Quantum Physics

More documents

Recommendations

Info

27.2 The Photoelectric Effect and the Particle Theory of Light 879A successful explanation of the photoelectric effect was given by Einstein in1905, the same year he published his special theory of relativity. As part of a generalpaper on electromagnetic radiation, for which he received the Nobel Prize in1921, Einstein extended Planck’s concept of quantization to electromagneticwaves. He suggested that a tiny packet of light energy or photon would be emittedwhen a quantized oscillator made a jump from an energy state E n nhf to thenext lower state E n1 (n 1)hf. Conservation of energy would require thedecrease in oscillator energy, hf, to be equal to the photon’s energy E, so thatE hf [27.5]where h is Planck’s constant and f is the frequency of the light, which is equal tothe frequency of Planck’s oscillator.The key point here is that the light energy lost by the emitter, hf, stays sharplylocalized in a tiny packet or particle called a photon. In Einstein’s model, a photonis so localized that it can give all its energy hf to a single electron in the metal.According to Einstein, the maximum kinetic energy for these liberated photoelectronsis Energy of a photonKE max hf [27.6] Photoelectric effect equationwhere is called the work function of the metal. The work function, which representsthe minimum energy with which an electron is bound in the metal, is on theorder of a few electron volts. Table 27.1 lists work functions for various metals.With the photon theory of light, we can explain the previously mentionedfeatures of the photoelectric effect that cannot be understood using concepts ofclassical physics:• Photoelectrons are created by absorption of a single photon, so the energy ofthat photon must be greater than or equal to the work function, else no photoelectronswill be produced. This explains the cutoff frequency.• From Equation 27.6, KE max depends only on the frequency of the light and thevalue of the work function. Light intensity is immaterial, because absorption ofa single photon is responsible for the electron’s change in kinetic energy.• Equation 27.6 is linear in the frequency, so KE max increases with increasingfrequency.• Electrons are emitted almost instantaneously, regardless of intensity, becausethe light energy is concentrated in packets rather than spread out in waves. Ifthe frequency is high enough, no time is needed for the electron to graduallyacquire sufficient energy to escape the metal.Experimentally, a linear relationship is observed between f and KE max , as sketchedin Figure 27.6. The intercept on the horizontal axis, corresponding to KE max 0,gives the cutoff frequency below which no photoelectrons are emitted, regardless oflight intensity. The cutoff wavelength c can be derived from Equation 27.6:KE max hf c 0 : hc hc[27.7]where c is the speed of light. Wavelengths greater than c incident on a materialwith work function don’t result in the emission of photoelectrons.cc 0TABLE 27.1Work Functions ofSelected MetalsMetal (eV)Na 2.46Al 4.08Cu 4.70Zn 4.31Ag 4.73Pt 6.35Pb 4.14Fe 4.50KE maxf c fFigure 27.6 A sketch of KE max versusthe frequency of incident light forphotoelectrons in a typical photoelectriceffect experiment. Photons withfrequency less than f c don’t havesufficient energy to eject an electronfrom the metal.INTERACTIVE EXAMPLE 27.3GoalPhotoelectrons from SodiumUnderstand the quantization of light and its role in the photoelectric effect.Problem A sodium surface is illuminated with light of wavelength 0.300 m. The work function for sodium is 2.46 eV.(a) Calculate the energy of each photon in electron volts, (b) the maximum kinetic energy of the ejected photoelectrons,and (c) the cutoff wavelength for sodium.
880 Chapter 27 Quantum PhysicsStrategyParts (a), (b), and (c) require substitution of values into Equations 27.5, 27.6, and 27.7, respectively.Solution(a) Calculate the energy of each photon.Obtain the frequency from the wavelength:Use Equation 27.5 to calculate the photon’s energy:c f : f cf 1.00 10 15 Hz 6.63 10 19 J (6.63 10 19 J) 3.00 108 m/s0.300 10 6 mE hf (6.63 10 34 J s)(1.00 10 15 Hz)1.00 eV1.60 10 19 J 4.14 eV(b) Find the maximum kinetic energy of thephotoelectrons.Substitute into Equation 27.6:KE max hf 4.14 eV 2.46 eV 1.68 eV(c) Compute the cutoff wavelength.Convert from electron volts to joules:Find the cutoff wavelength using Equation 27.7. 2.46 eV (2.46 eV)(1.60 10 19 J/eV) 3.94 10 19 Jc hc (6.63 1034 Js)(3.00 10 8 m/s)3.94 10 19 J 5.05 10 7 m 505 nmRemarkThe cutoff wavelength is in the yellow-green region of the visible spectrum.Exercise 27.3(a) What minimum-frequency light will eject photoelectrons from a copper surface? (b) If this frequency is tripled,find the maximum kinetic energy (in eV) of the resulting photoelectrons. (Answer in eV.)Answers (a) 1.13 10 15 Hz (b) 9.40 eVInvestigate the photoelectric effect for different materials and different wavelengths of light by logginginto PhysicsNow at www.cp7e.com and going to Interactive Example 27.3.APPLICATIONPhotocellsPhotocellsThe photoelectric effect has many interesting applications using a device calledthe photocell. The photocell shown in Active Figure 27.4 produces a current in thecircuit when light of sufficiently high frequency falls on the cell, but it doesn’tallow a current in the dark. This device is used in streetlights: a photoelectric controlunit in the base of the light activates a switch that turns off the streetlightwhen ambient light strikes it. Many garage-door systems and elevators use a lightbeam and a photocell as a safety feature in their design. When the light beamstrikes the photocell, the electric current generated is sufficiently large to maintaina closed circuit. When an object or a person blocks the light beam, the currentis interrupted, which signals the door to open.27.3 X-RAYSIn 1895 at the University of Wurzburg, Wilhelm Roentgen (1845–1923) was studyingelectrical discharges in low-pressure gases when he noticed that a fluorescentscreen glowed even when placed several meters from the gas discharge tube and
Page 1 and 2: Color-enhanced scanning electronmic
Page 3: 876 Chapter 27 Quantum PhysicsSolve
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 28 and 29: Problems 90151.time of 5.00 ms. Fin
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
Page 78 and 79:
29.4 The Decay Processes 951Strateg
Page 80 and 81:
29.4 The Decay Processes 953they we
Page 82 and 83:
29.6 Nuclear Reactions 955wounds on
Page 84 and 85:
29.6 Nuclear Reactions 957EXAMPLE 2
Page 86 and 87:
29.7 Medical Applications of Radiat
Page 88 and 89:
29.7 Medical Applications of Radiat
Page 90 and 91:
29.8 Radiation Detectors 963Figure
Page 92 and 93:
Summary 965Photo Researchers, Inc./
Page 94 and 95:
Problems 967CONCEPTUAL QUESTIONS1.
Page 96 and 97:
Problems 96924. A building has beco
Page 98 and 99:
Problems 97157. A by-product of som
Page 100 and 101:
This photo shows scientist MelissaD
Page 102 and 103:
30.1 Nuclear Fission 975Applying Ph
Page 104 and 105:
30.2 Nuclear Reactors 977Courtesy o
Page 106 and 107:
30.2 Nuclear Reactors 979events in
Page 108 and 109:
30.3 Nuclear Fusion 981followed by
Page 110 and 111:
30.3 Nuclear Fusion 983VacuumCurren
Page 112 and 113:
30.6 Positrons and Other Antipartic
Page 114 and 115:
30.7 Mesons and the Beginning of Pa
Page 116 and 117:
30.9 Conservation Laws 989LeptonsLe
Page 118 and 119:
30.10 Strange Particles and Strange
Page 120 and 121:
30.12 Quarks 993n pΣ _ Σ 0 Σ + S
Page 122 and 123:
30.12 Quarks 995charm C 1, its anti
Page 124 and 125:
30.14 Electroweak Theory and the St
Page 126 and 127:
30.15 The Cosmic Connection 999prot
Page 128 and 129:
30.16 Problems and Perspectives 100
Page 130 and 131:
Problems 100330.12 Quarks &30.13 Co
Page 132 and 133:
Problems 1005particles fuse to prod
Page 134 and 135:
Problems 100740. Assume binding ene
Page 136 and 137:
A.1 MATHEMATICAL NOTATIONMany mathe
Page 138 and 139:
A.3 Algebra A.3by 8, we have8x8 32
Page 140 and 141:
A.3 Algebra A.5EXERCISESSolve the f
Page 142 and 143:
A.5 Trigonometry A.7When natural lo
Page 144 and 145:
APPENDIX BAn Abbreviated Table of I
Page 146 and 147:
An Abbreviated Table of Isotopes A.
Page 148 and 149:
An Abbreviated Table of Isotopes A.
Page 150 and 151:
Some Useful Tables A.15TABLE C.3The
Page 152 and 153:
Answers to Quick Quizzes,Odd-Number
Page 154 and 155:
Answers to Quick Quizzes, Odd-Numbe
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
IndexPage numbers followed by “f
Page 170 and 171:
Current, 568-573, 586direction of,
Page 172 and 173:
Index I.5Fissionnuclear, 973-976, 9
Page 174 and 175:
Index I.7Magnetic field(s) (Continu
Page 176 and 177:
Polarizer, 805-806, 805f, 806-807Po
Page 178 and 179:
South poleEarth’s geographic, 626
Page 180 and 181:
CreditsPhotographsThis page constit
Page 182 and 183:
PEDAGOGICAL USE OF COLORDisplacemen
Page 184 and 185:
PHYSICAL CONSTANTSQuantity Symbol V
show all

Quantum Physics

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?