physics112- chapter40

8/3/2019 Physics112- chapter40

1/72

Chapter 40

Quantum Physics


2/72

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


3/72

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


4/72

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


5/72

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


6/72

Blackbody Radiation, final

l A black body is an ideal system that absorbsall radiation incident on it

l The electromagnetic radiation emitted by a


7/72

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


8/72

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


9/72

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


10/72

Active Figure 40.3

l Use the active figure toadjust the temperatureof the blackbody

l Study the emittedradiation

PLAYACTIVE FIGURE


11/72

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

=


12/72

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


13/72

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


14/72

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


15/72

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


16/72

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


17/72

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


18/72

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-


19/72

PlancksModel,

Graph


20/72

Active Figure 40.7

l Use the active figure toinvestigate the energylevels

l Observe the emissionof radiation of differentwavelengths

PLAYACTIVE FIGURE


21/72

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 -


22/72

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


23/72

Photoelectric Effect

l The photoelectric effect occurs when lightincident on certain metallic surfaces causeselectrons to be emitted from those surfaces


24/72

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


25/72

Active Figure 40.9

l Use the active figure tovary frequency or placevoltage

l Observe the motion ofthe electrons

PLAYACTIVE FIGURE


26/72

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


27/72

Active Figure 40.10

l Use the active figure tochange the voltagerange

l Observe the currentcurve for differentintensities of radiation


28/72

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)


29/72


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 Electrons are emitted almost instantaneously, even at verylow light intensities


30/72


31/72


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 The maximum kinetic energy of the photoelectronsincreases with increasing light frequency


32/72

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


33/72

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


34/72

Some WorkFunction

Values


35/72

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


36/72

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


37/72

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


38/72

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


39/72

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

= =


40/72

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


41/72

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


42/72

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


43/72

Compton Effect, Observations

l Comptons experimentsshowed that, at anygiven angle, only onefrequency of radiation is

observed


44/72

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


45/72

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

- = -


46/72

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


47/72

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


48/72

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


49/72

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= =


50/72

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

=


51/72

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


52/72

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


53/72

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


54/72

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


55/72

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


56/72

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


57/72

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


58/72

Wave Envelope

l The blue line represents the envelope function

l This envelope can travel through space with adifferent speed than the individual waves


59/72

Active Figure 40.20

l Use the active figure toobserve the movementof the waves and of thewave envelope

PLAYACTIVE FIGURE


60/72

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=


61/72

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 = = = =


62/72

Electron Diffraction, Set-Up


63/72

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


64/72

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


65/72

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


66/72

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


67/72

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


68/72

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


69/72

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


70/72

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


71/72

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


72/72

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

physics112- chapter40

Documents