Understanding Quantum Numbers in Chemistry

1. November 2, 2009 EXAM #3 HAS BEEN MOVED TO MONDAY, NOVEMBER 9TH Bring a Periodic Table to class this week

2. Four Quantum Numbers • n (1,2, …) size/energy of the orbital • l (0,1,2,…) shape of the orbital- s,p,d,f… • ml (-l to l) orientation of the orbital • ms (- ½, ½) spin up/down (magnetic moment) • How do we know these things? Absorption and emission spectra- electron energies Zeeman effect- spectrum splits when magnetic field applied; separates orbitals at the same energy level and led to discovery of electron spin

3. Electron Spin is the Source of Magnetism in Materials • Diamagnetic • Paramagnetic • Ferromagnetic (“real magnets”)

4. Pauli Exclusion Principle • No two electrons in an atom can have the same 4 quantum numbers • n, ℓ, mℓ define an orbital • Therefore: an orbital can hold two electrons, with opposite spins because ms can only be +1/2 or -1/2

5. Orbital Energies Only depends on distance from the nucleus • Electron-electron repulsion affects energy • Different for different orbital shapes

6. 3d ___ ___ ___ ___ ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 3 2 1s ___ 1 ENERGY 4f ___ ___ ___ ___ ___ ___ ___ 4d ___ ___ ___ ___ ___ 4p ___ ___ ___ 4s ___ 4 • For most atoms: • Energy increases as n increases: • 1 < 2 < 3 < 4 … • Energy increases as subshells go from s < p < d < f • At the same main shell level, a p orbital will be at a higher energy than an s orbital

7. Rules for filling orbitals • Pauli Exclusion Principle No two electrons can have the same 4 quantum numbers An orbital has a maximum of 2 electrons of opposite spin • Aufbau/Build-up Principle Lower energy levels fill before higher energy levels • Hund’s Rule Electrons only pair after all orbitals at an energy level have 1 electron • Madelung’s Rule Orbitals fill in the order of the value of n + l

8. Orbital Filling Order

9. Electron Configurations General Rule: electrons fill lowest energy orbitals first Sodium, Na as an example Na has 11 electrons. Fill 2 electrons per orbital till you run out A box represents an orbital. A arrow represents an electron.