Unit 6 Quantum Mechanics

+ Evolution of Atomic Theory Thomson (plum pudding) Rutherford + electron nucleus + Schrödinger (Quantum Mechanical Model) Bohr (planetary)

Bohr Model a.k.a. planetary model Energy levels A specific area around the nucleus where an e- is likely to be – all e- in the same energy level have the same energy N Valence shell

Bohr Model Pros: Electrons do move around nucleus Electrons exist in energy levels Cons: Electrons do not remain in “orbits”

Electron Configuration Breaking down the electron cloud. Electron hierarchy Energy levels (shells) Subshells (sublevels-s,p,d,f) Orbitals (clouds) Each atom has a certain number of energy levels (same as period number) (Principle Quantum # n) These energy levels contain a certain number of sublevels. (Angular Momentum Quantum # l - shape of the orbital) Each sublevel contains a certain number of orbitals. (n2)

Sublevels The number of sublevels an energy level contains is equal to the energy level number. (Principle Quantum # n) Example: Potassium is in period 4, which means it has 4 energy levels and 4 sublevels: (Principle Quantum # 4) Its 1st energy level has 1 sublevel(s) Its 2nd energy level has 2 sublevels (s,p) Its 3rd energy level has 3 sublevels (s,p,d) Its 4th energy level has 4 sublevels (s,p,d,f) So, potassium has a total of 10 sublevels. By analogy, if an atom is a building, each energy level would be a story. Each sublevel is like a room on that floor.

n = # of sublevels per level n2 = # of orbitals per level Quantum Numbers Principal level n = 1 n = 2 n = 3 Sublevel s s p s p d Orbital px py pz px py pz dxy dxz dyz dz2 dx2- y2 n = # of sublevels per level n2 = # of orbitals per level Sublevel sets: s-1, p-3, d-5, f-7 7

Sublevels Each sublevel has its own shape. (Quantum # l) The shape is based on calculated probability. The first sublevel (s - sharp) is sphere shaped. The second sublevel (p - principal) contains 3 orbitals which are each dumbbell shaped and follow the X, Y or Z axis.

Sublevels The third sublevel (d - diffuse) contains 5 orbitals which are each cloverleaf shaped except the last one which is like a dumbbell with a ring. Magnetic Quantum Number ( ml ) Orientation of orbital Specifies the exact orbital within each sublevel Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem 9

Sublevels The fourth sublevel (f - fundamental) is too complex to draw in 2D. Atomic orbital – the shape of space in which an e- of a given energy level is likely to be.

P S D F Sublevels The Periodic Table breaks down into 4 blocks. Each block represents one of the shapes or sublevels. That is the shape of the outer sublevel of the valence shell. P S D F

P S D F Sublevels Each sublevel has a number! Numbering sublevels : s & p # = Period # d # = Period # – 1 f # = Period #- 2 P S D F

Sublevels - Practice What is the name of the sublevel containing the outermost electron in the following elements? Lithium 2s Sulfur 3p Iron 4s 6s Erbium

Electron Filling 1.Aufbau Principle Electrons are assigned to energy levels, sublevels and orbitals based on three principles or rules. 1.Aufbau Principle Electrons enter the lowest energy level available. Not necessarily in numerical order. Example: 3s  3p  4s  3d Within an energy level, the s sublevel has the least energy, then p, then d, then f.

Aufbau The Aufbau diagram follows the Periodic Table read left to right, top to bottom. Lower energy fills up first. Note: the valence electrons are in the energy level with the highest number. Therefore Zirconium’s valence are in 5s, not 4d. P S D F

2. Pauli Exclusion Principle Each orbital can contain only 2 electrons. Therefore, sublevel # of orbitals total electrons held s 1 2 e- p 3 6 e- d 5 10 e- f 7 14 e- Total e- is also equal to the number of elements in one row of that block. (Formula 2n2 will tell the # of electrons for that energy level) Example: 1s contains two elements: H & He 2p contains six elements: B, C, N, O, F & Ne etc.

Electron spin Each e- revolves around the nucleus and rotates on its axis. They can rotate clockwise or counterclockwise. The spins are represented by arrows: Opposite spins will attract, like spins will repel. This is why a orbital cannot contain more than 2 e-.

Quantum Numbers Spin Quantum Number ( ms ) Electron spin  +½ or -½ An orbital can hold 2 electrons that spin in opposite directions. 18

3. Hund’s Rule When filling a sublevel that has multiple orbitals (p, d, f), put one e-, having the same spin, in each orbital until each has one, then start doubling up.

Electron Filling You must draw all the orbitals for a sublevel, even if they aren’t occupied. The reason is because the sublevels and orbitals represent probability. The orbitals show where the e- is likely to be, not necessarily where it is.

Summary!

Writing electron configurations: 1) Each electron that is added to an atom is placed in the lowest‐energy orbital that is available. (Aufbau) The orbitals are filled in the order which is read off the periodic table when reading in order of atomic number: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f 2)Each orbital can hold no more than two electrons. Two electrons in the same orbital must have opposite spins (the Pauli exclusion principle). 3)If two or more orbitals are available at the same energy level and same sublevel (degenerate orbitals), one electron is placed in each orbital until the available orbitals are occupied by one electron. Remember one electron in each orbital before you double up. (Hund’s Rule)

Writing Shorthand Method of writing e- configuration by skipping the boxes and arrows and just using numbers and letters. Example: Carbon 1s22s22p2 # e- in orbital E level 1s2 Orbital shape

Writing Shorthand - Practice For each element, write its e- configuration in shorthand. Lithium 1s22s1 Sulfur 1s22s22p63s23p4 Iron 1s22s22p63s23p64s23d6 Erbium 1s22s22p63s23p64s23d104p65s24d105p66s24f12

Identify that element 1s22s22p63s23p64s23d9 Copper 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p6 Radon Magnesium 1s22s22p63s2

Noble Gas Shorthand Electron configurations can get lengthy. We can shorten using noble gas. Sulfur 1s22s22p63s23p4 Neon 1s22s22p6 Sulfur [Ne] 3s23p4

Writing Noble Gas Shorthand - Practice For each element, write its e- configuration in noble gas shorthand. Beryllium [He]2s2 Arsenic [Ar]4s23d104p3 Silver [Kr]5s24d9 Lead [Xe]6s24f145d106p2

Drawing orbital diagram Though you have to be able to draw the s, p, d, & f shapes on the test, there’s a faster way to draw the e- configuration. Steps for drawing orbital diagram: 1. Using Aufbau, draw a set of boxes to represent the sublevel (s = 1, p = 3, d = 5, f = 7) 2. Using Pauli and Hund, fill the boxes with arrows to represent the electrons. 3. Keep going until all e- used up. Example: Carbon 1s 2s 2p

Drawing orbital diagrams - practice For each element, draw the boxes and arrows. Make sure to draw all the boxes for a sublevel (even if they’re not used) and write the name of the sublevel above or below each set of boxes. 1s 2s Lithium 1s 2s 2p 3s 3p Sulfur 1s 2s 2p 3s 3p 4s 3d Iron

Identify that element 1s 2s 2p 3s 3p 4s Calcium 1s 2s 2p 3s 3p 4s 3d Bromine

Noble Gas Notation Electron configurations can get lengthy. We can shorten using noble gas. 1s 2s 2p 3s 3p Sulfur 1s 2s 2p Steps for noble gas Find previous noble gas Put noble gas in brackets Write e- config. for the rest Neon 3s 3p Sulfur [Ne]

Noble e- configurations - practice For each element, draw the boxes and arrows. Make sure to draw all the boxes for a sublevel (even if they’re not used) and write the name of the sublevel above or below each set of boxes. 4s 3d Titanium [Ar] 5s 4d 5p Iodine [Kr] 7s 5f Uranium [Rn]

Ions Can draw e- configurations (boxes and arrows) and write shorthand and quantum numbers for ions just like for neutral (ground state) atoms. Only difference is ions have gained or lost e- 3s 3p S [Ne] [Ne] 3s23p4 3s 3p S2- [Ne] [Ne] 3s23p6 gained 2e-

Ions - Practice Draw e- configurations (boxes and arrows) and write shorthand and quantum numbers (outermost subshell only) Ga3+ from Ga 4s 3d 4p Ga [Ar] Ga: [Ar] 4s23d104p1 Ga3+ : [Ar] 3d10 lost 3e- from highest numbered energy level The highest numbered energy level contains the bonding electrons or valence electrons.

A Lewis symbol (Lewis dot diagram) is a symbol in which the electrons in the valence shell (outer energy level) of an atom or simple ion are represented by dots placed around the letter symbol of the element. Each dot represents one electron. Negative ions gain electrons and positive ions lose electron.

Lewis Dot Diagrams: Number of valence electrons is equal to group #. 1 2 3 4 5 6 7 8 I II III IV V VI VII VIII Hydrogen Oxygen Chlorine Chloride ion Cl‐1