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Transcript
Chapter7.TheQuantum‐MechanicalModeloftheAtom
StudentObjectives
7.1Schrödinger’sCat


Knowthatthebehaviorofmacroscopicobjectslikebaseballsisstrikinglydifferentfromthebehavior
ofmicroscopicobjectslikeelectrons.
Knowthatthequantum‐mechanicalmodelprovidesthebasisfortheorganizationoftheperiodic
tableandourunderstandingofchemicalbonding.
7.2TheNatureofLight







Defineandunderstandelectromagneticradiation.
Defineandunderstandamplitude,wavelength,andfrequency.
Usethespeedoflighttoconvertbetweenwavelengthandfrequency.
Knowtheelectromagneticspectrumanditsdifferentformsofradiation.
Knowandunderstandinterferenceanddiffractionandhowtheydemonstratethewavenatureof
light.
Knowandexplainthephotoelectriceffectandhowitdemonstratestheparticlenatureoflight.
Useequationstointerconvertenergy,wavelength,andfrequencyofelectromagneticradiation.
7.3AtomicSpectroscopyandtheBohrModel


Defineandunderstandatomicspectroscopyandemissionspectrum.
UnderstandhowtheBohrmodelexplainstheemissionspectrumofhydrogen.
7.4TheWaveNatureofMatter:ThedeBroglieWavelength,theUncertaintyPrinciple,andIndeterminacy






Knowthatelectronsandphotonsbehaveinsimilarways:bothcanactasparticlesandaswaves.
Knowthatphotonsandelectrons,evenwhenviewedasstreamsofparticles,stilldisplaydiffraction
andinterferencepatternsinadouble‐slitexperiment.
UsedeBroglie’srelationtointerconvertwavelength,mass,andvelocity.
KnowthecomplementarityofpositionandvelocitythroughHeisenberg’suncertaintyprinciple.
Knowthesimilaritiesanddifferencesinclassicalandquantum‐mechanicalconceptsoftrajectory.
Differentiatebetweendeterministicandindeterminacy.
7.5QuantumMechanicsandtheAtom


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Defineorbitalandwavefunction.
KnowthattheSchrödingerequationistheultimatesourceofenergiesandorbitalsforelectronsin
atoms.
Knowthepropertiesandallowedvaluesoftheprincipalquantumnumber,n.
Knowtheproperties,allowedvalues,andletterdesignationsoftheangularmomentumquantum
number,l.
Knowthepropertiesandallowedvaluesofthemagneticquantumnumber,m l .
Knowandunderstandhowatomicspectroscopydefinestheenergylevelsofelectronsinthe
hydrogenatom.
Calculatetheenergiesandwavelengthsofemittedandabsorbedphotonsforhydrogen.
100
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
7.6TheShapesofAtomicOrbitals






Defineprobabilitydensityandradialdistributionfunction.
Defineandunderstandnode.
Identifythenumberofnodesinaradialdistributionfunctionforansorbital.
Knowtheshapesofs,p,d,andforbitalsandtherelationshipstoquantumnumbers.
Knowthattheshapeofanatomisdictatedbythecombinedshapesofthecollectionoforbitalsfor
thatatom.
Defineandunderstandphase.
SectionSummaries
LectureOutline


Terms,Concepts,Relationships,Skills
Figures,Tables,andSolvedExamples
TeachingTips


SuggestionsandExamples
MisconceptionsandPitfalls
101
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
LectureOutline
Terms,Concepts,Relationships,Skills 7.1Schrödinger’sCat
 Thestrangenessofthequantumworlddoes
nottransfertothemacroscopicworld
7.2TheNatureofLight
 Electromagneticradiation
o waves
o amplitude
o wavelength
o frequency
o speed
 c=/
 Electromagneticspectrum
o radiowaves
o microwaves
o infrared
o visible
o ultraviolet
o X‐ray
o gamma
 Wavebehavior
o interference
 constructive
 destructive
o diffraction
 Particlebehavior
o photoelectriceffect
o photonorquantumoflight
 E=h=hc/
7.3AtomicSpectroscopyandtheBohrModel
 Atomicspectroscoy
o emissionspectrum
o Bohrmodel
Figures,Tables,andSolvedExamples

Introfigure:Artisticrepresentationof
Schrödinger’scat


Figure7.1ElectromagneticRadiation
unnumberedfigure:photooflightning
showingthespeedofsoundvs.light
Figure7.2WavelengthandAmplitude
Figure7.3ComponentsofWhiteLight
Figure7.4TheColorofanObject
Example7.1WavelengthandFrequency
Figure7.5TheElectromagneticSpectrum
unnumberedfigure:photosofmedicalX‐ray
ChemistryandMedicine:Radiation
TreatmentforCancer
unnumberedfigure:thermalimage
unnumberedfigures:constructiveand
destructiveinterference
unnumberedfigure:photoofwaterwave
interference
Figure7.6Diffraction
Figure7.7InterferencefromTwoSlits
Figure7.8ThePhotoelectricEffect
Figure7.9ThePhotoelectricEffect
Example7.2PhotonEnergy
Example7.3Wavelength,Energy,and
Frequency
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
unnumberedfigure:photoofneonsign
Figure7.10Mercury,Helium,andHydrogen
Figure7.11EmissionSpectra
Figure7.12TheBohrModelandEmission
Spectra
unnumberedfigure:photooffireworks
ChemistryinYourDay:Atomic
Spectroscopy,aBarCodeforAtoms
Figure7.13EmissionSpectraofOxygenand
Neon
Figure7.14FlameTestsforSodium,
Potassium,Lithium,andBarium
Figure7.15EmissionandAbsorption
SpectrumofMercury
102
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
TeachingTips
SuggestionsandExamples
7.1Schrödinger’sCat
7.2TheNatureofLight
 Waterwavesprovideapracticalexampleof
someofthepropertiesofwaves,especially
wavelengthandamplitude.
 Standingwavesisausefuldemonstration.
 Soundwavesarecomparedtothelightfrom
anexplodingfirework.
 Theuseofcolor(wavelength)andbrightness
(amplitude)inFigure7.2canbecomparedto
waterandair(sound)analogies.
 Theradiationtreatmentforcancerisa
positiveuseofradiation.Itsuseispossible
becausedeliverycanbecontrolledand
focused.
 Diffractionpatternsareveryinteresting;a
demonstrationwithwhiteandlaserlightcan
usemasksandpatternsthatcanbeprinted
ontoslidesoroverheads.[Lisensky,George
C.;Kelly,ThomasF.;Neu,DonaldR.;Ellis,
ArthurB.J.Chem.Educ.1991,68,91.]
 AlbertEinsteinwontheNobelPrizein
Physicsforthephotoelectriceffectandnot
forrelativity.
 Pointouttostudentsthatwecalculatethe
energyofaparticle(photon)usingawave
property(wavelengthorfrequency).
7.3AtomicSpectroscopyandtheBohrModel
 Demonstrationsofemissionspectraare
relativelysimple.Lampsoftenshowsingle
colors(sodiumvaporlamps).Mercurylamps
(lowpressure)orevenmercuryarclamps
usedforlighting(mediumandhighpressure)
havemanylinesandcolors.Redandgreen
laserpointersareeffective.
 Emissionspectraareusedinastronomyto
detectelementalmakeupofstars,planets,
andotherglowingbodies.
 Thecolorsinflametestscanbedemonstrated
easily.





MisconceptionsandPitfalls
Wavelengthsofelectromagneticradiation
likethesignalsforaradioorcellphonehave
verylittleenergy.GammaraysandX‐rays
aremuchmorelikelytodamagecellsand
tissue.
Radiationmayhaveanegativeconnotation,
butradiationkeepstheEarthwarmenough
toinhabit,andionizingradiationfrom
gammaraysandX‐rayscanbeuseful.
Theanalogywithwaterwavescangotoofar,
especiallywithrespecttothesignificanceof
amplitude.
TheBohrmodelpredictsemissionspectra
forHandforothersingle‐electronatoms,but
itisnotacorrectmodel.
Themostcommonmisconceptionabout
electronscomesfromtheBohrmodel:that
electronsmoveinorbitsasplanetsdo
aroundthesun.
103
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
LectureOutline
Terms,Concepts,Relationships,Skills 7.4TheWaveNatureofMatter:ThedeBroglie
Wavelength,theUncertaintyPrinciple,and
Indeterminacy
 Interference
o electrondiffraction
o particlebeam
o deBrogliewavelength:=h/mv
 Complementarypropertiesanduncertainty
o Heisenberg’suncertaintyprinciple:
x×mv≥h/4
 Determinacy,indeterminacy,andprobability
o classicalconceptoftrajectory
o quantummechanicalprobability
7.5QuantumMechanicsandtheAtom
 Orbital,aprobabilitymap
o Schrödingerequation
o hydrogenenergylevels





Figure7.16ElectronDiffraction
Example7.4DeBroglieWavelength
unnumberedfigure:illustrationofdouble‐
slitexperimentwithelectrons
unnumberedfigure:photoofWerner
Heisenberg
Figure7.17TheConceptofTrajectory
Figure7.18TrajectoryandProbability
Figure7.19TrajectoryofaMacroscopic
Object
Figure7.20TheQuantum‐MechanicalStrike
Zone








 1 
En  2.18  10 18 J 2  n 
o principalquantumnumber,n
o angularmomentumquantumnumber,l
o magneticquantumnumber,m l
Atomicspectroscopy
o excitationandradiation
o hydrogenatom

Figures,Tables,andSolvedExamples
 1
1
E  2.18  10 18 J 2  2  
n
 f ni 





unnumberedfigure:diagramofprincipal
energylevels
unnumbered figure: letter designations of l
quantumnumber
unnumbered figure: table of n, l, and m l quantumnumbersforn=1–3
Example7.5QuantumNumbersI
Example7.6QuantumNumbersII
Figure7.21ExcitationandRadiation
Figure 7.22 Hydrogen Energy Transitions and
Radiation
Example 7.7 Wavelength of Light for a
TransitionintheHydrogenAtom
104
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
TeachingTips
SuggestionsandExamples
7.4TheWaveNatureofMatter:ThedeBroglie
Wavelength,theUncertaintyPrinciple,and
Indeterminacy
 Anelectronexhibitswaveproperties,but
eachelectronhasthesamemassandthe
samechargeregardlessofwavelength.
 ConceptualConnection7.2ThedeBroglie
WavelengthofMacroscopicObjects
(illustratestheinsignificanceofthe
wavelengthsofmacroscopicobjects)
 Heisenberg’suncertaintyprinciplein
particularchallengesthecenturies‐old
scientifictenetthattwoexperiments
arrangedthesamewayshouldgiveidentical
results.
 Schrödinger’scatisapopularillustrationof
theabsurdityofquantummechanicsatthe
macroscopiclevel.
7.5QuantumMechanicsandtheAtom
 TheSchrödingerequationisamathematical
modelbeyondthescopeofthecourse.
Quantumnumbersareresultsofthe
applicationoftheSchrödingerequation.The
namesofthequantumnumbersmaybe
confusing,especiallytheangularmomentum
andmagneticquantumnumbers,asmost
studentswillhavenoconnectiontothe
meaningsofthoseterms.
 ConceptualConnection7.3TheRelationship
betweennandl
 ConceptualConnection7.4TheRelationship
Betweenlandml
 ConceptualConnection7.5EmissionSpectra




MisconceptionsandPitfalls
Electroninterferencepatternsoccureven
whentheelectronsgothroughthedouble
slitssinglyandcannotinteractwitheach
other.
Studentshaveahardtimevisualizingwhat
thewavelengthofaparticlemeans.
Studentsaremisledbytheprobabilistic
natureofquantummechanicsinmuchthe
samewaythatEinsteinwas.Theypresume
thatprobabilitiesmustbeinvokedbecauseof
anincompletenessinthetheory.
Theexactvaluesofn,l,andm l areobtained
onlythroughtediousmathematics.Thelogic
ofthemathematicsistheonlyguidinglightin
quantumtheorysinceitsbasicprinciplesare
socounterintuitiveinthemacroscopicworld.
105
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
LectureOutline
Terms,Concepts,Relationships,Skills 7.6TheShapesofAtomicOrbitals
 Orbitalrepresentations
o probabilitydensity
o radialdistributionfunction
o nodes
o orbitalsurfaceshapes
 s
 p
 d
 f
Figures,Tables,andSolvedExamples








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
Figure7.23The1sOrbital:Two
Representations
Figure7.24The1sOrbitalSurface
Figure7.25TheRadialDistributionFunction
forthe1sOrbital
unnumberedfigure:illustrationofnodeson
avibratingstring
Figure7.26ProbabilityDensitiesandRadial
DistributionFunctionsforthe2sand3s
Orbitals
Figure7.27The2pOrbitalsandTheirRadial
DistributionFunction
Figure7.28The3dOrbitals
Figure7.29The4fOrbitals
unnumberedfigure:illustrationofwaves
andphase
unnumberedfigures:illustrationsofphases
ofsandporbitals
Figure7.30WhyAtomsAreSpherical
106
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
TeachingTips
SuggestionsandExamples
7.6TheShapesofAtomicOrbitals
 Thedotrepresentationofprobabilityin
Figure7.22ismuchmorerealisticthanthe
solidsphereinFigure7.23.
 Astandingwaveversionofavibratingstring
canbedemonstratedwithaSlinkytoy.Two
studentscanbeusedtodemonstratezero,
one,ortwonodeswithoutmuchdifficulty.
 ConceptualConnection7.4TheShapesof
Atoms

MisconceptionsandPitfalls
Orbitalsdefinetheprobabilityoffindingan
electron.Theshapeandgraphical
representationmaysuggestaphysical
container.
107
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
Additional Problem for Photon Energy
(Example 7.2)
A 1-second pulse of a red laser pointer with a
wavelength of 635 nm contains 5.0 mJ of energy. How
many photons does it contain?
Given E pulse = 5.0 mJ
Sort
 = 635 nm
You are given the wavelength and total energy
of a light pulse and asked to find the number of
photons it contains.
Find number of photons
Strategize
Conceptual Plan
In the first part of the conceptual plan, calculate
the energy of an individual photon from its
wavelength.


In the second part, divide the total energy of the
pulse by the energy of each photon to get the
number of photons in a pulse.
hc
E 
Epulse
Ephoton
E photon

= number of photons
Relationships Used
E = hc/ (Equation 7.3)
Solve
Solution
Convert wavelength to meters and substitute the
values into the energy equation.
 = 635 nm 
Ephoton =
hc

10 9 m
= 6.35  10 7 m
1 nm
(6.626  10 34 J  s )(3.00  108
=
m
)
s
6.35  10 7 m
= 3.13  10 19 J
5.0 mJ 
10 3 J
= 5.0  10 3 J
1 mJ
number of photons =
Epulse
Ephoton
=
5.0  103 J
= 1.6  1016
3.13  1019 J
Convert the energy of the pulse to joules J.
Then divide by the energy of a single photon.
Check
The magnitude of the answer makes physical sense
since the pulse was much larger than the individual
photon energy.
108
Copyright © 2014 by Pearson Education, Inc.
Chapter7.TheQuantum‐MechanicalModeloftheAtom
Additional Problem for Wavelength of Light
for a Transition in the Hydrogen Atom
(Example 7.7)
Determine the wavelength of light emitted when an
electron in a hydrogen atom makes a transition from
an orbital in n = 5 to n = 4.
Sort
Given n = 5  n = 4
You are given the energy levels of an atomic
transition and asked to find the wavelength of
emitted light.
Find 
Strategize
Conceptual Plan
Calculate the energy of the electron in the n = 5
and n = 4 orbitals using Equation 7.7 and subtract
to find the difference.
E atom
E = E 4 – E 5
E atom
The negative value of the difference indicates that
the energy is being emitted. Convert the energy
value to a wavelength using Equation 7.3.

n = 5, n = 4

E photon
E atom = E photon

E 

hc

Relationships Used
E n = 2.18 x 1018 J (1 / n2) (Equation 7.7)
E = hc/ (Equation 7.3)
Solve
Solution
Follow the conceptual plan to solve the problem.
Round the answer to three significant figures to
reflect the three significant figures in the least
precisely known quantity (4750). These
conversion factors are all exact and therefore do
not limit the number of significant figures.
Eatom = E 4  E5

 1
 1 
=  2.18  10 18 J  2    2.18  1018 J  2  
4
 
 5 

1
 1
=  2.18  10 18 J  2  2 
4
5


=  4.90  1020 J
E photon = E atom = +4.90 x 1020 J hc
E
or


hc


E
(6.626  1034 J  s )(3.00  108 m/ s )
=
4.90  1020 J
Check
= 4.06  106 m
The units of the answer are correct (m). A
comparison with the values in Figure 7.21 indicates
that the answer should be in the infrared region.
Figure 7.5 confirms that the answer is within that
region.
109
Copyright © 2014 by Pearson Education, Inc.