Quantum Physics

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Problems 90151.time of 5.00 ms. Find (a) Johnny’s de Broglie wavelengthat this moment, (b) the uncertainty of hiskinetic energy measurement during such a period oftime, and (c) the percent error caused by such anuncertainty.Photons of wavelength 450 nm are incident on ametal. The most energetic electrons ejected from themetal are bent into a circular arc of radius 20.0 cm by amagnetic field with a magnitude of 2.00 10 5 T.What is the work function of the metal?52. A 200-MeV photon is scattered at 40.0° by a free protonthat is initially at rest. Find the energy (in MeV) ofthe scattered photon.53. A light source of wavelength illuminates a metal andejects photoelectrons with a maximum kineticenergy of 1.00 eV. A second light source of wavelength/2 ejects photoelectrons with a maximum kineticenergy of 4.00 eV. What is the work function of themetal?54. Red light of wavelength 670 nm produces photoelectronsfrom a certain photoemissive material. Greenlight of wavelength 520 nm produces photoelectronsfrom the same material with 1.50 times the maximumkinetic energy. What is the material’s workfunction?55.How fast must an electron be moving if all its kineticenergy is lost to a single x-ray photon (a) at the highend of the x-ray electromagnetic spectrum with awavelength of 1.00 10 8 m; (b) at the low end ofthe x-ray electromagnetic spectrum with a wavelengthof 1.00 10 13 m?56. Show that if an electron were confined inside anatomic nucleus of diameter 2.0 10 15 m, it wouldhave to be moving relativistically, while a proton confinedto the same nucleus can be moving at less thanone-tenth the speed of light.57. A photon strikes a metal with a work function andproduces a photoelectron with a de Broglie wavelengthequal to the wavelength of the original photon.(a) Show that the energy of this photon must havebeen given byE (m e c 2 /2)m e c 2 where m e is the mass of the electron. [Hint : Beginwith the conservation of energy, E m e c 2 √(pc)2 (m e c 2)2.] (b) If one of these photons strikesplatinum ( 6.35 eV), determine the resultingmaximum speed of the photoelectron that isemitted.58. In a Compton scattering event, the scattered photonhas an energy of 120.0 keV and the recoilingelectron has a kinetic energy of 40.0 keV. Find(a) the wavelength of the incident photon, (b) theangle at which the photon is scattered, and (c) therecoil angle of the electron. [Hint : Conserve bothmass–energy and relativistic momentum.]59. A woman on a ladder drops small pellets toward apoint target on the floor. (a) Show that, according tothe uncertainty principle, the average distance bywhich she misses the target must be at leastwhere H is the initial height of each pellet abovethe floor and m is the mass of each pellet. Assumethat the spread in impact points is given by x f x i (v x )t. (b) If H 2.00 m and m 0.500 g, whatis x f ?60. Show that the speed of a particle having de Brogliewavelength and Compton wavelength C h/(mc) is61. (a) Find the mass of a solid iron sphere 2.00 cm inradius. (b) Assume that it is at 20°C and has emissivity0.860. Find the power with which it is radiatingelectromagnetic waves. (c) If this sphere were alonein the Universe, at what rate would its temperaturebe changing? (d) Assume Wien’s law describes thesphere. Find the wavelength max of electromagneticradiation it emits most strongly. Although it emits aspectrum of waves having all different wavelengths,model its whole power output as carried by photonsof wavelength max . Find (e) the energy of one photonand (f) the number of photons it emits eachsecond. When the sphere is at thermal equilibriumwith its surroundings, it emits and also absorbs photonsat this rate.ACTIVITIESx f 2 m 1/2 2H g 1/4v 1. Use a black marker or pieces of dark electrical tapeto make a very dark area on the outside of a shoebox.Poke a hole in the center of the dark area with apencil. Now put a lid on the box, and compare theblackness of the hole with the blackness of the surroundingdark area. Based on your observation,explain why the radiation emitted from the hole islike that emitted from a black body.c√1 (/C) 2
902 Chapter 27 <strong>Quantum</strong> <strong>Physics</strong>2. On a clear night, go outdoors far from city lightsand find the constellation Orion. Your instructorshould be able to furnish you with a star chart toassist you in locating this grouping of stars.Look very carefully at the color of the two starsBetelgeuse and Rigel. (See Fig. A27.2.) Can youtell which star is hotter? Orion is visible only fromNovember through April in the evening sky, soif Orion is not visible when you go out, comparetwo of the brightest stars you can see, such asVega in the constellation Lyra and Arcturus inBoötes.John Chumack/Photo ResearchersBetelgeuseRigelFigure A27.2
Page 1 and 2: Color-enhanced scanning electronmic
Page 3: 876 Chapter 27 Quantum PhysicsSolve
Page 6 and 7: 27.2 The Photoelectric Effect and t
Page 8 and 9: 27.3 X-Rays 881even when black card
Page 10 and 11: 27.4 Diffraction of X-Rays by Cryst
Page 12 and 13: 27.5 The Compton Effect 885Exercise
Page 14 and 15: 27.6 The Dual Nature of Light and M
Page 16 and 17: 27.6 The Dual Nature of Light and M
Page 18 and 19: 27.8 The Uncertainty Principle 891w
Page 20 and 21: 27.8 The Uncertainty Principle 893E
Page 22 and 23: 27.9 The Scanning Tunneling Microsc
Page 24 and 25: Problems 897The probability per uni
Page 26 and 27: Problems 89917. When light of wavel
Page 30 and 31: “Neon lights,” commonly used in
Page 32 and 33: 28.2 Atomic Spectra 905l(nm) 400 50
Page 34 and 35: 28.3 The Bohr Theory of Hydrogen 90
Page 36 and 37: 28.3 Th Bohr Theory of Hydrogen 909
Page 38 and 39: 28.4 Modification of the Bohr Theor
Page 40 and 41: 28.6 Quantum Mechanics and the Hydr
Page 42 and 43: 28.7 The Spin Magnetic Quantum Numb
Page 44 and 45: 28.9 The Exclusion Principle and th
Page 46 and 47: 28.9 The Exclusion Principle and th
Page 48 and 49: 28.11 Atomic Transitions 921electro
Page 50 and 51: 28.12 Lasers and Holography 923is u
Page 52 and 53: 28.13 Energy Bands in Solids 925Ene
Page 54 and 55: 28.13 Energy Bands in Solids 927Ene
Page 56 and 57: 28.14 Semiconductor Devices 929I (m
Page 58 and 59: Summary 931(a)Figure 28.32 (a) Jack
Page 60 and 61: Problems 9335. Is it possible for a
Page 62 and 63: Problems 935tum number n. (e) Shoul
Page 64 and 65: Problems 93748. A dimensionless num
Page 66 and 67: Aerial view of a nuclear power plan
Page 68 and 69: 29.1 Some Properties of Nuclei 941T
Page 70 and 71: 29.2 Binding Energy 943130120110100
Page 72 and 73: 29.3 Radioactivity 94529.3 RADIOACT
Page 74 and 75: 29.3 Radioactivity 947INTERACTIVE E
Page 76 and 77: 29.4 The Decay Processes 949Alpha D
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29.4 The Decay Processes 951Strateg
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29.4 The Decay Processes 953they we
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29.6 Nuclear Reactions 955wounds on
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29.6 Nuclear Reactions 957EXAMPLE 2
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29.7 Medical Applications of Radiat
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29.7 Medical Applications of Radiat
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29.8 Radiation Detectors 963Figure
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Summary 965Photo Researchers, Inc./
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Problems 967CONCEPTUAL QUESTIONS1.
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Problems 96924. A building has beco
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Problems 97157. A by-product of som
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This photo shows scientist MelissaD
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30.1 Nuclear Fission 975Applying Ph
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30.2 Nuclear Reactors 977Courtesy o
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30.2 Nuclear Reactors 979events in
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30.3 Nuclear Fusion 981followed by
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30.3 Nuclear Fusion 983VacuumCurren
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30.6 Positrons and Other Antipartic
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30.7 Mesons and the Beginning of Pa
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30.9 Conservation Laws 989LeptonsLe
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30.10 Strange Particles and Strange
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30.12 Quarks 993n pΣ _ Σ 0 Σ + S
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30.12 Quarks 995charm C 1, its anti
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30.14 Electroweak Theory and the St
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30.15 The Cosmic Connection 999prot
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30.16 Problems and Perspectives 100
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Problems 100330.12 Quarks &30.13 Co
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Problems 1005particles fuse to prod
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Problems 100740. Assume binding ene
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A.1 MATHEMATICAL NOTATIONMany mathe
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A.3 Algebra A.3by 8, we have8x8 32
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A.3 Algebra A.5EXERCISESSolve the f
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A.5 Trigonometry A.7When natural lo
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APPENDIX BAn Abbreviated Table of I
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An Abbreviated Table of Isotopes A.
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An Abbreviated Table of Isotopes A.
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Some Useful Tables A.15TABLE C.3The
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Answers to Quick Quizzes,Odd-Number
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Answers to Quick Quizzes, Odd-Numbe
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IndexPage numbers followed by “f
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Current, 568-573, 586direction of,
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Index I.5Fissionnuclear, 973-976, 9
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Index I.7Magnetic field(s) (Continu
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Polarizer, 805-806, 805f, 806-807Po
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South poleEarth’s geographic, 626
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CreditsPhotographsThis page constit
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PEDAGOGICAL USE OF COLORDisplacemen
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PHYSICAL CONSTANTSQuantity Symbol V
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Quantum Physics

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