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3890ps10_10 - Physical Chemistry I Chem 3890 Fall 2010...

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Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 10 Fall 2010 Due: in class, Monday, November 29 Last revised: November 19, 2010 Additions/corrections: Problem 1 Consider the states of the H atom (no spin) with principal QN n = 20. 1. Use Mathematica (see www.chem.cornell.edu/gse1/3890_hydogenic_wfs.nb ) to calculate a Table of expectation values ( r 2 ) nlscript for n = 20, lscript = 0 , 1 ,...,n - 1. The quantity radicalbig ( r 2 ) nlscript is a measure of the effective size of the atom in the different lscript states. How does radicalbig ( r 2 ) nlscript depend on lscript (qualitatively)? 2. Make plots of the radial probability distribution P n,lscript ( r ) vs r for lscript = 0 and lscript = n - 1 = 19 (2 plots). Be sure to take the range of r large enough to see the full structure of P . (Measure r in atomic units [Bohr radii, a 0 ].) We now proceed to estimate the expectation values for the smallest ( lscript = 0) and largest ( lscript = n - 1) values of lscript , respectively.
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