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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.