1. Quantum Mechanics and Atomic Orbitals Bohr and Einsteinparticle nature of light DeBrogliewave nature of particles Schrödinger theoretical descriptions of atoms Heisenberg Dirac quantum or wave mechanics wave function =  every allowed e - state has unique  to calculate energyuse Ĥ Ĥ Ĥ  = E 

2. solved for hydrogen wave functions energies  2 = probability distribution Ĥ Ĥ  = E   E probability of finding an e - in H at a particular distance from the nucleus orbital

3. requires3 quantum numbers n lmlml principal 1, 2, 3, … size and energy angular momentum 0, 1, 2, …, (n - 1) shape magnetic -l, …, l orientation “address”

4. orbitalrequires 3quantum numbers n lmlml principal quantum numbersize energy as n increasesorbitals become larger e - is further from the nucleus n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

5. orbitalrequires 3quantum numbers n lmlml angular momentumshapen - 1 n = 1l = 0 n = 2 l = 0, 1 n = 3 l = 0, 1, 2 n = 4 l = 0, 1, 2, 3 designated by letters l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital 0 

6. n = 1l = 0 n = 2 l = 0, 1 n = 3 l = 0, 1, 2 n = 4 l = 0, 1, 2, 3 designated by letters l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 s p d f

7. orbitalrequires 3quantum numbers n lmlml magnetic quantum number-l,…, l n = 1l = 0m = 0 n = 2l = 0m = 0 l = 1m = -1 m = 0 m = 1 n = 3l = 0m = 0 l = 2 l = 1m = -1 m = 0 m = 1 m = -2 m = -1 m = 0 m = 1 m = 2 rows s p s p d 1 1 3 3 1 51 s orbital 3 p orbitals 5 d orbitals

8. 1 s orbital 3 p orbitals 5 d orbitals n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 p d f s each orbital holds 2e - 4 th quantum number msms f orbitals 7 spin  

9. 1s orbital spherical 22 2s and 3s 22

10. 1p orbital 2p orbitals3 dumbbell shape 3p, 4p, 5p etc.similar shapeslarger

11. d orbitals3 5 cloverleaf larger n same shapeslarger

12. Pauli exclusion principle Polyelectronic Atoms no 2 electrons same 4 quantum numbers lowest energy orbitalsfill first 1s orbital is lowest energy H1e - 1s11s1 He2e - 1s21s2   which orbital fills next? 2s2s 2p2p 3s3s 3p3p 4s4swhere is 3d?

13. 1s 2s 2p x 2p y 2p z 3s 3p x 3p y 3p z 4s 3d 3d 3d 3d 3d H He Li Be B C no! Hund’s ruleparallel spins N O F Ne Na [Ne]

14. K [Ar] 4s4s 3d xz 3d xy 3d yz 3d x2-z2 3d z2 4px4px Ca [Ar] Sc [Ar] Ti [Ar] V Cr [Ar] no half full shellstable Mn [Ar] Cu [Ar] no full shell stable