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chem3322_hwk3 - a and b where b = 2 a Write down the...

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Chem 3322 homework #3 – due Feb. 5, 2010 Problem 1 – particle on a ring The “4n+2 rule” is a well-known rule in organic chemistry: the planar, aromatic form of carbocyclic systems of the type (CH) m ( eg. benzene in the case of m=6) are particularly stable for values of m given by m = 4 n + 2 ( n = 1 , 2 , 3 , . . . ) (1) In other words, m=6, 10, 14, . . . . If the π electrons in these systems are treated as free electrons on a ring, explain how the 4n+2 rule logically follows. Hint: closed-shell systems, that is, in which all energy levels are fully occupied, have enhanced stability in atoms and molecules. Problem 2 – particle in a two-dimensional box Consider a particle in a two-dimensional box of side lengths
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Unformatted text preview: a and b , where b = 2 a . Write down the quantum numbers corresponding to the first 5 energy levels of this system. Note any degeneracies. Problem 3 – particle on a ring The π electrons in benzene can be approximated as particles on a ring. Calculate the diameter of this “electron ring” if it is assumed that a transition occurring at 260.0 nm corresponds to an electron going from n = 3 to n = 4. Compare this diameter to the diameter of a benzene molecule, if you approximate the carbon hexagon with a circle. Problem 4 Do problem P15.32 from the course textbook. 1...
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