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Chapter 27Chapter 27
Quantum PhysicsQuantum 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
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
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
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
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
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
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
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?
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
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?
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
Production of X-raysProduction of X-rays
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
Diffraction pattern
for NaCl
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…
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
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.
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
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
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
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
Eƒ
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
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
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
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
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?
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
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
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?
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?