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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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