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Quantum Mechanics and Atomic Orbitals Bohr and Einstein particle nature of light DeBroglie wave nature of particles Schrödinger theoretical descriptions of atoms quantum or wave mechanics wave function = every allowed e- state has unique to calculate energy use Ĥ Ĥ=E Ĥ=E wave functions energies E 2 = probability distribution probability of finding an e- in H at a particular distance from the nucleus solved for hydrogen orbital orbital requires 3 quantum numbers n l ml magnetic -l, …, l orientation angular momentum 0, 1, 2, …, (n - 1) shape principal 1, 2, 3, … size and energy “address” orbital requires 3 quantum numbers n l ml principal quantum number size energy as n increases orbitals become larger e- is further from the nucleus n=1 n=2 n=3 n=4 n=5 n=6 n=7 orbital requires 3 quantum numbers n l ml angular momentum shape 0 n - 1 n=1 l=0 designated by letters n = 2 l = 0, 1 l = 0 s orbital n = 3 l = 0, 1, 2 l = 1 p orbital n = 4 l = 0, 1, 2, 3 l = 2 d orbital l = 3 f orbital n=1 n=2 n=3 n=4 l=0 l = 0, 1 l = 0, 1, 2 l = 0, 1, 2, 3 designated by letters l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital s p n=1 n=2 n=3 n=4 n=5 n=6 n=7 d f orbital requires 3 quantum numbers n l ml magnetic quantum number -l,…, l s row s n=3 l=0 n=1 l=0 m=0 1 p s l=1 n=2 l=0 m=0 1 p l = 1 m = -1 d m=0 3 l=2 m=1 1 s orbital 3 p orbitals 5 d orbitals m=0 1 m = -1 m=0 3 m=1 m = -2 m = -1 5 m=0 m=1 m=2 1 s orbital 3 p orbitals 5 d orbitals each orbital holds 2e- 4th quantum number ms spin 7 f orbitals s p n=1 n=2 n=3 n=4 n=5 n=6 n=7 d f 2 1s orbital spherical 2 2s and 3s dumbbell shape 3p, 4p, 5p etc. 1p orbital 2p orbitals 3 similar shapes larger 3 d orbitals 5 cloverleaf larger n same shapes larger Polyelectronic Atoms Pauli exclusion principle no 2 electrons same 4 quantum numbers lowest energy orbitals fill first 1s orbital is lowest energy H 1e- 1s1 He 2e- 1s2 which orbital fills next? 2s 2p 3s 3p 4s where is 3d? 1s 2s 2px 2py 2pz 3s 3px 3py 3pz 4s 3d 3d 3d 3d 3d H He Li Be B C N O F Ne Na [Ne] Hund’s rule parallel spins 4s 3dxz 3dyz 3dxy 3dx2-z2 3dz2 4px K [Ar] Ca [Ar] Sc [Ar] Ti [Ar] V [Ar] half full shell stable Cr [Ar] Mn [Ar] full shell stable Cu [Ar]