《结构化学 Structural Chemistry》课程教学资源（课件讲稿）Chapter 2 Atomic Structure

Brief SummaryofChapter1能量量子化A.自B. 测不准原理：4xAporAEAt≥h微观粒子波动性--运动粒子在空间出现的几率分布1.几率密度分布函数/22. 正交归一性：/*4,dt= i呈现波的特征--几率波！3.本征函数/方程：Ay=aY4.Schrodinger方程：iho/at=H量子力学的统计学本质(定态）IH(r) = EY(r)量子力学体系的状态函数5.态叠加原理：Y=Zc;V，A;=A,-波函数(r,t)求平均值：=/*Adt//y*Ydt简单体系：维势箱= Zc?A/ Zc?1HP=EP2h?ZnxI1EsinW=(n, = 1,2,3,...一2)边界条件18mi=1-3i-1-3

Brief Summary of Chapter 1 微观粒子波动性-运动粒 子在空间出现的几率分布 呈现波的特征-几率波！ 简单体系 : i维势箱 1) Ĥ = E 2) 边界条件 量子力学的统计学本质 量子力学体系的状态函数 -波函数(r,t) A. 能量量子化 B. 测不准原理：xp or Et  ħ 1. 几率密度分布函数 || 2 2. 正交归一性： i *jd = ij 3. 本征函数/方程： Â = a 4. Schrödinger方程：iħ/t = Ĥ (定态) Ĥ(r) = E(r) 5. 态叠加原理: = cii , Âi = Aii 求平均值: = *Âd /*d = ci 2Ai / ci 2 2 2 2 8       m h H T V T  ˆ ˆ ˆ    1 3 sin 2 i i i i i l n x l   ( 1,2,3,.) 8 1 3 2 2 2      i i i i n l n m h E

Chapter 2 Atomicstructure12

Chapter 2 Atomic structure

AtomThe basicbuilding blockof all matters.The smallestparticle of an element that has thesame propertiesastheelement.Composed of a central nucleusand anelectroncloudElectroncloud:notreallyacloudofelectrons,butan informal description of the probability wave ofelectronsinconstantmotion!2

• The basic building block of all matters. • The smallest particle of an element that has the same properties as the element. Atom • Composed of a central nucleus and an “electron cloud ”. • Electron cloud：not really a cloud of electrons, but an informal description of the probability wave of electrons in constant motion!

EvolutionofAtomic:Models1803,AtomicTheory"byJohnDalton1904, “Plum pudding' model proposed by J.J. Thomson afterhis discovery of electron (1897)in cathoderaysCrookestubei.e.,negatively charged electronsembeddedinauniformlydistributedpositive charge

Evolution of Atomic Models i.e., negatively charged electrons embedded in a uniformly distributed positive charge. • 1803, “Atomic Theory” by John Dalton. Crookes tube • 1904, “Plum pudding” model proposed by J.J. Thomson after his discovery of electron (1897) in cathode rays

History of Atomic Models191l, disproval of Thomson's model!BeamofalphaparticlesDeflectedScatteredRadioactivealphaparticlesalphaparticlessourceGeiger and Marsden with E.Rutherfordperformed ascattering experiment withalpha particles (He2+) shot onLead-linedCirculara thin gold foilbexwithholefluorescentscreenMostparticlesGoldfoilpassstraightthroughundeflectedAlphagoldfoilGold folloariclesDeflectionangle@z90alpha sourceexpected米上10-3500alpha particles(predicted by Thomson model)10-4observed(observed by Rutherford et al.)

History of Atomic Models Geiger and Marsden with E. Rutherford performed a scattering experiment with alpha particles (He2+) shot on a thin gold foil. 10-3500 (predicted by Thomson model) 10-4 (observed by Rutherford et al.) • 1911, disproval of Thomson’s model! Deflection angle  90

History of Atomic Models1912:Rutherfordproposedthe“PlanetaryModel "of the atomi.e., positively charged coresurrounded by electrons(1908Nobelprizechemistryofradioactivesubstances)Rutherford estimated the diameter of nucleus to be only about 10-15m. The diameter of an atom, however, was known to be 10-10 m,about 100 000 times larger. Thus most of an atom is empty space.12

History of Atomic Models  1912: Rutherford proposed the “Planetary Model ” of the atom, i.e., positively charged core surrounded by electrons. Rutherford estimated the diameter of nucleus to be only about 10-15 m. The diameter of an atom, however, was known to be 10-10 m, about 100 000 times larger. Thus most of an atom is empty space. (1908 Nobel prize chemistry of radioactive substances)

The planetary model failed in explaining why collapses ofelectronsintonucleusdonotoccur!1)AccordingtoMaxwelltheoryof-eelectronelectromagnetism,astheelectronorbits aroundthenucleus,itacceleratesandhenceradiates-eprotonenergy.2)Thetypicaltimefortheelectrontocollapsesintothenucleuswouldbeabout 10-8s3)Thespectrumofradiationwouldbecontinuous12

1) According to Maxwell theory of electromagnetism, as the electron orbits around the nucleus, it accelerates and hence radiates energy. 2) The typical time for the electron to collapses into the nucleus would be about 10-8 s. 3) The spectrum of radiation would be continuous. +e proton -e electron The planetary model failed in explaining why collapses of electrons into nucleus do not occur!

1913:NielsBohr proposed hisBohrmodel ofthe atom withincorporation of the idea of“quanta"(by Plank & Einstein)TheBohrModelExplanationoftheThreeSeriesofSpectralLinesn=6=0月三56n=5n=4Infrarede)n=3Visiblen=2Visible-100seriesInfraredseriesUltraviolet series-200Ultraviolet-218circular orbits with fixed energyB100200andangularmomentumWavelength (nm)

 1913: Niels Bohr proposed his Bohr model of the atom with incorporation of the idea of “quanta” (by Plank & Einstein). circular orbits with fixed energy and angular momentum

BohratomFMerits:+Zei)Explains why atoms are stableii) Predicts energy is quantizediii)ExplainsHatomspectraDemerits:iv)Fails to predict fine spectral structure ofH)Fails for many-electron atomseisclassicalparticlee in orbit'at fixed r corresponding to a quantumnumber.12

Bohr atom Merits: i) Explains why atoms are stable ii) Predicts energy is quantized iii) Explains H atom spectra Demerits: iv) Fails to predict fine spectral structure of H v) Fails for many-electron atoms e - is classical particle e - in ‘orbit’ at fixed r corresponding to a quantum number. v F -e r +Ze

Bohr atome-is a classicalparticlee- in ‘orbit' at fixed r1（1926）Schrodinger atom1)Electronconfinedinan atomshould also behave like a wave.Schrodinger equation!2)Nofixed orbits but electrondensity distribution3)For3-D,weneedthree12quantum numbers n, l, m

Schrödinger atom (1926) 1) Electron confined in an atom should also behave like a wave. 2) No fixed orbits but electron density distribution 3) For 3-D, we need three quantum numbers n, l, ml Bohr atom e - is a classical particle e - in ‘orbit’ at fixed r Schrödinger equation！