11_Hatom_new

01 3 2 typical cartesian 3d orbitals definition of

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Unformatted text preview: in most texts dx2y2 dxy 18 9/30/2013 , ℓ, ℓ, Electron Spin and the Quantum Number Stern-Gerlach Experiment • • • beam of silver atoms in inhomogeneous magnetic field splits into two beams Ag [Kr]4d105s1 has no orbital angular momentum Since the beam can be split by an inhomogeneous magnetic field, there must be some other form of angular momentum which we call “spin”. Silver atoms have only spin angular momentum 19 9/30/2013 One More Quantum Number, Spin There is one more quantum number, but it doesn’t fall out of the theory we have been doing. You need Dirac’s relativistic theory (beyond the scope of this course). Instead, the concept of spin is introduced empirically by the Stern-Gerlach experiment. Electron Spin Eigenvalues 1 , 1/2 , , 1/2 spin quantum number 1/2 projection of spin on z-axis with or against a field The magnetic moment of the electron is called B the Bohr magneton. Atoms have Hydrogen-Like Wavefunctions Hyperchem demo: ab initio calculation on a Cl atom looking at orbitals. Do they look like H-atom orbitals? Cl 2p orbital Z=nuclear charge, doesn’t have to be 1 Hydrogen-like Radial Wavefunctions (n l 1)! 2 Z Rnl (r ) 2n[(n l )!]3 na0 l 3 / 2 2Zr r l e Zr /( na0 ) L2ll1 n na0 20 9/30/2013 Hydrogen Atom nlm (r , , ) Rnl (r )Yl m ( , ) where (n l 1)! 2 Rnl (r ) 2n[(n l )!]3 na0 (2l 1)(l m )! Yl ,m ( , ) 2(l m )! principle quantum number azimuthal quantum number magnetic quantum number l 3 / 2 2r r l e r /( na0 ) L2ll1 n na0 eq. 6.47 1/ 2 Pl|m| (cos ) 0 1,2,3 … ℓ 1 0, 1, 2, … 1 im e 2 eq. 6.30 almost ℓ Hydrogen-Like Orbitals – Add Z (n l 1)! 2 Z Rnl (r ) 2n[(n l )!]3 na0 rn 2Zr r l e Zr /( na0 ) L2ll1 n na0 n 2 a0 1 ( 1...
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This document was uploaded on 01/19/2014.

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