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Chapter 27 Chapter 27 Quantum Physics Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

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Page 1: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Chapter 27Chapter 27

Quantum PhysicsQuantum Physics

Conceptual questions: 1,3,9,10

Quick Quizzes: 1,2,3

Problems: 13,42,43,51

Page 2: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Problems which classical Problems which classical physics could not solvephysics could not solve

Blackbody RadiationBlackbody Radiation E&M radiation emitted by a heated objectE&M radiation emitted by a heated object

Photoelectric EffectPhotoelectric Effect Emission of electrons by an illuminated Emission of electrons by an illuminated

metalmetal X-Ray DiffractionX-Ray Diffraction The Compton EffectThe Compton Effect Spectral Lines Emitted by AtomsSpectral Lines Emitted by Atoms

Page 3: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Blackbody RadiationBlackbody Radiation

An object at any temperature is known An object at any temperature is known to emit electromagnetic radiation, called to emit electromagnetic radiation, called thermal radiationthermal radiation Stefan’s Law, the power radiated by an Stefan’s Law, the power radiated by an

object, P = object, P = A e T A e T44

T-temperature, A-area, e-emissivity, T-temperature, A-area, e-emissivity, =5.669 10=5.669 10-8-8 W/m W/m22 K K44

The spectrum of the radiation depends on The spectrum of the radiation depends on the temperature and properties of the the temperature and properties of the objectobject

Page 4: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Blackbody Radiation Blackbody Radiation GraphGraph

The wavelength of the The wavelength of the peak of the blackbody peak of the blackbody distribution was found distribution was found to follow to follow Wein’s Wein’s Displacement LawDisplacement Law λλmaxmax T = 0.2898 x 10 T = 0.2898 x 10-2-2 m • m •

K K λλmaxmax is the wavelength at is the wavelength at

the curve’s peakthe curve’s peak

Page 5: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

The Ultraviolet Catastrophe and The Ultraviolet Catastrophe and Planck’s theoryPlanck’s theory

Classical theory predicted Classical theory predicted infinite energy at low infinite energy at low wavelengths wavelengths

Planck hypothesized that Planck hypothesized that the blackbody radiation the blackbody radiation was produced by was produced by resonatorsresonators

The resonators could only The resonators could only have have discrete energiesdiscrete energies EEnn = n h = n h ƒƒ

n is called the n is called the quantum quantum numbernumber

ƒ is the frequency of vibrationƒ is the frequency of vibration h is h is Planck’s constantPlanck’s constant, 6.626 , 6.626

x 10x 10-34-34 J s J s

Page 6: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Photoelectric EffectPhotoelectric Effect

When light strikes E, When light strikes E, photoelectrons are photoelectrons are emittedemitted

Electrons collected Electrons collected at C and passing at C and passing through the through the ammeter are a ammeter are a current in the circuitcurrent in the circuit

C is maintained at a C is maintained at a positive potential by positive potential by the power supplythe power supply

Page 7: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Photoelectric Current/Voltage Photoelectric Current/Voltage GraphGraph

Classical theory could Classical theory could not explain:not explain: The stopping The stopping

potential is potential is independent of the independent of the radiation intensityradiation intensity

The maximum kinetic The maximum kinetic energy of the energy of the photoelectrons is photoelectrons is independent of the independent of the light intensitylight intensity

The maximum kinetic The maximum kinetic energy of the energy of the photoelectrons photoelectrons increases with increases with increasing light increasing light frequencyfrequency

Page 8: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Einstein’s ExplanationEinstein’s Explanation

Light is a collection of photons (not Light is a collection of photons (not waves)waves)

The photon’s energy would be E = hThe photon’s energy would be E = hƒƒ E=nhf-(n-1)hfE=nhf-(n-1)hf Each photon can give all its energy to an Each photon can give all its energy to an

electron in the metalelectron in the metal The maximum kinetic energy of the The maximum kinetic energy of the

liberated photoelectron is KE = hliberated photoelectron is KE = hƒ – Φƒ – Φ Φ is called the Φ is called the work functionwork function of the metal of the metal

Page 9: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Verification of Einstein’s Verification of Einstein’s TheoryTheory

Problem 27-13. What wavelength of light would have to fall on sodium (work function 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 x 106 m/s?

Page 10: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

PhotocellsPhotocells

Photocells are an application of the Photocells are an application of the photoelectric effectphotoelectric effect

When light of sufficiently high When light of sufficiently high frequency falls on the cell, a frequency falls on the cell, a current is producedcurrent is produced

ExamplesExamples Streetlights, garage door openers, Streetlights, garage door openers,

elevatorselevators

Page 11: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Problem 27-13Problem 27-13

What wavelength of light would What wavelength of light would have to fall on sodiumhave to fall on sodium (with a work (with a work function of 2.46 eV) if it is to emit function of 2.46 eV) if it is to emit electronselectrons with a maximum speed with a maximum speed of 1.0 × 10of 1.0 × 1066 m/s? m/s?

Page 12: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

X-RaysX-Rays

Electromagnetic radiation with short Electromagnetic radiation with short wavelengthswavelengths Wavelengths less than for ultravioletWavelengths less than for ultraviolet Wavelengths are typically about 0.1 nmWavelengths are typically about 0.1 nm X-rays have the ability to penetrate X-rays have the ability to penetrate

most materials with relative easemost materials with relative ease Discovered and named by Roentgen Discovered and named by Roentgen

in 1895in 1895

Page 13: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Production of X-raysProduction of X-rays

Page 14: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Schematic for X-ray Schematic for X-ray DiffractionDiffraction A continuous beam A continuous beam

of X-rays is incident of X-rays is incident on the crystalon the crystal

The diffracted The diffracted radiation is very radiation is very intense in certain intense in certain directionsdirections These directions These directions

correspond to correspond to constructive interference constructive interference from waves reflected from waves reflected from the layers of the from the layers of the crystalcrystal

Page 15: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Diffraction pattern

for NaCl

Page 16: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Bragg’s LawBragg’s Law

Bragg’s LawBragg’s Law gives the gives the conditions for constructive conditions for constructive interferenceinterference2 d sin 2 d sin θ = m λ m = 1, 2, θ = m λ m = 1, 2,

3…3…

Page 17: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Compton ScatteringCompton Scattering

Compton assumed Compton assumed the photons acted the photons acted like other particles like other particles in collisionsin collisions

Energy and Energy and momentum were momentum were conservedconserved

The shift in The shift in wavelength iswavelength is

)cos1(cm

h

eo

Page 18: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

QUICK QUIZ 27.1An x-ray photon is scattered by an electron. The frequency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases,(c) remains the same.

Page 19: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

A photon of energy E0 strikes a free electron, with the scattered photon of energy E moving in the direction opposite that of the incident photon. In this Compton effect interaction, the resulting kinetic energy of the electron is (a) E0 , (b) E , (c) E0 E , (d) E0 + E , (e) none of the above.

QUICK QUIZ 27.2

Page 20: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Photons and Photons and Electromagnetic WavesElectromagnetic Waves

Light has a dual nature. It exhibits Light has a dual nature. It exhibits both wave and particle both wave and particle characteristicscharacteristics Applies to all electromagnetic radiationApplies to all electromagnetic radiation

The photoelectric effect and The photoelectric effect and Compton scattering offer evidence Compton scattering offer evidence for the particle nature of lightfor the particle nature of light

Interference and diffraction offer Interference and diffraction offer evidence of the wave nature of lightevidence of the wave nature of light

Page 21: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Wave Properties of Wave Properties of ParticlesParticles

In 1924, Louis de Broglie In 1924, Louis de Broglie postulated that postulated that because photons because photons have wave and particle have wave and particle characteristics, perhaps all forms characteristics, perhaps all forms of matter have both propertiesof matter have both properties

Furthermore, the frequency and Furthermore, the frequency and wavelength of matter waves can wavelength of matter waves can be determinedbe determined

Page 22: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

de Broglie Wavelength de Broglie Wavelength and Frequencyand Frequency

The The de Broglie wavelengthde Broglie wavelength of a of a particle is particle is

The frequency of matter waves isThe frequency of matter waves is

mv

h

h

Page 23: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

A non-relativistic electron and a non-relativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles: (a) speed, (b) kinetic energy, (c) momentum, (d) frequency?

QUICK QUIZ 27.3

Page 24: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

The Electron MicroscopeThe Electron Microscope The electron microscope The electron microscope

depends on the wave depends on the wave characteristics of electronscharacteristics of electrons

Microscopes can only Microscopes can only resolve details that are resolve details that are slightly smaller than the slightly smaller than the wavelength of the radiation wavelength of the radiation used to illuminate the used to illuminate the objectobject

The electrons can be The electrons can be accelerated to high accelerated to high energies and have small energies and have small wavelengthswavelengths

Page 25: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

The Uncertainty PrincipleThe Uncertainty Principle

When measurements are made, the When measurements are made, the experimenter is always faced with experimenter is always faced with experimental uncertainties in the experimental uncertainties in the measurementsmeasurements Classical mechanics would allow for Classical mechanics would allow for

measurements with arbitrarily small measurements with arbitrarily small uncertaintiesuncertainties

Quantum mechanics predicts that a Quantum mechanics predicts that a barrier to measurements with barrier to measurements with ultimately small uncertainties does ultimately small uncertainties does existexist

Page 26: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

Mathematically,Mathematically,

It is physically impossible to It is physically impossible to measure simultaneously the exact measure simultaneously the exact position and the exact linear position and the exact linear momentum of a particlemomentum of a particle

Another form of the principle deals Another form of the principle deals with energy and time: with energy and time:

4

hpx x

4

htE

Page 27: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Problem 27-43Problem 27-43

In the ground state of hydrogen, In the ground state of hydrogen, the uncertainty of the position of the uncertainty of the position of the electron is roughly 0.10 nm. If the electron is roughly 0.10 nm. If the speed of the electron is on the the speed of the electron is on the order of the uncertainty in its order of the uncertainty in its speed, how fast is the electron speed, how fast is the electron moving?moving?

Page 28: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Thought Experiment – the Thought Experiment – the Uncertainty PrincipleUncertainty Principle

A thought experiment for viewing an electron with a powerful A thought experiment for viewing an electron with a powerful microscopemicroscope

In order to see the electron, at least one photon must bounce off itIn order to see the electron, at least one photon must bounce off it During this interaction, momentum is transferred from the photon During this interaction, momentum is transferred from the photon

to the electronto the electron Therefore, the light that allows you to accurately locate the Therefore, the light that allows you to accurately locate the

electron changes the momentum of the electronelectron changes the momentum of the electron

Page 29: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Scanning Tunneling Scanning Tunneling Microscope (STM)Microscope (STM)

Allows highly detailed Allows highly detailed images with resolution images with resolution comparable to the size comparable to the size of a single atomof a single atom

A conducting probe A conducting probe with a sharp tip is with a sharp tip is brought near the brought near the surfacesurface

The electrons can The electrons can “tunnel” across the “tunnel” across the barrier of empty spacebarrier of empty space

Page 30: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

Conceptual questionsConceptual questions

1. If you observe objects inside a very hot 1. If you observe objects inside a very hot kiln, it is difficult to discern the shapes of the kiln, it is difficult to discern the shapes of the objects. Why?objects. Why?

3. Are the blackbodies really black?3. Are the blackbodies really black? 9. In the photoelectric effect, explain why the 9. In the photoelectric effect, explain why the

stopping potential depends on the frequency stopping potential depends on the frequency of the light but not on the intensity.of the light but not on the intensity.

10. Which has more energy, a photon of 10. Which has more energy, a photon of ultraviolet radiation or a photon of yellow ultraviolet radiation or a photon of yellow light?light?

Page 31: Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

ProblemsProblems

42. A 50-g ball moves at 30.0 m/s. If its 42. A 50-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of speed is measured to an accuracy of 0.10%, what is the minimum uncertainty 0.10%, what is the minimum uncertainty in its position?in its position?

51. 51. Photons of wavelength 450 nm are Photons of wavelength 450 nm are incident on a metal. The most energetic incident on a metal. The most energetic electrons ejected from the metal are bent electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 magnetic field with a magnitude of 2.00 × 10× 10–5–5 T. What is the work function of the T. What is the work function of the metal?metal?