Download Dr Ball`s lectures – review

Electronicstructureofatoms
Introduction
• Topics:propertiesofatoms,lightandtheinteractionsbetweenthem.
• Lightinteractswithelectronsonatoms,andhasbeenanimportanttooltoprobeatomic
properties.
• Fromsuchstudyhascomethetheoryofquantummechanics,whichexplainstheelectronic
structureofatoms,orbitalenergylevelsandpatternsofchemicalbehaviourintheperiodic
table.
• Electronsofanatomdetermineitschemicalproperties(isotopesofanelementhavenearly
identicalchemicalproperties).
Thephotoelectriceffect
• Eachphotonhasanenergythatisdirectlyproportionaltoitsfrequency:
• Ephoton=hvphoton
• Here,histhePlanck’sconstant6.626x10-34Js
• Theenergyofaphotonwiththresholdfrequencyv0correspondstothebindingenergyofan
electron(explainingthresholdenergy).
• Anelectron’skineticenergyisthedifferencebetweenthephotonenergyandthebinding
energy.
• Ekinetic(electron)=hv-hv0
Example:Calculateenergyofredlightwithwavelength700nmandofbluelightwith
wavelength470nm.
Answer:
Weknowthatc=λvandthatE=hv.Ourconstantsarec=2.998x108m/sand
h=6.626x10-34Js.WewanttosolveforE.
RearrangingtheZirstequation:v=c/λ=2.998x108/700x10-9=4.28x1014s-1.
Substitutingintothesecondequation:E=6.626x10-34x4.28x1014=2.84x10-19J.Thisisthe
energyofredlight.
Forbluelight,combiningthetwoequations:
E=(6.626x10-34x2.998x108)/(470x10-9)=4.23x10-19.Thisishigherenergythanred
light.
Quantisationofenergy
• AgasheatedbypassageofelectriccurrentemitslightatafewspeciZicwavelengths.These
arecalledlinespectra.
• Notallwavelengthswereemitted.Thisneededtobeexplained.
• ResultswereexplainedbyassumingthatatomsandphotonscanonlyhavecertainspeciZic
valuesfortheirenergies–thisisthenotionofquantisation.
• AccordingtoBohr(1913):
• Atomscanonlyadoptcertain,discreteenergylevels.
• Anatomchangingtoalowerenergylevelwouldloseadiscreteamountofenergy,which
wouldthenbeemittedasacertainfrequencyoflight(alineemission).
• Inaparticularsample,manylineswouldsimultaneouslyundergovarioustransitions
betweenallallowableenergylevels,andthiswouldcauseasetoflinestobeemitted
whoseenergiescorrespondtotheenergydifferencesbetweentheenergylevels.
• Whenanatomgoesfromahigherenergyleveltoalowerone,aphotonisemittedwith
energyE=hv,whichisequaltothedifferencebetweenthetwolevels.
• Inasampleofmanyatoms,theintensityofthelightemittedataparticularfrequencywould
dependonthenumberofatomsundergoingthecorrespondingenergystateatonetime.
Thisisrandom.
• Groundstate–thisisthelowestenergystateforanatomatanyonetime.
• Excitedstate–thisisoneofaninZinitenumberofenergystateswithenergiesabovethe
groundstate.
Atomicspectra
• Absorption–atomsabsorbspeciZicandcharacteristicfrequenciesoflightastheymoveup
energylevels.
• Emission–atomsemitspeciZicandcharacteristicfrequenciesoflight(photons)asthey
movedownenergylevels.
• Eachelementhasauniqueabsorptionandemissionspectrum,whichprovidesinformation
aboutitsatomicstructure.
• Inthecaseofabsorptionspectra,polychromaticwhitelightpassesthroughasampleofgas,
e.g.inatube.ThegaseousatomsabsorbspeciZicfrequenciesanddonotabsorbothers,
whichleavesdarkbandsintheobservablespectrum.