Lecture26, 3-14-08

Lecture26, 3-14-08 - The d-Orbitals l = 2(This...

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The d-Orbitals l = 2 (This means “d-orbital”) m l = -2, -1, 0, 1, 2 (This means “five d-orbitals”) Electron densities between axes indicated by subscript Electron densities along axes indicated by subscripts
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Nodal Planes in Orbitals z x y p z orbital xz plane yz plane xy plane z x y d xy orbital
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-2E-17 -1.8E-17 -1.6E-17 -1.4E-17 -1.2E-17 -1E-17 -8E-18 -6E-18 -4E-18 -2E-18 0 03 . 2 Energy (J) Allowed Energies of Hydrogen-Like Atoms The Schrödinger equation can be solved for an electron bound by a nucleus of any charge. What happens with other “Hydrogen-like” nuclei, e.g. He 2+ , N 6+ ? The potential energy function for a nucleus of atomic number (and hence charge) Z is:- V ( r ) = -Z e 2 / r. The allowed energies now become That is, the energy of the bound states is lowered by the increased attraction of the more highly charged nucleus. 24 2 22 2 2 nR mZ e Z EE nn =− h HH e + Li 2+ Hydrogen-like atoms have been created in the laboratory and detected in space, and provide experimental verification of these allowed energies.
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Orbital Energies of Multielectron Atoms • All elements have the same number of orbitals (s,p, d, and etc.). • In hydrogen orbitals with the same n value all have the same energy regardless of l, m l • In other elements there are orbital energy differences as a result of the presence of other electrons in the atom. • The presence of more than one electron changes the energy of the electron orbitals • It is the repulsion of electrons for each other that causes orbitals with different values of l to have different energies
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Degenerate Energy Levels of Hydrogen are Partially Split in Heavier Atoms
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Electron Spin
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Lecture26, 3-14-08 - The d-Orbitals l = 2(This...

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