PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Tentative material to be covered for Exam 2 (Wednesday, October 27)Chapter 16 Quantum Mechanics and the Hydrogen Atom16.1 Waves and Light16.2 Paradoxes in Classical Physics16.3 Planck, Einstein, and Bohr16.4 Waves, Particles, and the Schroedinger Equation16.5 The Hydrogen AtomChapter 17 Many-Electron Atoms and Chemical Bonding17.1 Many-Electron Atoms and the Periodic Table17.2 Experimental Measures of Orbital Energies17.3 Sizes of Atoms and Ions17.4 Properties of the Chemical Bond17.5 Ionic and Covalent Bonds17.6 Oxidation States and Chemical BondingChapter 18 Molecular Orbitals, Spectroscopy, and Chemical Bonding18.1 Diatomic Molecules18.2 Polyatomic Molecules18.3 The Conjugation of Bonds and Resonance Structures18.4 The Interaction of Light with Molecules18.5 Atmospheric Chemistry and Air PollutionChapter 16 Quantum Mechanics and the Hydrogen Atom16.1 Waves and LightAtomic Spectra I16.2 Paradoxes in Classical PhysicsUltraviolet Catastrophe Photoelectric effect16.3 Planck, Einstein, and BohrPlanck’s Constant, Quanta and PhotonsBohr AtomAtomic Spectra II16.4 Waves, Particles, and the Schroedinger EquationSchroedinger Equation (Wave Equation)16.5 The Hydrogen AtomSizes and Shapes of OrbitalsElectron SpinReview of the development of the Bohr atomA Movie from the Mechanical UniverseSchroedinger: If electrons are waves, their postion and motion in space must obey a wave equation.Solutions of wave equations yield wavefunctions, , which contain the information required to describe ALL of the properties of the wave.Provides a picture of the electronic distributions of the electrons about an the nucleus of an atom and about the connected nuclei of a molecule.Schroedinger thinking about his equation.Particles are out, waves are in. But the mathematics of waves is very complex!Wavefunctions and orbitalsObital: defined by the quantum numbers n, l and ml Orbital is a wavefunctionOrbital is a region of space occupied by an electronOrbitals has energies, shapes and orientation in spaceQuantum Numbers (QN)Principal QN:n = 1, 2, 3, 4……Angular momentum QN:l = 0, 1, 2, 3…. (n -1)Rule: l = (n - 1)Magnetic QN:ml = …-2, -1, 0, 1, 2, ..Rule: -l….0….+lShorthand notation for orbitalsRule: l = 0, s orbital; l = 1, p orbital; l = 2, d orbitall = 3, f orbital1s, 2s, 2p, 3s, 3p, 4s, 4p, 4d, etc.Recall the gaps between the energy levels of the H atom. Big initial gap and then smaller and smaller gaps.The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of nshell = all orbitals with the same value of nsubshell = all orbitals with the same value of n and lan orbital is fully defined by three quantum numbers, n, l, and mlEach shell of QN = n contains n subshellsn = 1, one subshelln= 2, two subshells, etcEach subshell of QN = l, contains 2l + 1 orbitals l = 0, 2(0) + 1 = 1l = 1, 2(1) + 1 = 3Sizes, Shapes, and orientations of orbitalsn determines size; l determines shapeml determines orientationNodes in orbitals: s orbitals: 1s no nodes, 2s one node, 3s two nodesNodes in orbitals: 2p orbitals: angular node that passes through the nucleusOrbital is “dumb bell” shapedImportant: the + and - that is shown for a p orbital refers to the mathematical sign of the wavefunction, not electric charge!Nodes in orbitals: 3d orbitals: two angular nodes that passes through the nucleusOrbital is “four leaf clover” shapedd orbitals are important for metalsThe fourth quantum number: Electron Spinms = +1/2 (spin up) or -1/2 (spin down)Spin is a fundamental property of electrons, like its charge and mass. (spin up)(spin down)Electrons in an orbital must have different values of ms This statement demands that if there are two electrons in an orbital one must have ms = +1/2 (spin up) and the other must have ms = -1/2 (spin down) This is the Pauli Exclusion PrincipleAn empty orbital is fully described by the three quantum numbers: n, l and ml An electron in an orbital is fully described by the four quantum numbers: n, l, ml and msChapter 17 Many-Electron Atoms and Chemical Bonding17.1 Many-Electron Atoms and the Periodic Table17.2 Experimental Measures of Orbital Energies17.3 Sizes of Atoms and Ions17.4 Properties of the Chemical Bond17.5 Ionic and Covalent Bonds17.6 Oxidation States and Chemical BondingChapter 17 The Many Electron AtomGoal: Construct the periodic table based on quantum numbers(1) Solve the wave equation exactly for the H atom(2) Use the exact orbitals for the H atom as a starting approximation for the many electron atom(3) Quantum numbers obtained for H atom used to describe the many electron atomThe orbital approximation for a many electron atom:The electrons are described by the same four quantum numbers as the H atom, but the energies of the orbits depend on both n and l (but not on ml)Ground state electron configuration of a many electron atom: Governs reactivity under normal conditionImagine a bare nucleus of charge +ZImagine empty orbitals surrounding the nucleusFill the orbital with Z electrons for the neutral atomTwo Principles:Aufbau principle: fill lowest energy orbital firstPauli exclusion principle: each electron must have four different quantum numbers (maximum of 2 electrons in an orbital).The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of nshell = all orbitals with the same value of nsubshell = all orbitals with the same value of n and lan orbital is fully defined by three quantum numbers, n, l, and mlRelative orbital energies for the multielectron atom.The energy of an orbital of a multielectron atom depends on n and l (but not ml)2s < 2p3s < 3p <3dNote energy levels are getting closer together for n = 3This means that factors ignored may have to be consideredConstructing the periodic table by filling orbitals with electrons.Construction of the first row of the periodic table.Electron configurations.Aufbau: Fill 1s orbital firstPauli: no more than two electrons in the 1s orbitalThe basis of the octet rule: filling a shell1s subshell filled with 2He = stable electron core given symbol [He].Filling the orbitals of 3Li, 4Be and 5BAufbau: Fill 1s orbital