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 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 Will an electron fill the 1s or the 2s orbital first? Energy 2px 2py 2pz 2s 1s

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 If we have 7 electrons, how will they fill in the below orbitals? Energy 2px 2py 2pz 2s 1s

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. If we have 8 electrons, how will they be arranged? Energy 2px 2py 2pz 2s 1s

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 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 Orbitals Energy Level 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 shapes Max electrons Starts at energy level s p d f Chapter 5

Orbitals and Energy Levels 4p 4d 4f n = 4 and so on.... 3s 3p 3d n = 3 Increasing energy 2s 2p n = 2 1s n = 1

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 2s 1s 3s 4s 2p 3p 4p 3d Energy

Electron Configuration Let’s determine the electron configuration for Phosphorus Need to account for 15 electrons Chapter 5

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p Chapter 5

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p The first to electrons go into the 1s orbital Notice the opposite spins only 13 more Chapter 5

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p 3s 2p The next electrons go into the 2s orbital only 11 more Chapter 5

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p The next electrons go into the 2p orbital only 5 more Chapter 5

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p The next electrons go into the 3s orbital only 3 more Chapter 5

Increasing energy 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 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 1s2 2s2 2p4 Ti 1s2 2s2 2p6 3s2 3p6 3d2 4s2 Br 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5 Core format O [He] 2s2 2p4 Ti [Ar] 3d2 4s2 Br [Ar] 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?