Ch_7-4_QM_atoms

Ch_7-4_QM_atoms - FE11 DIFFERENT REPRESENTATIONS OF H 1s...

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E11 DIFFERENT REPRESENTATIONS OF H 1s ORBITAL (GROUND STATE WAVE FUNCTION) 0 / 1 ra s Ae Ψ= 0 2 2/ 2 1 s Ae 0 0.529 a = Å 0 0.5 1 1.5 2 2.5 3 00 . 511 . 522 . 53 99% 4 π r 2 | ψ | 2 0.529A o mp r = 0.7 3 A 9 o r = | ψ | 2 Probability Distance, r, from nucleus (Å)
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( ) ,, l nlm r θϕ Ψ Wave functions for an Atom: 4 quantum numbers are needed to fully specify the state of an electron. E12 l = angular momentum quantum number (number of planar nodes, shape) n = 1, 2, 3, . . . l = 0, 1, 2, 3, . . . n-1 m l = - l , - l +1, . . ., 0, 1, 2, . . ., l n = principle quantum number—energy and size (the larger n, the greater the energy and the bigger the orbital) m l = magnetic quantum number (orientation of orbital) s, p, d, f, . . . n, l , and m l define an electron orbital: m s = electron spin quantum number (orientation of electron) m s = , or -½, +½ Each electron orbital can have up to 2 electrons in it—one spin up and one spin down
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(p x , p y , p z ) (3 p orbita (d xy , d yz , d xz ,d x 2 , d x 2 -y 2 ) ls) (5 d orbitals) (7 f orbitals)
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s Orbitals (s for spherical, l = 0) Radial nodes: 0 1 2 Total nodes = n-1
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p Orbitals (p for peanut, l = 1) 2 p orbitals 1 of the 3 p orbitals
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This note was uploaded on 11/23/2010 for the course CHEM 005 taught by Professor Ellis during the Spring '08 term at NJIT.

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Ch_7-4_QM_atoms - FE11 DIFFERENT REPRESENTATIONS OF H 1s...

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