1Chem C1403 Lecture 11. Wednesday, October 12, 2005End of Chapter 16, into Chapter 17Electron configurations of multielectron atoms andthe periodic properties of atoms.Magic (Quantum) numbers from the solutions of thewave equation: orbitals of the H atom: n, l and ml.The size, shape and orientation of orbitalsElectron spinMultielectron atomsElectron configurations of multielectron atoms2l = 0, s orbital;l = 1, p orbital;l = 2, d orbital;l = 3, f orbitalRelative energies of theorbitals of a one electronatom:1s << 2s = 2p < 3s = 3p = 3d,etc.Shorthand notation (nicknames) for orbitals:All orbitals of the samevalue of n have the sameenergy!3For a one electron atomthe energy of anelectron in an orbitalonly depends on n.Thus,1s (only orbital)2s = 2p3s = 3p = 3d4s = 4p = 4d = 4f4The relative energies of orbitals of the H atom follow the samepattern as the energies of the orbits of the H atom.4s, 4p, 4d, 4f3s, 3p, 3d2s, 2p1sSchroedingerH atomBohr H atom5n determines sizeand energy;l determines shape;ml determinesorientationns orbitalsnp orbitals Obital: A wavefunction defined by the quantum numbers n,l and ml (which are solutions of the wave equation)An orbital is a region of space occupied by an electronOrbitals has energies, shapes and orientation in space6Fig 16-19The hydrogen s orbitals (solutions to theSchroedinger equation)Value of Ψ as a function of thedistance r from the nucleusProbability of finding anelectron in a spherical shell orradius r from the nucleus(Ψ24π r2). r2 captures volume.Radius of 90%Boundary sphere:r1s = 1.4 År2s = 3.3 År3s = 10 Å7Electronprobability xspace occupiedas a function ofdistance fromthe nucleusThe larger thenumber of nodesin an orbital, thehigher the energyof the orbital8Nodes in orbitals: 2p orbitals:angular node that passes through thenucleusOrbital is “dumb bell” shapedImportant: the + and - that is shownfor a p orbital refers to themathematical sign of thewavefunction, not electric charge!Important: The picture of an orbitalrefers to the space occupied by aSINGLE electron.pxpypz9Nodes in 3d orbitals:two angular nodes thatpasses through thenucleusOrbital is “four leafclover” shapedd orbitals are important formetals(Chapter 19)d orbitals10Fig 16-21The five d orbitals of a one electron atom11The f orbitals of a one electron atomThis is getting a little complicated!12A need for a fourth quantum number: electron spinA beam of H atoms inthe 1s state is split intotwo beams when passedthrough a magneticfield. There must betwo states of H whichhave a different energyin a magnetic field.Conclusion: one morequantum number isneeded.13The fourth quantum number: Electron Spin(spin up)(spin down)Spin: a fundamental property of electrons, like charge and mass.Spin: another manifestation of angular momentum at the quantumlevel!ms = +1/2 (spin up) or -1/2 (spin down)14A singlet state:one spin up, one spindownA triplet state:both spins up orboth spins downTwo electron spins can “couple” with one another toproduce singlet states and triplet states.15An empty orbital is fully described by the three quantumnumbers: n, l and mlAn electron in an orbital is fully described by the fourquantum numbers: n, l, ml and msTwo electrons in a single orbital must havedifferent values of msThis statement demands that if there are twoelectrons 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 Principle16Shells and subshells define energy of theelectrons in atoms.17Magic numbers of electronsPauli Exclusion Principle says in effect that no twoelectrons in the same atom can have the same fourquantum numbers (states) this leads to a 2(n)2 rulefor the number of electrons in a given shell:n=1 2en=2 8en=3 18en=4 32n=5 50Wolfgang PauliNobel Prize for 1945 for the discovery of the Exclusion Principle18Exercises using quantum numbers:Are the following orbitals possible orimpossible?(1) A 2d orbital(2) A 5s orbital19The possible values of l can be range from n - 1 to 0.(1) Is a 2d orbital possible?If n = 2, the possible values of l are 1 (= n -1) and 0.The first d orbitals are possible for n = 3.This means that 2s (l = 0) and 2p (l = 1) orbitals arepossible, but 2d (l = 2) is impossible.20(2) Is a 5s orbital possible?For n = 5, the possible values of l are 4 (g), 3 (f), 2(d), 1 (p) and 0 (s).So 5s, 5p, 5d, 5f and 5g orbitals are possible.21Is the electron configuration 1s22s3 possible?The Pauli exclusion principle forbids anyorbital from having more than twoelectrons under any circumstances.Since any s orbital can have a maximum of twoelectrons, a 1s22s3 electronic configuration isimpossible, since 2s3 means that there areTHREE electrons in the 2s orbital.22Summary of quantum numbers and their interpretation23Summary: The energy of an orbital of a hydrogen atom or anyone electron atom only depends on the value of nEach shell of QN = ncontains n subshellsn = 1, one subshelln= 2, two subshells, etcEach subshell of QN = l,contains 2l + 1 orbitalsl = 0, 2(0) + 1 = 1l = 1, 2(1) + 1 = 3shell = 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 ml24Chapter 17 Many-Electron Atoms andChemical Bonding17.1 Many-Electron Atoms and thePeriodic Table17.2 Experimental Measures of OrbitalEnergies17.3 Sizes of Atoms and Ions17.4 Properties of the Chemical Bond17.5 Ionic and Covalent Bonds17.6 Oxidation States and ChemicalBonding25The Original Periodic Table26Learning Goals: Construct the periodic tablebased on quantum numbers Solve the wave equation exactly for the HatomUse the exact orbitals for the H atom as astarting approximation for the manyelectron atomUse quantum numbers obtained for H atom used todescribe the many electron atom and build theelectron configurations of atoms: periodic table27Quantum mechanics: makes quantitative, experimentallyverifiable prediction about the properties of one electron,hydrogen orbital like atoms: atomic sizes, oxidation statesand bonding through out the periodic table.The orbital approximation: The electron density of anisolated many-electron atom is approximately the sumof the electron densities of each of the individualelectrons taken separately.For atoms with more than one electron,approximations are required in order to makequantitative quantum mechical approximations.28The Pauli exclusion principle and magic number ofelectrons.Two equivalent