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200902 - 1 Chem 104A UC Berkeley Electron motion...

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Unformatted text preview: 1 Chem 104A, UC, Berkeley Electron motion: wavefunction ψ Schrodinger wave equation (1926): nergy potrntiale V y totalenerg E s Planck h mass m s coordinate z y x ion eigenfunct on wavefuncti E V z y x m h : : ' : : : , , / : ) ( 8 2 2 2 2 2 2 2 2 ψ ψ ψ ψ ψ ψ π = + ∂ ∂ + ∂ ∂ + ∂ ∂ − ∧ ∧ = H E H ψ ψ : Hamiltonian operator Describes spatial properties of electron. Must be: single valued, continuous, normalized Chem 104A, UC, Berkeley Converting to polar coordinates: ) , ( ) ( , , , , φ θ ψ l l m l l n m l n Y r R ⋅ = ) ( , r R l n ) , ( , φ θ l m l Y Radial part Angular part 2 Chem 104A, UC, Berkeley n=1,2,3,4….= principle quantum number (1): determine the energy of the electron (2): indicate approximately the effective volume of the orbital. 2 2 2 4 2 2 2 2 n k h n e m r e E e n n − = − = − = π n=1 2 3 Chem 104A, UC, Berkeley l = angular momentum (or shape) quantum number 0,1,2,3,4…… s, p, d, f….....
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200902 - 1 Chem 104A UC Berkeley Electron motion...

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