physics112- chapter40
TRANSCRIPT
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Chapter 40
Quantum Physics
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Need for Quantum Physics
l Problems remained from classical mechanics thatrelativity didnt explain
l Attempts to apply the laws of classical physics to
explain the behavior of matter on the atomic scalewere consistently unsuccessful
l Problems included:
l Blackbody radiation
l The electromagnetic radiation emitted by a heated object
l Photoelectric effectl Emission of electrons by an illuminated metal
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Quantum MechanicsRevolution
l Between 1900 and 1930, another revolutiontook place in physics
l A new theory called quantum mechanicswas
particles of microscopic size
l The first explanation using quantum theorywas introduced by Max Planck
l Many other physicists were involved in othersubsequent developments
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Blackbody Radiation
l An object at any temperature is known toemit thermal radiation
l Characteristics depend on the temperature and
l The thermal radiation consists of a continuousdistribution of wavelengths from all portions of theem spectrum
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Blackbody Radiation, cont.
l At room temperature, the wavelengths of thethermal radiation are mainly in the infrared region
l As the surface temperature increases, the
wavelength changesl It will glow red and eventually white
l The basic problem was in understanding theobserved distribution in the radiation emitted by ablack body
l Classical physics didnt adequately describe the observeddistribution
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Blackbody Radiation, final
l A black body is an ideal system that absorbsall radiation incident on it
l The electromagnetic radiation emitted by a
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Blackbody Approximation
l A good approximation of ablack body is a small holeleading to the inside of ahollow object
l
absorber
l The nature of the radiationleaving the cavity throughthe hole depends only onthe temperature of thecavity
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Blackbody Experiment Results
l The total power of the emitted radiationincreases with temperature
l Stefans law (from Chapter 20):
s=s
l The peak of the wavelength distribution shiftsto shorter wavelengths as the temperatureincreases
l Wiens displacement law
l lmaxT = 2.898 x 10-3 m.K
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Intensity of BlackbodyRadiation, Summary
l The intensity increaseswith increasingtemperature
l The amount of radiation
increasing temperaturel The area under the curve
l The peak wavelengthdecreases with
increasing temperature
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Active Figure 40.3
l Use the active figure toadjust the temperatureof the blackbody
l Study the emittedradiation
PLAYACTIVE FIGURE
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Rayleigh-Jeans Law
l An early classical attempt to explainblackbody radiation was the Rayleigh-Jeanslaw
l At long wavelengths, the law matchedexperimental results fairly well
( ) 4I ,B T
=
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Rayleigh-Jeans Law, cont.
l At short wavelengths, therewas a major disagreementbetween the Rayleigh-Jeans law and experiment
l known as the ultravioletcatastrophe
l You would have infiniteenergy as the wavelengthapproaches zero
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Max Planck
l 1858 1847
l German physicist
l Introduced the concept
of uantum of actionl In 1918 he was
awarded the NobelPrize for the discoveryof the quantized nature
of energy
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Plancks Theory of BlackbodyRadiation
l In 1900 Planck developed a theory ofblackbody radiation that leads to an equationfor the intensity of the radiation
l
This e uation is in com lete a reement withexperimental observations
l He assumed the cavity radiation came fromatomic oscillations in the cavity walls
l
Planck made two assumptions about thenature of the oscillators in the cavity walls
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Plancks Assumption, 1
l The energy of an oscillator can have onlycertain discrete values Enl En= nh
l is the frequency of oscillation
l h is Plancks constant
l This says the energy is quantized
l
Each discrete energy value corresponds to adifferent quantum state
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Plancks Assumption, 2
l The oscillators emit or absorb energy whenmaking a transition from one quantum stateto anotherl The entire energy difference between the initial
and final states in the transition is emitted orabsorbed as a single quantum of radiation
l An oscillator emits or absorbs energy only when itchanges quantum states
l
The energy carried by the quantum of radiation isE = h
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Energy-Level Diagram
l An energy-level diagramshows the quantized energylevels and allowedtransitions
l
axis
l Horizontal lines representthe allowed energy levels
l The double-headed arrowsindicate allowed transitions
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More About Plancks Model
l The average energy of a wave is the averageenergy difference between levels of theoscillator, weighted according to the
l This weighting is described by the Boltzmanndistribution law and gives the probability of astate being occupied as being proportional to
where Eis the energy of the stateBE k Te-
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PlancksModel,
Graph
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Active Figure 40.7
l Use the active figure toinvestigate the energylevels
l Observe the emissionof radiation of differentwavelengths
PLAYACTIVE FIGURE
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Plancks WavelengthDistribution Function
l Planck generated a theoretical expression forthe wavelength distribution
22I ,
hc T =
l h = 6.626 x 10-34 J.s
l h is a fundamental constant of nature
Be -
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Plancks WavelengthDistribution Function, cont.
l At long wavelengths, Plancks equationreduces to the Rayleigh-Jeans expression
l At short wavelengths, it predicts an
decreasing wavelength
l This is in agreement with experimental results
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Photoelectric Effect
l The photoelectric effect occurs when lightincident on certain metallic surfaces causeselectrons to be emitted from those surfaces
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Photoelectric Effect Apparatus
l When the tube is kept in thedark, the ammeter readszero
l When plate E is illuminatedby light having an
appropr a e wave eng , acurrent is detected by theammeter
l The current arises fromphotoelectrons emitted fromthe negative plate and
collected at the positiveplate
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Active Figure 40.9
l Use the active figure tovary frequency or placevoltage
l Observe the motion ofthe electrons
PLAYACTIVE FIGURE
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Photoelectric Effect, Results
l At large values of DV, thecurrent reaches a maximumvalue
l All the electrons emitted atEare collected at C
increases as the intensity ofthe incident light increases
l When DVis negative, thecurrent drops
l When DVis equal to or more
negative than DVs, thecurrent is zero
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Active Figure 40.10
l Use the active figure tochange the voltagerange
l Observe the currentcurve for differentintensities of radiation
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Photoelectric Effect Feature 1
l Dependence of photoelectron kinetic energy on lightintensityl Classical Prediction
l Electrons should absorb energy continually from the
electroma netic wavesl As the light intensity incident on the metal is increased, the
electrons should be ejected with more kinetic energy
l Experimental Result
l The maximum kinetic energy is independent of lightintensity
l The maximum kinetic energy is proportional to the stoppingpotential (DVs)
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Photoelectric Effect Feature 2
l Time interval between incidence of light and ejectionof photoelectronsl Classical Prediction
l At low light intensities, a measurable time interval should
ass between the instant the li ht is turned on and the timean electron is ejected from the metal
l This time interval is required for the electron to absorb theincident radiation before it acquires enough energy toescape from the metal
l Experimental Result
l Electrons are emitted almost instantaneously, even at verylow light intensities
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Photoelectric Effect Feature 4
l Dependence of photoelectron kinetic energyon light frequency
l Classical Prediction
frequency of the light and the electric kinetic energy
l The kinetic energy should be related to the intensity ofthe light
l Experimental Result
l The maximum kinetic energy of the photoelectronsincreases with increasing light frequency
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Photoelectric Effect Features,Summary
l The experimental results contradict all fourclassical predictions
l Einstein extended Plancks concept of
uantization to electroma netic wavesl All electromagnetic radiation can be
considered a stream of quanta, now calledphotons
l A photon of incident light gives all its energyh to a single electron in the metal
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Photoelectric Effect, WorkFunction
l Electrons ejected from the surface of themetal and not making collisions with othermetal atoms before escaping possess the
max
l Kmax= h
l is called the work function
l The work function represents the minimum energy
with which an electron is bound in the metal
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Some WorkFunction
Values
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Photon Model Explanation ofthe Photoelectric Effect
l Dependence of photoelectron kinetic energyon light intensity
l Kmax is independent of light intensity
function
l Time interval between incidence of light andejection of the photoelectron
l Each photon can have enough energy to eject anelectron immediately
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Photon Model Explanation ofthe Photoelectric Effect, cont.
l Dependence of ejection of electrons on lightfrequency
l There is a failure to observe photoelectric effect
,the photon must have more energy than the workfunction in order to eject an electron
l Without enough energy, an electron cannot beejected, regardless of the light intensity
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Photon Model Explanation ofthe Photoelectric Effect, final
l Dependence of photoelectron kinetic energyon light frequency
l Since Kmax= h
,increase
l Once the energy of the work function is exceeded
l There is a linear relationship between the kineticenergy and the frequency
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Cutoff Frequency
l The lines show thelinear relationshipbetween Kand
l The slope of each line
l The x-intercept is thecutoff frequencyl This is the frequency
below which no
photoelectrons areemitted
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Cutoff Frequency andWavelength
l The cutoff frequency is related to the workfunction through c = / h
l The cutoff frequency corresponds to a cutoff
wavelen th
l Wavelengths greater than lc incident on a
material having a work function do notresult in the emission of photoelectrons
c
c
c hc
= =
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Arthur Holly Compton
l 1892 1962
l American physicist
l Director of the lab at
the Universit ofChicago
l Discovered theCompton Effect
l Shared the Nobel Prize
in 1927
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The Compton Effect,Introduction
l Compton and Debye extended with Einsteinsidea of photon momentum
l The two groups of experimenters
the classical wave theory
l The classical wave theory of light failed toexplain the scattering of x-rays from electrons
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Compton Effect, ClassicalPredictions
l According to the classical theory, em wavesincident on electrons should:
l Have radiation pressure that should cause the
l Set the electrons oscillating
l There should be a range of frequencies for thescattered electrons
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Compton Effect, Observations
l Comptons experimentsshowed that, at anygiven angle, only onefrequency of radiation is
observed
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Compton Effect, Explanation
l The results could be explained by treating thephotons as point-like particles having energyh
l isolated system of the colliding photon-electron are conserved
l This scattering phenomena is known as the
Compton effect
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Compton Shift Equation
l The graphs show thescattered x-ray forvarious angles
l The shifted peak, iscaused by thescattering of freeelectrons
l This is called theCompton shift equation
( )1' cosoe
h
m c
- = -
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Compton Wavelength
l The factor h/mecin the equation is called theCompton wavelength and is
0002 43 nmh
= = .
l The unshifted wavelength, o, is caused by x-rays scattered from the electrons that aretightly bound to the target atoms
em c
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Photons and Waves Revisited
l Some experiments are best explained by thephoton model
l Some are best explained by the wave model
l e must accept ot mo e s an a m t t atthe true nature of light is not describable interms of any single classical model
l Also, the particle model and the wave model
of light complement each other
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Louis de Broglie
l 1892 1987
l French physicist
l Originally studiedhistor
l Was awarded theNobel Prize in 1929 forhis prediction of thewave nature of
electrons
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Wave Properties of Particles
l Louis de Broglie postulated that becausephotons have both wave and particlecharacteristics, perhaps all forms of matter
l The de Broglie wavelength of a particle is
h h
p mu= =
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Frequency of a Particle
l In an analogy with photons, de Brogliepostulated that a particle would also have afrequency associated with it
l These equations present the dual nature ofmatter
l Particle nature, pand E
l Wave nature, and
h
=
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Davisson-Germer Experiment
l If particles have a wave nature, then underthe correct conditions, they should exhibitdiffraction effects
l wavelength of electrons
l This provided experimental confirmation ofthe matter waves proposed by de Broglie
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Complementarity
l The principle of complementarity statesthat the wave and particle models of eithermatter or radiation complement each other
l describe matter or radiation adequately
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Electron Microscope
l The electron microscoperelies on the wavecharacteristics of electrons
l The electron microscope
because it has a very shortwavelength
l Typically, the wavelengthsof the electrons are about100 times shorter than that
of visible light
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Quantum Particle
l The quantum particle is a new model that isa result of the recognition of the dual nature
l Entities have both particle and wave
l We must choose one appropriate behavior inorder to understand a particular phenomenon
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Ideal Particle vs. Ideal Wave
l An ideal particle has zero size
l Therefore, it is localizedin space
l An ideal wave has a single frequency and is
l Therefore,it is unlocalizedin space
l A localized entity can be built from infinitelylong waves
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Particle as a Wave Packet
l Multiple waves are superimposed so that one of itscrests is at x= 0
l The result is that all the waves add constructively atx= 0
l ere s es ruc ve n er erence a every po nexcept x= 0
l The small region of constructive interference iscalled a wave packetl The wave packet can be identified as a particle
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Active Figure 40.19
l Use the active figure tochoose the number ofwaves to add together
l Observe the resulting
wave packet
l The wave packetrepresents a particle
PLAYACTIVE FIGURE
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Wave Envelope
l The blue line represents the envelope function
l This envelope can travel through space with adifferent speed than the individual waves
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Active Figure 40.20
l Use the active figure toobserve the movementof the waves and of thewave envelope
PLAYACTIVE FIGURE
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Speeds Associated with WavePacket
l The phase speed of a wave in a wave packet isgiven by
phasev
k=
l This is the rate of advance of a crest on a single wave
l The group speed is given by
l This is the speed of the wave packet itself
gdv
dk=
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Speeds, cont.
l The group speed can also be expressed interms of energy and momentum
2 1dE d p
l This indicates that the group speed of thewave packet is identical to the speed of the
particle that it is modeled to represent
2 2g
dp dp m m = = = =
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Electron Diffraction, Set-Up
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Electron Diffraction,Experiment
l Parallel beams of mono-energetic electronsthat are incident on a double slit
l The slit widths are small compared to theelectron wavelen th
l An electron detector is positioned far from theslits at a distance much greater than the slitseparation
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Electron Diffraction, cont.
l If the detector collectselectrons for a longenough time, a typicalwave interference patternis produced
l This is distinct evidencethat electrons areinterfering, a wave-likebehavior
l The interference patternbecomes clearer as thenumber of electronsreaching the screenincreases
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Active Figure 40.22
l Use the active figure toobserve thedevelopment of theinterference pattern
l Observe the destructionof the pattern when youkeep track of which slitan electron goesthrough
Please replace withactive figure 40.22
PLAYACTIVE FIGURE
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Electron Diffraction, Equations
l A maximum occurs when
l This is the same equation that was used for light
l This shows the dual nature of the electron
sind m=
l e e ectrons are etecte as part c es at alocalized spot at some instant of time
l The probability of arrival at that spot is determinedby finding the intensity of two interfering waves
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Electron Diffraction Explained
l An electron interacts with both slitssimultaneously
l If an attempt is made to determineexperimentally which slit the electron goes
,interference patternl It is impossible to determine which slit the electron
goes through
l In effect, the electron goes through both slitsl The wave components of the electron are present
at both slits at the same time
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Werner Heisenberg
l 1901 1976
l German physicist
l Developed matrixmechanics
l Many contributionsinclude:
l Uncertainty principle
l Recd Nobel Prize in 1932
l Prediction of two forms ofmolecular hydrogen
l Theoretical models of thenucleus
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The Uncertainty Principle,Introduction
l In classical mechanics, it is possible, inprinciple, to make measurements witharbitrarily small uncertainty
l fundamentally impossible to makesimultaneous measurements of a particlesposition and momentum with infinite accuracy
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Heisenberg UncertaintyPrinciple, Statement
l The Heisenberg uncertainty principlestates: if a measurement of the position of a
particle is made with uncertainty Dx and a
component of momentum is made withuncertainty Dpx, the product of the twouncertainties can never be smaller than /2
2xx pD
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Heisenberg UncertaintyPrinciple, Explained
l It is physically impossible to measuresimultaneously the exact position and exactmomentum of a particle
l from imperfections in practical measuringinstruments
l The uncertainties arise from the quantum
structure of matter
H i b U i
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Heisenberg UncertaintyPrinciple, Another Form
l Another form of the uncertainty principle canbe expressed in terms of energy and time
D D
l This suggests that energy conservation canappear to be violated by an amount DE aslong as it is only for a short time interval Dt
2D D