1

Quantum Mechanics Orbital (“electron cloud”) Region in space where there is 90% probability of finding an electron 90% probability of finding the electron Orbital Electron Probability vs. Distance 40 30 Electron Probability (%) 20 10 50 100 150 200 250 Distance from the Nucleus (pm) Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 2

Orbitals The location of an electron is described with 4 terms. - Energy Level - Sublevel - Orbital - Spin

Energy Level Describes the energy and distance from the nucleus. Whole numbers, ranging from 1 to 7.

Orbital Shapes – s sublevel S for Sphere An orbital can contain up to 2 electrons. The s sublevel contains only 1 orbital.

P Sublevel P for Petal or Peanut 3 orbitals present in this sublevel. Each orbital can only have 2 electrons.

D Sublevel D for Double-Petal 5 orbitals present in this sublevel.

F Sublevel F for Flower 7 orbitals present in this sublevel.

s sublevel p sublevel d sublevel f sublevel

Total # of electrons in Energy Level Summary Energy Level Sublevels Present # of Orbitals Total # of electrons in Energy Level 1 2 3 4

Arrangement of E- Electrons are arranged according to a few rules. Aufbau Principle Pauli’s Exclusion Principle Hund’s Rule

Aufbau Principle As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to orbitals Electrons fill in low energy orbitals before high energy orbitals

Aufbau Principle Increasing energy He with 2 electrons 1s 2s 3s 4s 5s 3d 4d 5d 7p 6d 4f 5f He with 2 electrons * orbital energy order found on periodic table

s sublevel p sublevel d sublevel f sublevel

Pauli’s Exclusion Each orbital can only hold 2 electrons and they will have opposite spins. Example

Hund’s Rule When there are multiple orbitals, one electron goes in each before pairing takes place.

Orbital Notation Orbital Notation shows the energy level, sublevel, orbital, and spin for every electron in an atom.

Practice Step 1: Start by drawing out the orbitals in the correct order. Step 2: Determine the total number of electrons.

Practice Step 3: Start arranging the electrons Step 4: Follow the rules!

Quantum Numbers Four Quantum Numbers: Specify the “address” of each electron in an atom UPPER LEVEL Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 21

Quantum Numbers Principal Quantum Number ( n ) Angular Momentum Quantum # ( l ) Magnetic Quantum Number ( ml ) Spin Quantum Number ( ms ) Schrödinger used three quantum numbers (n, l, and ml) to specify any wave functions. • Quantum numbers provide information about the spatial distribution of the electron. 22

Quantum Numbers 1. Principal Quantum Number ( n ) Energy level Size of the orbital A whole number 1-7 1s 2s s Orbitals – Orbitals with l = 0 are s orbitals and are spherically symmetrical, with the greatest probability of finding the electron occurring at the nucleus. – All orbitals with values of n > 1 and l  0 contain one or more nodes. – Three things happen to s orbitals as n increases: 1. they become larger, extending farther from the nucleus 2. they contain more nodes 3. for a given atom, the s orbitals become higher in energy as n increases due to the increased distance from the nucleus 3s Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 23

Quantum Numbers f d s p 2. Angular Momentum Quantum # ( l ) Energy sublevel Shape of the orbital f = 3 d = 2 f d S = 0 P=1 s p Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 24

Quantum Numbers 3. Magnetic Quantum Number ( m ) Orientation of orbital Specifies the exact orbital within each sublevel m = A number from –l to +l Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 25

d-orbitals Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 336 26

Quantum Numbers 4. Spin Quantum Number ( s) Electron spin  +½ or -½ An orbital can hold 2 electrons that spin in opposite directions. Analyzing the emission and absorption spectra of the elements, it was found that for elements having more than one electron, nearly all the lines in the spectra were pairs of very closely spaced lines. Each line represents an energy level available to electrons in the atom so there are twice as many energy levels available than predicted by the quantum numbers n, l, and ml. Applying a magnetic field causes the lines in the pairs to split apart. Uhlenbeck and Goudsmit proposed that the splittings were caused by an electron spinning about its axis. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 27

Quantum Numbers Pauli Exclusion Principle No two electrons in an atom can have the same 4 quantum numbers. Each electron has a unique “address”: Wolfgang Pauli 1. Principal #  2. Ang. Mom. #  3. Magnetic #  4. Spin #  energy level sublevel (s,p,d,f) orbital electron Wolfgang Pauli determined that each orbital can contain no more than two electrons. Pauli exclusion principle: No two electrons in an atom can have the same value of all four quantum numbers (n, l, ml , ms). By giving the values of n, l, and ml, we specify a particular orbit. Because ms has only two values (+½ or -½), two electrons (and only two electrons) can occupy any given orbital, one with spin up and one with spin down. Pauli's Exclusion Principle. Put bluntly, this states that "No two electrons in one atom can have the same values for all four quantum numbers". (My interpretation of the Principal and not a direct quote) This essentially means that a maximum of only two electrons can occupy a single orbital. When two electrons occupy an orbital they must have opposed spin (i.e. different values for the spin quantum number). We are now beginning to see how the electronic configuration of the elements is built up. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 28

Allowed Sets of Quantum Numbers for Electrons in Atoms Level n 1 2 3 Sublevel l Orbital ml Spin ms 1 -1 2 -2 = +1/2 = -1/2 Allowed Sets of Quantum Numbers for Electrons in Atoms 29