spectrum of white light contains dark lines. 11. Spectra How do the emission spectra of incandescent solids and atomic gases differ? In what ways are they similar? SOLUTION: Incandescent solids produce spectra consisting of a continuous band of colors, whereas gases produce spectra made up of a set of discrete lines. All spectra are created by energy-level transitions in atoms. 12. Orbit Radius A helium ion behaves like a hydrogen atom. The radius of the ion’s lowest energy level is 0.0265 nm. According to Bohr’s model, what is the radius of the second energy level? SOLUTION: 2 The radius depends on n , so the second level would have a radius four times the first, or 0.106 nm. 13. Bohr Model Hydrogen has been detected transitioning from the 101st to the 100th energy levels. What is the radiation’s wavelength? Where in the electromagnetic spectrum is this emission? SOLUTION: The wavelength indicates the radiation is a microwave. −15 14. Critical Thinking The nucleus of a hydrogen atom has a radius of about 1.5×10 m. If you were to build a model of the hydrogen atom using a softball (r = 5 cm) to represent the nucleus, where would you locate an electron in the n = 1 Bohr orbit? Would it be in your classroom? SOLUTION: −15 −16 −11 The scale is 5 cm = 1.5×10 m, or 1 cm = 3.0×10 m. The Bohr radius is 5.3×10 m. In our model −11 −16 5 eSolutions Manual Powered by Cognero this would be (5.3×10 /3 0×10 ) 1 cm = 1.8×10 cm, or 1.8 km. This is beyond the classroom and Page 5 probably off school property. Chapter 28 Practice Problems, Review, and Assessment The wavelength indicates the radiation is a microwave. −15 14. Critical Thinking The nucleus of a hydrogen atom has a radius of about 1.5×10 m. If you were to build a model of the hydrogen atom using a softball (r = 5 cm) to represent the nucleus, where would you locate an electron in the n = 1 Bohr orbit? Would it be in your classroom? SOLUTION: −15 −16 −11 The scale is 5 cm = 1.5×10 m, or 1 cm = 3.0×10 m. The Bohr radius is 5.3×10 m. In our model −11 −16 5 this would be (5.3×10 /3 0×10 ) 1 cm = 1.8×10 cm, or 1.8 km. This is beyond the classroom and probably off school property. Section 2 The Quantum Model of the Atom: Review 15. MAIN IDEA Although it was able to accurately predict the behavior of hydrogen, in what ways did Bohr’s atomic model have serious shortcomings? SOLUTION: The Bohr model could not predict the behavior of any other atom besides hydrogen. The model also could not explain why the laws of electromagnetism do not apply within the atom. 16. Quantum Model Explain why the Bohr model of the atom conflicts with the Heisenberg uncertainty principle, whereas the quantum model does not. SOLUTION: The uncertainty principle does not allow a particle to have both a precisely known position and a precisely known momentum at the same time. The Bohr orbits would require both these quantities. 17. Pumping Atoms Explain whether green light could be used to pump a red laser. Why could red light not be used to pump a green laser? SOLUTION: Yes; green photons have enough energy to excite atoms into energy levels from which the atom can emit red light. Red photons do not have enough energy to put the atoms in energy levels high enough to enable them to emit green photons. 18. Lasers Explain how a laser makes use of stimulated emission to produce coherent light. SOLUTION: When a photon strikes an atom in the excited state, it stimulates the excited atom to emit a photon of the same energy and in step with the incident photon. The incident photon remains unchanged and these two photons in turn strike other excited atoms, producing more and more in-step, coherent light. 19. Laser Light What are four characteristics of laser light that make it useful? SOLUTION: concentrated, high power; directional; single wavelength; coherent light 20. Critical Thinking Suppose an electron cloud were reduced to almost the size of the nucleus. Use the Heisenberg uncertainty principle to explain why this process would require adding a tremendous amount of energy. SOLUTION: The smaller the electron cloud, the more precisely we know the position of the electrons. If a particle’s position is well known, its momentum must be uncertain. The uncertainty of the momentum can be large only if momentum itself is large. Therefore, the kinetic energy of the electron also must be large, and it takes lots of energy to do this. Chapter Assessment Section 1 Bohr's Model of the Atom: Mastering Concepts eSolutions Manual - Powered by Cognero Page 6 21. BIG IDEA Describe how Rutherford determined that the positive charge in an atom is concentrated in a tiny region, SOLUTION: The smaller the electron cloud, the more precisely we know the position of the electrons. If a particle’s position is well known, its momentum must be uncertain. The uncertainty of the momentum can be large Chapter Practice Problems, Review, and Assessment only 28 if momentum itself is large. Therefore, the kinetic energy of the electron also must be large, and it takes lots of energy to do this. Chapter Assessment Section 1 Bohr's Model of the Atom: Mastering Concepts 21. BIG IDEA Describe how Rutherford determined that the positive charge in an atom is concentrated in a tiny region, rather than spread throughout the atom. SOLUTION: He directed a beam of α particles at a thin metal sheet and measured the number of particles deflected at various angles. The small but significant number deflected at wide angles indicates a concentrated nucleus. 22. How does the Bohr model explain why the absorption spectrum of hydrogen contains exactly the same wavelengths as its emission spectrum? SOLUTION: Bohr said the energy of an emitted photon or an absorbed photon is equal to the change in energy of the atom, which can have only specific values. 23. Review the planetary model of the atom. What are some of the problems with a planetary model of the atom? SOLUTION: As the electrons undergo centripetal acceleration, they would lose energy and spiral into the nucleus. In addition, all atoms should radiate at all wavelengths, not discrete wavelengths. 24. Analyze and critique the Bohr model of the atom. What three assumptions did Bohr make in developing his model? SOLUTION: Bohr's model correctly predicted values for hydrogen's spectrum, but was unable to predict other elements' spectra. Bohr's assumptions include quantized energy levels, atom emits or absorbs radiation only when it changes states, and angular momentum is quantized. 25. Gas-Discharge Tubes Describe how line spectra from gas-discharge tubes are produced. SOLUTION: Energy is supplied to the gas, which causes the electrons to excite and move to higher energy levels. The electrons then give off the difference in energy between energy levels as they drop back down to a less excited state. The energy differences between levels corresponds to spectral lines. 26. How does the Bohr model account for the spectra emitted by atoms? SOLUTION: Photon wavelengths are determined by the difference in energies of allowed levels as electrons jump inward to stationary states. 27. Explain why line spectra produced by hydrogen gas-discharge tubes are different from those produced by helium gas-discharge tubes. SOLUTION: Each element has a different configuration of electrons and energy levels. Chapter Assessment Section 1 Bohr's Model of the Atom: Mastering Problems 28. A calcium atom drops from 4.68 eV above the ground state to 2.93 eV above the ground state. What is the wavelength of the photon emitted? (Level 1) SOLUTION: eSolutions Manual - Powered by Cognero Page 7 27. Explain why line spectra produced by hydrogen gas-discharge tubes are different from those produced by helium gas-discharge tubes. SOLUTION: Chapter 28 Practice Problems, Review, and Assessment Each element has a different configuration of electrons and energy levels. Chapter Assessment Section 1 Bohr's Model of the Atom: Mastering Problems 28. A calcium atom drops from 4.68 eV above the ground state to 2.93 eV above the ground state. What is the wavelength of the photon emitted? (Level 1) SOLUTION: 29. A calcium atom in an excited state, E2, has an energy level 1.88 eV above the ground state. A photon of energy 2.03 eV strikes the calcium atom and is absorbed by it. To what energy level is the calcium atom raised? Refer to Figure 18. (Level 1) SOLUTION: 1.88 eV + 2.03 eV = 3.91 eV This energy corresponds to level E6. 30. A calcium atom is in an excited state at the E7 energy level. How much energy is released when the atom drops down to the E3 energy level? Refer to Figure 18. SOLUTION: 2 31. A photon of orange light with a wavelength of 6.00×10 nm enters a calcium atom in the E8 excited state and ionizes the atom. What kinetic energy will the electron have as it is ejected from the atom? Refer to Figure 18. (Level 1) SOLUTION: eSolutions Manual - Powered by Cognero Page 8 30. A calcium atom is in an excited state at the E7 energy level. How much energy is released when the atom drops down to the E3 energy level? Refer to Figure 18. SOLUTION: Chapter 28 Practice Problems, Review, and Assessment 2 31. A photon of orange light with a wavelength of 6.00×10 nm enters a calcium atom in the E8 excited state and ionizes the atom. What kinetic energy will the electron have as it is ejected from the atom? Refer to Figure 18. (Level 1) SOLUTION: 32. A mercury atom is in an excited state at the E6 energy level. Refer to Figure 19. (Level 2) a. How much energy would be needed to ionize the atom? b. How much energy would be released if the atom dropped down to the E2 energy level instead? SOLUTION: a. E6 = 7.72 eV 10.44 eV − 7.72 eV = 2.72 eV b. E2 = 4.66 eV 7.72 eV − 4.66 eV = 3.06 eV 33. A mercury atom in an excited state has an energy of −4.98 eV. It absorbs a photon that raises it to the next-higher energy level. What are the energy and the frequency of the photon that is absorbed? Refer to Figure 19. (Level 2) SOLUTION: E5 − E = −3.74 eV − (−4.98 eV) = 1.24 eV eSolutions Manual 4 - Powered by Cognero E = hf Page 9 10.44 eV − 7.72 eV = 2.72 eV b. E2 = 4.66 eV Chapter 28 Practice Problems, and Assessment eV = 3.06 Review, eV 7.72 eV − 4.66 33. A mercury atom in an excited state has an energy of −4.98 eV. It absorbs a photon that raises it to the next-higher energy level. What are the energy and the frequency of the photon that is absorbed? Refer to Figure 19. (Level 2) SOLUTION: E5 − E4 = −3.74 eV − (−4.98 eV) = 1.24 eV E = hf 34. What energies are associated with a hydrogen atom’s energy levels of E2, E3, E4, E5, and E6? (Level 2) SOLUTION: 35. Ranking Task Rank the following energy transitions of hydrogen atoms according to the energy of the released photon, from least to greatest. Specifically indicate any ties. (Level 2) A: from n = 5 to n = 3 B: from n = 5 to n = 4 C: from n = 4 to n = 2 D: from n = 3 to n = 2 E: from n = 2 to n = 1 SOLUTION: eSolutions Manual - Powered by Cognero Page 10 Chapter 28 Practice Problems, Review, and Assessment 35. Ranking Task Rank the following energy transitions of hydrogen atoms according to the energy of the released photon, from least to greatest. Specifically indicate any ties. (Level 2) A: from n = 5 to n = 3 B: from n = 5 to n = 4 C: from n = 4 to n = 2 D: from n = 3 to n = 2 E: from n = 2 to n = 1 SOLUTION: 36. Reverse Problem Write a physics problem with real-life objects for which the following equation would be part of the solution: (Level 3) SOLUTION: A correct form of the answer is, “What is the energy of a photon emitted when a hydrogen atom transitions from the n = 3 state to the ground state?” 37. For a hydrogen atom with an electron in the n = 3 Bohr orbital, find the following. (Level 3) a. radius of the orbital b. electrostatic force between the proton and the electron c. centripetal acceleration of the electron d. orbital electron speed; compare to speed of light SOLUTION: a. b. eSolutions Manual - Powered by Cognero Page 11 A correct form ofProblems, the answer is, “What the energy of a photon emitted when a hydrogen atom Chapter 28 Practice Review, andisAssessment transitions from the n = 3 state to the ground state?” 37. For a hydrogen atom with an electron in the n = 3 Bohr orbital, find the following. (Level 3) a. radius of the orbital b. electrostatic force between the proton and the electron c. centripetal acceleration of the electron d. orbital electron speed; compare to speed of light SOLUTION: a. b. c. d. Chapter Assessment Section 2 The Quantum Model of the Atom: Mastering Concepts −4 38. Lasers A laboratory laser has a power of only 0.8 mW (8×10 lamp? W). Why is it brighter than the light of a 100-W SOLUTION: Light is concentrated into a narrow beam, rather than being spread over a wide area. 39. What properties of laser light led to its use in light shows? eSolutions Manual - Powered by Cognero SOLUTION: Lasers are directional and single, pure colors. Page 12 38. Lasers A laboratory laser has a power of only 0.8 mW (8×10 lamp? W). Why is it brighter than the light of a 100-W SOLUTION: Chapter Problems, and Assessment Light28is Practice concentrated into a Review, narrow beam, rather than being spread over a wide area. 39. What properties of laser light led to its use in light shows? SOLUTION: Lasers are directional and single, pure colors. Chapter Assessment Section 2 The Quantum Model of the Atom: Mastering Problems 40. DVD Players Lasers used in the DVD players such as the one shown in Figure 20 typically emit light at 640 nm. What is the difference, measured in eV, between the two lasing energy levels? (Level 1) SOLUTION: 41. The laser beam’s power equals the photon energy times the number of photons per second that are emitted. (Level 2) a. If you want a laser at 840 nm to have the same power as one at 427 nm, how many times more photons per second are needed? b. Find the number of photons per second in a 5.0-mW 840-nm laser. SOLUTION: a. b. eSolutions Manual - Powered by Cognero Page 13 Chapter 28 Practice Problems, Review, and Assessment 41. The laser beam’s power equals the photon energy times the number of photons per second that are emitted. (Level 2) a. If you want a laser at 840 nm to have the same power as one at 427 nm, how many times more photons per second are needed? b. Find the number of photons per second in a 5.0-mW 840-nm laser. SOLUTION: a. b. 42. HeNe Lasers The HeNe lasers used in many classrooms can be made to lase at three wavelengths: 632.8 nm, 543.4 nm, and 1152.3 nm. (Level 3) a. Find the energy difference between the two states involved in the generation of each wavelength. b. Identify the color of each wavelength. SOLUTION: a. substituting the three values of λ gives 1.96 eV, 2.28 eV, and 1.08 eV. b. red, green, and infrared respectively Chapter Assessment: Applying Concepts 43. Northern Lights The northern lights shown in Figure 21 are caused by high-energy particles from the Sun striking atoms high- in Earth’s If you looked at these lights through a spectrometer, would you see a continuous eSolutions Manual Powered by atmosphere. Cognero Page 14 or line spectrum? Explain. SOLUTION: substituting the three values of λ gives 1.96 eV, 2.28 eV, and 1.08 eV. Chapter 28 Practice Problems, Review, and Assessment b. red, green, and infrared respectively Chapter Assessment: Applying Concepts 43. Northern Lights The northern lights shown in Figure 21 are caused by high-energy particles from the Sun striking atoms high in Earth’s atmosphere. If you looked at these lights through a spectrometer, would you see a continuous or line spectrum? Explain. SOLUTION: Line spectrum; the light comes from gas mixture made of specific elements. 44. If white light were emitted from Earth’s surface and observed by someone in space, would its spectrum appear to be continuous? Explain. SOLUTION: No; as white light passed through Earth’s atmosphere, certain energies would be absorbed by the gases composing the atmosphere. Its spectrum, therefore, would have black lines on it. 45. Is money a good example of quantization? Is water? Explain. SOLUTION: Yes; money comes in only certain discrete values. No; water seems to come in any possible quantity. 46. A certain atom has four energy levels, with E4 being the highest and E1 being the lowest. If the atom can make transitions between any two levels, how many spectral lines can the atom emit? Which transition produces the photon with the highest energy? SOLUTION: Six lines are possible. E4 → E1 has the highest energy photon. 47. A photon is emitted when an electron in an excited hydrogen atom drops through energy levels. What is the maximum energy that the photon can have? If this same amount of energy were given to the atom in the ground state, what would happen? SOLUTION: The maximum energy is 13.6 eV. This is also the ionization energy for hydrogen. The electron would have enough energy to leave the nucleus. 48. Compare the quantum mechanical theory of the atom with the Bohr model. SOLUTION: The Bohr model has fixed orbital radii. The present model gives a probability of finding an electron at a location. The Bohr model allows for calculation of only hydrogen atoms. The present model can be used for all elements. Chapter Assessment: Mixed Review 49. A 14.0-eV photon enters a hydrogen atom in the ground state and ionizes it. With what kinetic energy will the electron be ejected from the atom? (Level 1) SOLUTION: It takes 13.6 eV to ionize the atom, so 14.0 eV − 13.6 eV = 0.4 eV kinetic energy. 50. A hydrogen atom is in the n = 2 level. (Level 2) a. If a photon with a wavelength of 332 nm strikes the atom, show that the atom will be ionized. b. Assume the electron receives the excess energy from the atom’s ionization. What will be the kinetic energy of the electron in joules? eSolutions Manual - Powered by Cognero SOLUTION: a. Page 15 49. A 14.0-eV photon enters a hydrogen atom in the ground state and ionizes it. With what kinetic energy will the electron be ejected from the atom? (Level 1) SOLUTION: Chapter 28 Practice Problems, Review, and Assessment It takes 13.6 eV to ionize the atom, so 14.0 eV − 13.6 eV = 0.4 eV kinetic energy. 50. A hydrogen atom is in the n = 2 level. (Level 2) a. If a photon with a wavelength of 332 nm strikes the atom, show that the atom will be ionized. b. Assume the electron receives the excess energy from the atom’s ionization. What will be the kinetic energy of the electron in joules? SOLUTION: a. Yes, the atom is ionized. b. 51. A beam of electrons strikes atomic hydrogen gas. What minimum electron energy is needed for the hydrogen atoms to emit the red light produced when the atom goes from the n = 3 to the n = 2 state? (Level 3) SOLUTION: There must be enough energy to transition a stable hydrogen atom to the n = 3 state. 52. The most precise spectroscopy experiments use “two-photon” techniques. Two photons with identical wavelengths are directed at the target atoms from opposite directions. Each photon has half the energy needed to excite the atoms from the ground state to the desired energy level. What laser wavelength is needed for a precise study of the energy difference between n = 1 and n = 2 in hydrogen? (Level 3) SOLUTION: eSolutions Manual - Powered by Cognero Page 16 Chapter 28 Practice Problems, Review, and Assessment 52. The most precise spectroscopy experiments use “two-photon” techniques. Two photons with identical wavelengths are directed at the target atoms from opposite directions. Each photon has half the energy needed to excite the atoms from the ground state to the desired energy level. What laser wavelength is needed for a precise study of the energy difference between n = 1 and n = 2 in hydrogen? (Level 3) SOLUTION: For each laser, Chapter Assessment: Thinking Critically 53. Apply Concepts The result of projecting the spectrum of a high-pressure mercury vapor lamp onto a wall in a dark room is shown in Figure 22. What are the differences in energy levels for each of the three visible lines? SOLUTION: 54. Interpret Scientific Illustrations After the emission of the visible photons described in the previous problem, the mercury atom continues to emit photons until it reaches the ground state. From an inspection of Figure 22, determine whether any of these photons would be visible. Explain. eSolutions Manual - Powered by Cognero Page 17 Chapter 28 Practice Problems, Review, and Assessment 54. Interpret Scientific Illustrations After the emission of the visible photons described in the previous problem, the mercury atom continues to emit photons until it reaches the ground state. From an inspection of Figure 22, determine whether any of these photons would be visible. Explain. SOLUTION: No. The three highest energy lines leave the atom in states at least 4.64 eV above the ground state. A photon with this energy has a wavelength of 267 nm in the ultraviolet. The change from E4 to E2 involves an energy change of only 0.79 eV, resulting in light with a wavelength of 1570 nm in the infrared. 55. Analyze and Conclude A positronium atom consists of an electron and a positron bound together. Although the lifetime of this “atom” is very short—on the average, one-seventh of a microsecond—its energy levels can be measured. The Bohr model can be used to calculate energies with the mass of the electron replaced by one-half its mass. Describe how the orbital radii and the energy of each level would be affected. What would be the wavelength of the E2 to E1 transition? SOLUTION: The radii would be twice as large because m appears in the denominator of the equation. The energies would be half as large because m appears in the numerator. Therefore, the wavelengths would be twice as large. Thus, the light emitted from E2 to E1 would be twice that for hydrogen: (2)(122 nm) = 244 nm. 56. Problem Posing Complete this problem so that it can be solved using the Bohr model of the hydrogen atom: “A hydrogen atom is in its ground state…” SOLUTION: A possible form of the correct answer would be, “…when it absorbs a photon and goes to the third excited state. What was the energy of the photon?” Chapter Assessment: Writing in Physics 57. Research the history of atomic models. Describe each model. Identify its strengths and weaknesses. SOLUTION: Students should describe the “raisin pudding” model, a classical planetary model, the Bohr model, and the quantum model. The first explains how atoms can have electrons and mass but fails to describe the results of Rutherford’s experiments. The planetary model explains electrons and Rutherford’s results but is unstable and would collapse in about 1 ns. Bohr’s model explains known spectra and fits Rutherford’s nuclear model but has unexplained assumptions and fails the uncertainty principle. It is also unable to describe atoms with more than one electron. The quantum model can explain all known facts but requires computers to solve the equations. 58. Green laser pointers emit light with a wavelength of 532 nm. Research the type of laser used in this type of pointer, and describe its operation. Indicate whether the laser is pulsed or continuous. SOLUTION: Page 18 It uses a pulsed Nd laser at 1064 nm. The IR is put into a “frequency doubling” crystal. Light with half that wavelength, or 532 nm, results. eSolutions Manual - Powered by Cognero results of Rutherford’s experiments. The planetary model explains electrons and Rutherford’s results but is unstable and would collapse in about 1 ns. Bohr’s model explains known spectra and fits Rutherford’s nuclear model but has unexplained assumptions and fails the uncertainty principle. It is also unable to describe atoms with more than one electron. The quantum model can explain all known facts Chapter 28 Practice Problems, Review, Assessment but requires computers to solve the and equations. 58. Green laser pointers emit light with a wavelength of 532 nm. Research the type of laser used in this type of pointer, and describe its operation. Indicate whether the laser is pulsed or continuous. SOLUTION: It uses a pulsed Nd laser at 1064 nm. The IR is put into a “frequency doubling” crystal. Light with half that wavelength, or 532 nm, results. Chapter Assessment: Cumulative Review 59. A 1.0-m-long wire shown in Figure 23 is moving at a speed of 4.0 m/s at right angles to Earth’s magnetic field where the magnetic induction is 5.0×10 −5 T. What is the EMF induced in the wire? SOLUTION: EMF = BLv = (5.0×10−5 T)(1.0 m)(4.0 m/s) −4 = 2.0×10 V = 0.20 mV 60. The force on a test charge of +3.00×10 charge? −7 C is 0.027 N. What is the electric field strength at the position of the test SOLUTION: 61. A technician needs a 4-Ω resistor but only has 1-Ω resistors. Is there a way to combine what she has? Explain. SOLUTION: Yes. Put four 1Ω resistors in series. RT = R1 + R2 + R3 + R4 8 4 62. The electrons in a beam move at 2.8×10 m/s in an electric field of 1.4×10 N/C. What value must the magnetic field have if the electrons pass through the crossed fields undeflected? SOLUTION: eSolutions Manual - Powered by Cognero Page 19 63. Consider modifications needed for J.J. Thomson’s cathode-ray tube so that it could accelerate protons rather than electrons. Then answer these questions: a. To select particles of the same velocity, would the ratio E/B have to be changed? Explain. 61. A technician needs a 4-Ω resistor but only has 1-Ω resistors. Is there a way to combine what she has? Explain. SOLUTION: Yes. 28 PutPractice four 1Ω resistors series. and Assessment Chapter Problems,in Review, RT = R1 + R2 + R3 + R4 8 4 62. The electrons in a beam move at 2.8×10 m/s in an electric field of 1.4×10 N/C. What value must the magnetic field have if the electrons pass through the crossed fields undeflected? SOLUTION: 63. Consider modifications needed for J.J. Thomson’s cathode-ray tube so that it could accelerate protons rather than electrons. Then answer these questions: a. To select particles of the same velocity, would the ratio E/B have to be changed? Explain. b. For the deflection caused by the magnetic field alone to remain the same, would the B field have to be made smaller or larger? Explain. SOLUTION: a. b. 64. The stopping potential needed to reflect all the electrons ejected from a metal is 7.3 V. What is the electrons’ maximum kinetic energy in joules? SOLUTION: eSolutions Manual - Powered by Cognero Page 20