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Chapter 5 Quantum Theory and Electron Configurations Quantum-Mechanical Model of the Atom • Since the Bohr model had a very limited use, a new and very different model of the atom exists • The Quantum Mechanical Model (1926) contains: Quantum energy levels Dual wave/particle nature of electrons Electron clouds • In the new model, don’t know exactly where electrons are - only know probabilities of where they could be Heisenberg Uncertainty Principle • Heisenberg Uncertainty Principle = impossible to know both the velocity (or momentum) and position of an electron at the same time The Quantum Mechanical Model Chapter 5 Quantum Mechanical Model • Einstein (1905) Light consists of quanta, called photons Photoelectric Effect – Sunlight striking a sheet of metal will knock off the outermost electrons and move, causing an electric current • de Broglie (1924) = Photons both particles and waves • Davisson (1927) = Electrons both particles and waves Quantum-Mechanical Model of the Atom • Orbital = region around nucleus where an electron with a given energy level will probably (90%) be found • Four kinds of orbitals s - spherical in shape, lowest orbital for every energy level p - dumbbell shaped, second orbital d - complex “flower” shape, third orbital f - very complex shape, highest orbital s-orbitals • All s-orbitals are spherical. • As n increases, the s-orbitals get larger. p- orbitals • Three p-orbitals: px, py, and pz Lie along the x-, y- and z- axes of a Cartesian system. Dumbbell shaped, gets larger as n increases d and f - orbitals • There are five d and seven f-orbitals. Quantum Mechanical Model • Principle Energy Levels (n) Labeled from 1-7 First energy level is n=1 Contains sublevels (s, p, d and f) • Each energy level contains the number of sublevels equal to it’s value for n – If n=3, there are three sublevels Quantum Mechanical Model • In each sublevel there are atomic orbitals • Atomic orbitals – describe a space where an electron is likely to be found Type of subshell Shape of orbitals Number of orbitals Orbital ‘names’ s Spherical 1 s p Dumbbell 3 px, py, pz d Cloverleaf (and one donut) 5 f Multi-lobed 7 Quantum Mechanical Model • Each orbital can contain two electrons. • Since negative-negative repel, these electrons occupy the orbital with opposite spins. Quantum Mechanical Model • The total number of orbitals of an energy level is n2. For the third principle energy level, n=3, which means there are 9 orbitals • These orbitals are 3s, 3px, 3py, 3pz and the 5 d orbitals • Remember, we no longer think of orbitals as concentric circles, but we can say that n=4 extends farther from the nucleus than n=1. Valence Electrons • Only those electrons in the highest principle energy level Electron Configuration and Orbital Notation • Aufbau Principle – electrons fill lower energy orbitals first, “bottom-up” n=1 fills before n=3 Energ y • Will an electron fill the 1s or the 2s orbital first? 2s 1s 2px 2py 2pz Electron Configuration &Orbital Notation • Hund’s Rule – electrons enter same energy orbitals so that each orbital has one electron before doubling up Each of the first electrons to enter the equal energy orbitals must have the same spin Energ y If we have 7 electrons, how will they fill in the below orbitals? 2s 1s 2px 2py 2pz Electron Configuration and Orbital Notation • Pauli Exclusion Principle – an orbital can contain no more than 2 electrons. Electrons in the same orbital must have different spins. Energ y • If we have 8 electrons, how will they be arranged? 2s 1s 2px 2py 2pz Apartment Analogy • • • • Atom is the building Floors are energy levels Rooms are orbitals Only two people per room Orbital Diagrams • Draw each orbital as a box. • Each electron is represented using an arrow. Up arrows – clockwise spin Down arrows – counter-clockwise spin • Determine the total number of electrons involved. • Start with the lowest energy level (1s) and start filling in the boxes according the rules we just learned. Transition Metal Exceptions • Can move from the highest filled s orbital to create a fully filled, or half filled d or f • TRANSITION METAL EXCEPTIONS Total # of electrons in an Energy Level • 2n2 • n=1 2 x 12 + = 2 • n=2 2 x 22 + = 8 • n=3 2 x 32 + = 18 • • • • n=4 n=5 n=6 n=7 Chapter 5 Orbitals and Energy Levels Principal Sublevels Energy Level Orbitals n=1 1s 1s (one) n=2 2s , 2p 2s (one) + 2p (three) n=3 3s , 3p , 3d 3s (one) + 3p (three) + 3d (five) n=4 4s, 4p, 4d, 4f 4s (one) + 4p (three) + 4d (five) + 4f (seven) Chapter 5 Summary # of Max shapes electrons s p d f Chapter 5 Starts at energy level Orbitals and Energy Levels n=4 Increasing energy n=3 n=2 n=1 1s 2p 2s 3d 3p 3s 4f 4d 4p 4s and so on.... Orbital Diagrams • Orbital diagrams are used to show placement of electrons in orbitals. • Need to follow three rules (Aufbau, Pauli, Hund’s) to complete diagrams Li Be B C N Ne Na Orbital Diagram 4p 3d Energy 4s 3p 3s 2p 2s 1s Electron Configuration • Let’s determine the electron configuration for Phosphorus • Need to account for 15 electrons Chapter 5 Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 3d 4s 3p 3s 2p 2s 1s Chapter 5 5f 4f Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 3d 4s 3p 3s 2p 2s 5f • The first to electrons go into the 1s orbital • Notice the opposite spins • only 13 more 1s Chapter 5 4f Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 3s 2p 4f 3d 4s 3p 5f • The next electrons go into the 2s orbital • only 11 more 2s 1s Chapter 5 Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 3d 4s 3s 2s 3p • The next electrons go into the 2p orbital 2p • only 5 more 1s Chapter 5 5f 4f Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 3d 4s 3s 2s 3p • The next electrons go into the 3s orbital 2p • only 3 more 1s Chapter 5 5f 4f Increasing energy 7s 6s 5s 4s 7p 6p 6d 5d 5p 4d 4p 3p • 3s 2s 1s 2p • • • 5f 4f 3d The last three electrons go into the 3p orbitals. They each go into separate shapes 3 unpaired electrons 1s22s22p63s23p3 Chapter 5 Writing Electron Configuration • Determine the total number of electrons. • Write the principle energy level number as a coefficient, the letter for the subshell, and an exponent to represent the number of electrons in the subshell. • He: 1s2 The Kernel (Noble Gas) Notation • Determine the total number of electrons • Find the previous noble gas and put its symbol in brackets • Write the configuration from that noble gas forward as usual Writing electron configurations • Examples • • • O Ti Br • Core format • • • O Ti Br 1s2 2s2 2p4 1s2 2s2 2p6 3s2 3p6 3d2 4s2 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5 [He] [Ar] [Ar] 2 s 2 2 p4 3d2 4 s 2 3d10 4s2 4p5 Chapter 5 Quantum Numbers • Each electron can be described by four numbers unique to that electron (like a fingerprint) • “n” – the principal quantum # describes the principal energy level, n=1, 2, 3…,7 • “l” – describes the shape of subshell s subshell = 0 p subshell = 1 d subshell = 2 f subshell = 3 • “m” –describes the orientation , m = -l….0….+l • “s” – describes the spin, s=1/2 or -1/2 Quantum Numbers • Example: Look at carbon’s orbital diagram which contains 6 electrons. What are the quantum #s for the last electron to be filled? • Example: Look at Vanadium’s Kernel notation. Do the orbital diagram for only the valence electrons. What are the quantum #’s for the second to last electron to be filled?