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1、Copyright Cengage Learning.All rights reserved,2,Different Colored Fireworks,Copyright Cengage Learning.All rights reserved,3,Questions to Consider,Why do we get colors?Why do different chemicals give us different colors?,Copyright Cengage Learning.All rights reserved,4,Electromagnetic Radiation,One
2、 of the ways that energy travels through space.Three characteristics:WavelengthFrequencySpeed,Copyright Cengage Learning.All rights reserved,5,Characteristics,Wavelength()distance between two consecutive peaks or troughs in a wave.Frequency()number of waves(cycles)per second that pass a given point
3、in spaceSpeed(c)speed of light(2.9979108 m/s),6,The Nature of Waves,Wave Function,k:angular wave numberT:period:angular frequency,sinusoidal wave,superposition,constructive interference,destructive interference,Standing Wave 驻波,y=(2A sin kx)cos t,Two Dimensional Wave,Different behaviors of waves and
4、 particles.,Copyright Cengage Learning.All rights reserved,18,Classification of Electromagnetic Radiation,Pickle Light,Copyright Cengage Learning.All rights reserved,19,Energy can be gained or lost only in whole number multiples of.A system can transfer energy only in whole quanta(or“packets”).Energ
5、y seems to have particulate properties too.,Copyright Cengage Learning.All rights reserved,20,Energy is quantized.Electromagnetic radiation is a stream of“particles”called photons.Plancks constant=h=6.626 10-34 Js,Copyright Cengage Learning.All rights reserved,21,The Photoelectric effect,Copyright C
6、engage Learning.All rights reserved,Energy has massDual nature of light:Electromagnetic radiation(and all matter)exhibits wave properties and particulate properties.,Copyright Cengage Learning.All rights reserved,23,E=mc2,Continuous spectrum(results when white light is passed through a prism)contain
7、s all the wavelengths of visible lightLine spectrum each line corresponds to a discrete wavelength:Hydrogen emission spectrum,Copyright Cengage Learning.All rights reserved,24,Refraction of White Light,Copyright Cengage Learning.All rights reserved,The Line Spectrum of Hydrogen,Copyright Cengage Lea
8、rning.All rights reserved,Significance,Only certain energies are allowed for the electron in the hydrogen atom.Energy of the electron in the hydrogen atom is quantized.,Copyright Cengage Learning.All rights reserved,27,Why is it significant that the color emitted from the hydrogen emission spectrum
9、is not white?How does the emission spectrum support the idea of quantized energy levels?,Copyright Cengage Learning.All rights reserved,28,CONCEPT CHECK!,Electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.Bohrs model gave hydrogen atom energy levels consiste
10、nt with the hydrogen emission spectrum.Ground state lowest possible energy state(n=1),Copyright Cengage Learning.All rights reserved,29,Electronic Transitions in the Bohr Model for the Hydrogen Atoma)An Energy-Level Diagram for Electronic Transitions,Copyright Cengage Learning.All rights reserved,30
11、,Electronic Transitions in the Bohr Model for the Hydrogen Atomb)An Orbit-Transition Diagram,Which Accounts for the Experimental Spectrum,Copyright Cengage Learning.All rights reserved,31,For a single electron transition from one energy level to another:E=change in energy of the atom(energy of the e
12、mitted photon)nfinal=integer;final distance from the nucleusninitial=integer;initial distance from the nucleus,Copyright Cengage Learning.All rights reserved,32,The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain allowed circular orbits for the elect
13、ron.As the electron becomes more tightly bound,its energy becomes more negative relative to the zero-energy reference state(free electron).As the electron is brought closer to the nucleus,energy is released from the system.,Copyright Cengage Learning.All rights reserved,33,Bohrs model is incorrect.T
14、his model only works for hydrogen.Electrons move around the nucleus in circular orbits.,Copyright Cengage Learning.All rights reserved,34,What color of light is emitted when an excited electron in the hydrogen atom falls from:n=5 to n=2n=4 to n=2n=3 to n=2Which transition results in the longest wave
15、length of light?,Copyright Cengage Learning.All rights reserved,35,blue,=434 nmgreen,=486 nmorange/red,=657 nm,EXERCISE!,Wave Properties of Matter,De Broglie deduced that the particle and wave properties are related by the following expression:is the wavelength associated with the particlem is the m
16、ass(in kg)u is the velocity(in m/s)The wavelength calculated from this equation is known as the de Broglie wavelength.,Diffraction of Electrons,X-ray diffraction pattern of aluminum foil,Electron diffraction pattern of aluminum foil.,We do not know the detailed pathway of an electron.Heisenberg unce
17、rtainty principle:There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time.x=uncertainty in a particles position(m)=uncertainty in a particles momentumh=Plancks constant,Copyright Cengage Learning.All rights reserved,39,Quantum(
18、wave)Mechanics,Time-independent Schrodinger wave equation with solutions called stationary-state functions.,The wave function must satisfy,1.y must be single-valued at all points.,2.The total area under y2(x)must be equal to unity or,3.y must be smooth or dy/dx must be continuous at all points.,Qual
19、itative Aspects of the Wavefunction,Ground-state wave function is a compromise to minimize each term.,The Schrdinger Equation,HY=EY,The wavefunction y contains all the dynamical information about the system it describes.The trick is to determine what y is.And to figure out how to extract the desired
20、 information.The Schrdinger equation is a secular equation(久期方程)!(operator)(eigenfunction)=(eigenvalue)(same eigenfunction),Solving Schrdinger Equation,算符,本征函数,本征值,Exact solution in polar spherical coordinates(r,q,f)results in three quantum numbers that indicate the allowed quantum states.,Schrdinge
21、r Equation for Hydrogen,principal quantum number,n:n=1,2,3,angular momentum quantum number,l:l=0,1,n-1,magnetic quantum number,ml:ml=-l,.-1,0,+1,+l,atomic orbital:wavefunction for a single electron which describes the position of the electron,Hydrogen and hydrogen-like atoms orbital energy depends o
22、nly on n.,n1 multiple orbitals exist corresponding to different combination of n and l.They are,collectively called an energy shell,degenerate:have the same energy,subshell:Within an energy shell,a given set of distinct orbitals exist with the same value of l.,Physical Meaning of a Wave Function(),T
23、he square of the function indicates the probability of finding an electron near a particular point in space.Probability distribution intensity of color is used to indicate the probability value near a given point in space.,Copyright Cengage Learning.All rights reserved,48,Probability Distribution fo
24、r the 1s Wave Function,Copyright Cengage Learning.All rights reserved,49,Radial Probability Distribution,Copyright Cengage Learning.All rights reserved,50,Nickel(110),Cesium&Iodine on Copper(111),a molecule assembled from 8 cesium and 8 iodine atoms,Relative Orbital Size,Difficult to define precisel
25、y.Orbital is a wave function.Picture an orbital as a three-dimensional electron density map.Hydrogen 1s orbital:Radius of the sphere that encloses 90%of the total electron probability.,Copyright Cengage Learning.All rights reserved,55,Principal quantum number(n)size and energy of the orbital.Angular
26、 momentum quantum number(l)shape of atomic orbitals(sometimes called a subshell).Magnetic quantum number(ml)orientation of the orbital in space relative to the other orbitals in the atom.,56,Quantum Numbers for the First Four Levels of Orbitals in the Hydrogen Atom,For principal quantum level n=3,de
27、termine the number of allowed subshells(different values of l),and give the designation of each.#of allowed subshells=3l=0,3sl=1,3pl=2,3d,Copyright Cengage Learning.All rights reserved,59,EXERCISE!,For l=2,determine the magnetic quantum numbers(ml)and the number of orbitals.magnetic quantum numbers=
28、2,1,0,1,2 number of orbitals=5,Copyright Cengage Learning.All rights reserved,60,EXERCISE!,Radial and Angular Parts of the Wavefunction,1s Orbital,Copyright Cengage Learning.All rights reserved,Three Representations of the Hydrogen 1s,2s,and 3s Orbitals,Copyright Cengage Learning.All rights reserved
29、,64,2px Orbital,Copyright Cengage Learning.All rights reserved,2py Orbital,Copyright Cengage Learning.All rights reserved,2pz Orbital,Copyright Cengage Learning.All rights reserved,The Boundary Surface Representations of All Three 2p Orbitals,Copyright Cengage Learning.All rights reserved,68,3dx2-y2
30、 Orbital,Copyright Cengage Learning.All rights reserved,3dxy Orbital,Copyright Cengage Learning.All rights reserved,3dxz Orbital,Copyright Cengage Learning.All rights reserved,3dyz Orbital,Copyright Cengage Learning.All rights reserved,3dz2,Copyright Cengage Learning.All rights reserved,The Boundary
31、 Surfaces of All of the 3d Orbitals,Copyright Cengage Learning.All rights reserved,74,Representation of the 4f Orbitals in Terms of Their Boundary Surfaces,Copyright Cengage Learning.All rights reserved,75,Electron Spin,Electron spin quantum number(ms)can be+or-.Pauli exclusion principle-in a given
32、atom no two electrons can have the same set of four quantum numbers.An orbital can hold only two electrons,and they must have opposite spins.,Copyright Cengage Learning.All rights reserved,76,Quantum Numbers,The electron spin quantum number(ms)is used to specify an electrons spin.There are two possi
33、ble directions of spin.Allowed values of ms are+and.,Quantum Numbers,A beam of atoms is split by a magnetic field.Statistically,half of the electrons spin clockwise,the other half spin counterclockwise.,Atoms with more than one electron.Electron correlation problem:Since the electron pathways are un
34、known,the electron repulsions cannot be calculated exactly.When electrons are placed in a particular quantum level,they“prefer”the orbitals in the order s,p,d,and then f.,Copyright Cengage Learning.All rights reserved,79,Wavefunctions for Many Electron Atoms,For helium(He):function of six position v
35、ariables,x1,y1,and z1 for electron 1 and x2,y2,and z2 for electron 2.,For an atom with N electrons,Schrodinger equation for helium(He),Potential energy term:,Electron-electron repulsions not present in hydrogen.,Without electron-electron repulsions,where f denotes an orbital for an individual electr
36、on,leads to unsatisfactory results.,Solution:self-consistent field(Hartree/SCF)method,Self-consistent field(Hartee/SCF)method,For an atom with N electrons,Schematic representation of SCF method,SCF orbitals can be described using the same set of quantum numbers(n,l,ml).,The four quantum number(n,l,m
37、l,ms)completely label an electron in any orbital in any atom.,Computationally intensive accomplished by sophisticated computer programs.,Penetration Effect,A 2s electron penetrates to the nucleus more than one in the 2p orbital.This causes an electron in a 2s orbital to be attracted to the nucleus m
38、ore strongly than an electron in a 2p orbital.Thus,the 2s orbital is lower in energy than the 2p orbitals in a polyelectronic atom.,Copyright Cengage Learning.All rights reserved,85,Orbital Energies,Copyright Cengage Learning.All rights reserved,A Comparison of the Radial Probability Distributions o
39、f the 2s and 2p Orbitals,Copyright Cengage Learning.All rights reserved,87,The Radial Probability Distribution of the 3s Orbital,Copyright Cengage Learning.All rights reserved,88,A Comparison of the Radial Probability Distributions of the 3s,3p,and 3d Orbitals,Copyright Cengage Learning.All rights r
40、eserved,89,Factors Affecting Atomic Orbital Energies,Additional electron in the same orbital,An additional electron raises the orbital energy through electron-electron repulsions.,Additional electrons in inner orbitals,Inner electrons shield outer electrons more effectively than do electrons in the
41、same sublevel.,Higher nuclear charge lowers orbital energy(stabilizes the system)by increasing nucleus-electron attractions.,The effect of nuclear charge on orbital energy.,Shielding,Energy of orbitals in a single electron atom,Energy only depends on principal quantum number n,Energy of orbitals in
42、a multi-electron atom,Energy depends on n and l,Order of orbitals(filling)in multi-electron atom,1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s,Graphical representation of Madelungs rule,Paramagnetic,unpaired electrons,Diamagnetic,all electrons paired,Diamagnetism and Paramagnetism,Paramagnetic-attracted by a
43、magnet,Diamagnetic slightly repelled by a magnet,Gouy balance-provides direct evidence of electron configurations,Originally constructed to represent the patterns observed in the chemical properties of the elements.Mendeleev is given the most credit for the current version of the periodic table beca
44、use he emphasized how useful the periodic table could be in predicting the existence and properties of still unknown elements.,Copyright Cengage Learning.All rights reserved,100,Aufbau(building-up)Principle,orbital energy negative amount of energy required to remove an electron from a given orbital,
45、An electron configuration is constructed according to the Pauli exclusion principle,so that the total energy of the configuration is a minimum.,Aufbau Principle,As protons are added one by one to the nucleus to build up the elements,electrons are similarly added to hydrogen-like orbitals.An oxygen a
46、tom has an electron arrangement of two electrons in the 1s subshell,two electrons in the 2s subshell,and four electrons in the 2p subshell.Oxygen:1s22s22p4,Copyright Cengage Learning.All rights reserved,102,Hunds Rule,The lowest energy configuration for an atom is the one having the maximum number o
47、f unpaired electrons allowed by the Pauli principle in a particular set of degenerate(same energy)orbitals.,Copyright Cengage Learning.All rights reserved,103,electron configuration how electrons are distributed among the various atomic orbitals,orbital diagram pictorial representation of the electr
48、on configuration which shows the spin of the electron,Pauli Exclusion Principle,No two electrons in an atom can have the same four quantum numbers(n,l,ml,ms).,Effect of radial probability function for Ar,3 distinct shells,Orbital Diagram,A notation that shows how many electrons an atom has in each o
49、f its occupied electron orbitals.Oxygen:1s22s22p4 Oxygen:1s 2s 2p,Copyright Cengage Learning.All rights reserved,106,Valence Electrons,The electrons in the outermost principal quantum level of an atom.1s22s22p6(valence electrons=8)The elements in the same group on the periodic table have the same va
50、lence electron configuration.,Copyright Cengage Learning.All rights reserved,107,The Orbitals Being Filled for Elements in Various Parts of the Periodic Table,Copyright Cengage Learning.All rights reserved,108,Determine the expected electron configurations for each of the following.a)S 1s22s22p63s23
