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Quantum Mechanics and Atomic Orbitals

Quantum Mechanics and Atomic Orbitals. Bohr and Einstein. particle nature of light. DeBroglie. wave nature of particles. theoretical descriptions of atoms. Schr ödinger . Heisenberg. quantum or wave mechanics. Dirac. = . wave function. has unique . every allowed e - state.

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Quantum Mechanics and Atomic Orbitals

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

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

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

  4. 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

  5. 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 s orbital l = 0 n = 3 l = 0, 1, 2 p orbital l = 1 n = 4 l = 0, 1, 2, 3 d orbital l = 2 f orbital l = 3

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

  7. orbital requires 3 quantum numbers n l ml magnetic quantum number -l,…, l s row s 1 n = 3 l = 0 m = 0 n = 1 l = 0 m = 0 1 p s l = 1 m = -1 n = 2 l = 0 m = 0 1 3 m = 0 p l = 1 m = -1 m = 1 d 3 m = 0 l = 2 m = -2 m = 1 m = -1 1 s orbital 5 m = 0 3 p orbitals m = 1 5 d orbitals m = 2

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

  9. 2 1s orbital spherical 2 2sand3s

  10. 1p orbital dumbbell shape 2p orbitals 3 3p, 4p, 5p etc. similar shapes larger

  11. 3 d orbitals 5 cloverleaf larger n same shapes larger

  12. Polyelectronic Atoms Pauli exclusion principle same 4 quantum numbers no 2 electrons lowest energy orbitals fill first 1sorbital is lowest energy  H 1e- 1s1 2s He 2e- 1s2   2p 3s which orbital fills next? 3p 4s where is 3d?

  13. 1s 2s 2px 2py 2pz 3s 3px3py3pz 4s 3d 3d 3d 3d 3d H He Li Be no! Hund’s rule parallel spins B C N O F Ne Na [Ne]

  14. 4s 3dxy 3dx2-z2 3dz2 4px 3dxz 3dyz K [Ar] Ca [Ar] Sc [Ar] Ti [Ar] half full shell stable V [Ar] no Cr [Ar] Mn [Ar] stable full shell Cu [Ar] no

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