Chapter4:ChemicalBonding(StructureofCompounds)4.3Electron-DotSymbolsLearningOutcomesAftertoday’svideoyoushouldbeabletoDrawtheelectron-dotstructureinsimplemoleculescontainingatomsofthefirstthreerowsofthePeriodicTableandsolveproblemsconcerningthestructureofsimplemoleculesandions.Discernwhichofanumberofresonanceformspossessesthedominantstructure.•Oneofthemostconvenientwaystopicturethesharingofel...
Chapter3:PeriodicClassificationofElements3.1GeneralCharacteristicsofGroupsandPeriodsNaAuPbKSbTlHgPdBiSnRhLaAgInCeNametheElementsandPlaceTheminTheirGroupsssodiumAu(groupXI)goldPb(groupXIV)leadK(groupI)potassiumSb(groupXV)antimonyTl(groupXIII)thalliumHg(groupXII)mercuryPd(groupX)palladiumBi(groupXV)bismuthSn(groupXIV)tinRh(groupIX)rhodiumLa(groupIII)lanthanumAg(groupXI)silverIn(groupXIII)indiumCe...
Chapter2:AtomicTheory2.3Atomicnumbers,compositionofthenucleusAtomicTheory•Thenumberofprotonsorelectronsiscalledtheatomicnumber.•Thenumberofprotonsandneutronsiscalledthemassnumberoratomicmassorweight.•Anexampleofanisotopeofcarboncouldbe14C,whichisusedinfactinthedatingofancientmaterials.•Thetermnuclideisappliedinageneralwaytoanucleuswithaspecifiednumberofprotonsandneutrons.Forexample,thenucle...
Chapter3:PeriodicClassificationoftheElements3.4AtomicNumberandtheInfluenceonPhysicalPropertiesAsatomicnumberincreasesdensitywillincreasebutwillalsobeaffectedbythepackingofatomsinalattice,whichwillalsoaffectthemeltingandboilingpointsoftransitionelements.Theionizationenergyislinkedtotheavailabilityof(an)electron(s)asshowninthefollowingdiagrams.3.4TheConceptofAtomicNumberIncreasewithMeltingPoint,B...
Chapter3:PeriodicClassificationofElements3.1GeneralCharacteristicsofGroupsandPeriodsNaAuPbKSbTlHgPdBiSnRhLaAgInCeNametheElementsandPlaceTheminTheirGroupsssodiumAu(groupXI)goldPb(groupXIV)leadK(groupI)potassiumSb(groupXV)antimonyTl(groupXIII)thalliumHg(groupXII)mercuryPd(groupX)palladiumBi(groupXV)bismuthSn(groupXIV)tinRh(groupIX)rhodiumLa(groupIII)lanthanumAg(groupXI)silverIn(groupXIII)indiumCe...
Chapter2:AtomicTheory2.5Pauli’sExclusionPrincipleQuantumNumbersinMoreDetail1.Theprincipalquantumnumber,n,canhavepositiveintegralvalues1,2,3,...Asnincreases,theorbitalbecomeslarger,andtheelectronspendsmoretimefartherfromthenucleus.Anincreaseinnalsomeansthattheelectronhasahigherenergyandisthereforelesstightlyboundtothenucleus.2.Thesecondquantumnumber—theangularmomentumquantumnumber,l-canhaveint...
阶线性齐次微分方程()(1)11()...()()0(4.11)nnnnypxypxypxy等价于一阶线性齐次方程组d()(4.12)dYAxYx4.1.2阶线性齐次微分方程的一般理论阶线性非齐次微分方程()(1)11()...()()()(4.5)nnnnypxypxypxyfx定义4.1函数组称为在区间上线性相关,如果存在一组不全为零的数,使得在区间上恒成立.反之，如果只当时使(4.13)在上成立，则称函数组在上线性无关.n,...,,211122))+()0(4.13)nnxxx...
第四章阶线性微分方程本章主要介绍阶线性微分方程的一般理论和求解方法.将把阶线性微分方程化成等价的一阶线性微分方程组，这样就可以把第3章的主要结论自然地应用到本章内容中.即把阶线性微分方程作为一阶线性微分方程组的特例加以处理，以避免推导上的重复.4.1阶线性微分方程的一般理论4.1.1线性微分方程的一般概念阶线性微分方程()(1)11()()()()(4.5)nnnnypxypxypxyfxL(1)(1)000000(),(),,()(4.6)nnyxyyxyyx...
4.2阶常系数线性齐次方程解法()(1)110(4.21)nnnnyayayayL111()0(4.25)nnnnPaaaL4.2.2特征根有重根设是方程(4.25)的重根（实的或复的），由定理4.8知是(4.21)的一个解，如何求出其余的个解呢？1(1)kkne1x1k考虑二阶常系数方程，并假设24pq0ypyq特征方程为，由于，所以是二重根，它对应的解为20pq24pq12p21epxy由刘维尔公式可求出与无关...
4.3阶常系数线性非齐次方程解法()(1)11()(4.33)nnnnyayayayfxL阶常系数线性非齐次方程其中4.3.2第二类型非齐次方程特解的待定系数解法(1)(2)()e[()cos()sin]xmmfxPxxPxx根据欧拉公式，有eeeecos,sin22ixixixixxxi于是，可以改写成()fx设上式中与是的次数不高于的多项式，但二者至少有一个的次数为.m(1)()Pxm(2)()Pxxmm(1)(2)(1)()(2)(-)eeee()()e()e22()e+()e(4.41)ixixixix...
Chapter2:AtomicTheoryAtomicTheory2.2Propertiesofsub-atomicparticles•ThenuclearatomwasfinallyputforwardbyRutherford10whodemonstratedthattheatomhasanucleuscontainingprotonsandneutronsandelectronsspinaroundit.•Thechargeofanelectronwascalculatedat–1.602x10-19Candthatofaprotonat+1.602x10-19C.•Theneutronwasunchargedandsubsequentlydiscoveredin1932bytheBritishscientistJamesChadwick13.•Thevastmajor...
Chapter2:AtomicTheory2.4QuantumNumbers2.4.1Bohr’sModeloftheHydrogenAtomandTheory2.4.2Heisenberg’sUncertaintyPrinciple2.4.3TheSchrödingerEquation•Rutherford’smodeloftheatomdidnotdescribethenatureoftheatomfully,butthequantumtheorydid.•MaxPlanck,aGermanphysicist,assumedthatenergycanbereleasedorabsorbedbyatomsinfixedamountsi.e.quantaandproposedthattheenergyofasinglequantaequalsaconstantmultip...
Chapter2:AtomicTheory2.4QuantumNumbers2.4.1Bohr’sModeloftheHydrogenAtomandTheory2.4.2Heisenberg’sUncertaintyPrinciple2.4.3TheSchrödingerEquationWernerHeisenbergdiscussedthedualnatureofmatteralsoandhowitplacedafundamentallimitationonhowpreciselywecanknowboththelocationandthemomentumofanyobject.2.4.2Heisenberg’sUncertaintyPrincipleAtthesub-atomiclevel,thisisimportantashisuncertaintyprinciples...
Chapter3:PeriodicClassificationofElements3.2AlkaliMetalsandTransitionElementsinDepth3.2.1Group1–TheAlkaliMetals3.2.2TransitionElements3.2.1GroupI–TheAlkaliMetals•Thealkalimetalsaresoftmetallicsolidsthathavehighthermalandelectricalconductivities.•Theelementshavelowdensitiesandmeltingpointsandallformionswitha1+charge.•Theyreactwithhydrogentoformhydrides,sulphurtoformsulphidesandchlorinetofor...
Chapter1:Introduction1.1IntroductiontoBasicChemistrySyllabuscontentSyllabuscontentSyllabuscontentSyllabuscontent1.1.Classificationofmatter•Mattercanexistasasolid,liquidorgas(orvapour).•Gaseshavenofixedvolumeorshapewhereasliquidshaveafixedvolumebutnotshape.Solidsarefixedinbothrespects.•Gasesarethestateofhighestenergyandcanbecompressedwhereasliquidsandsolidscannot.ClickontheGIFtoactivatethencl...
Chapter1:Introduction1.4UnitsofMeasurement•TheSIunits(SystèmeInternationald’Unités)areuniversallyappliedtodayandhavesevenbasicunits.•Prefixesareusedthroughoute.g.millimeter=1x10-3m.•TemperatureisrelativetotheCelsiusscalebasedonthefreezingpointofwaterbeing0°C.•TheKelvinscaleistheabsolutescale,whichisthelowestpossibletemperature:0K=-273.15°C.•TheFahrenheitscaleiscommonlyemployedintheWes...
Chapter1:Introduction1.6StandardDeviationAsetofanalyticalresultsshouldindicatetheprecision:__=WhereNisthenumberofmeasurementsisthemeanvaluexiisanindividualvalueisthesumofthosevaluesResultsarefinallyquotedas.1.6StandardDeviationN.B.Variance=themeansquareddeviationNowtrysomeofthesequestionsthenchecktheanswersPrecisionandAccuracyThetermsprecisionandaccuracyareoftenusedindiscussingtheun...
Chapter2:AtomicTheory2.1Moderntheoryofatomicstructureandsub-atomicparticlesAtomicTheorySyllabuscontent2.1.ModernTheoryofAtomicStructureandSub-AtomicParticlesThefirstmeaningfulatomictheorywaspublishedbyJohnDaltonwhopostulatedthefollowing:•Eachelementiscomposedofextremelysmallparticlescalledatoms.•Allatomsofagivenelementareidentical,buthavedifferentproperties(includingdifferentmassesduetoisotop...
Chapter3:PeriodicClassificationoftheElements3.3IndividualClassificationofAlkalineEarthElements,Chalcogens,HalogensandNobleGases3.3.2GroupXVI-TheChalcogens3.3.3GroupXVII-TheHalogensLearningOutcomesAfterwatchingthisvideo,youshouldbeabletoUnderstandandappreciatehowthephysicalandchemicalpropertiesofGroupXVIAndGroupXVIIelementschangegoingdowneachgroup.Beabletoexplaintheusesofelementsineachgroup.Desc...
Chapter4:ChemicalBonding(StructureofCompounds)4.5TypesofCompounds,PropertiesandFormulae4.5.1Bondingtypes4.5.2Semiconductors4.5.3Polymers4.5.4NanomaterialsVocabularyExerciseLookatpage544ofthetextbookanddefinethefollowingterms:•Polymer•Monomer•Plastic•Thermoplastic•Thermosettingplastic•ElastomerThismodelshowspartofthepoly(ethene)polymerchain..ThePropertiesofPoly(ethene)PolymersofCommercialI...
