chem120a_ps6_sp07

chem120a_ps6_sp07 - Chem 120A Problem Set 6 Out: Wed. March...

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Chem 120A Problem Set 6 Out: Wed. March 28, 2007; Due: Fri. April 6, 2007 1. a) Starting with the radial Schr¨odinger equation for the hydrogen atom and a guessed solution of the form R ( r ) = ( 1 + br ) e - ar (1) find a and b such that this solution works. b) Normalize the solution in a). c) Find < r > for this solution. d) Find the values of r where the radial probability density is maximal. 2. The first line in the Lyman series of spectral lines for the Hydrogen atom corresponds to the n = 1 n = 2 transition. a) If the interaction between radiation and the electron is V = e E · r = e ( E x x + E y y + E z z ) , which ( n , l , m ) states mix with the state ( 1 , 0 , 0 ) to give this absorption line (the Lyman α line)? (Hint: review the discussion on selection rules in Ratner and Schatz, Ch. 4.5.) b) What is its wavelength? c) In which region of the electromagnetic spectrum is this line found?
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chem120a_ps6_sp07 - Chem 120A Problem Set 6 Out: Wed. March...

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