Lec+13+2015+158a

# Lec+13+2015+158a - F Grieman Hydrogen-like atoms Radial...

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Hydrogen-like atoms Radial Functions Probability: Radial Distribution Function Complete One Electron Wave Functions Begin Multi-electron Atoms: Perturbation Theory F. Grieman 1/14 Exam Friday!!! Closed Book Bring Pencils, No Calculator or Phone 55 minutes, Come by 9:55 a.m. Q&A Tonight, 7:30-9:30 pm

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2/14 Rydberg Constant (Ry) in terms of fundamental constants!!! Classical Turning Pts. n r (Bohr radii) 1 2 2 8 3 18 4 32 4 3 2 1 n
Normalization 1 = < | > = <R|R> < | > < | > Independently || || || normalized 1 1 1 d r 2 dr sin d d limits 0 → ∞ 0→ 0→2 Probabilities P(e) very different than Bohr We will look at R, R*R, r 2 R*R, Y, And then Pd = R*Rr 2 dr Y*Ysin d d 3/14

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Nodes: angular nodes n- -1 radial nodes n-1 total nodes Fall off as -Zr Fall off more slowly As –Zr/2 radial node Fall off even more slowly } Compare position and amplitudes 4/14 R a d i a l W a v e F u n c t i o n s R 2 n, ℓ R a d i a l P r o b.
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