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lecture3 - 4 Lecture 3 II Where are the electrons in atoms...

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4 Lecture 3, January 18, 2008 II. Where are the electrons in atoms? A. Schrödinger wave equation 1. Ψ = wavefunction; the function of a moving electrons, treated as a standing wave. 2. Heisenberg: probability is more important that the actual value of Ψ . The probability of the wavefunction is related to Ψ 2 ; while Ψ can be either positive or negative, Ψ 2 is always positive (which is consistent with the fact that probability cannot be negative). 3. It's easier to express wavefunctions in three dimensions in polar coordinates: z = r cos " x = r sin " cos # y = r sin " sin # where θ = the angle from the z axis and φ = the angle from the x axis. 4. Schrödinger's wave equation Ψ can be broken up into two separate functions: one that depends only on the distance of the electron from the nucleus (R) and one that depends only on the angle of the electron with respect to the x, y, and z axes (Y): " n , l , m r , # , $ ( ) = R n , l r ( ) Y l , m # , $ ( ) Notice the subscripts on each function; there are multiple solutions to the wavefunction that will give acceptable energies as determined experimentally from atomic line spectra. The
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