chem3322_hwk3_soln - Chem 3322 homework#3 solutions out of...

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Chem 3322 homework #3 solutions – out of 25 marks Problem 1 – 5 marks 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. solution: All levels are doubly degenerate except for the ground state. Since two (spin-paired) electrons can fit into each state, the ”closed-shell” configurations have 2, 6, 10, 14, ... electrons, i.e. 4n+2. Problem 2 – 8 marks Consider a particle in a two-dimensional box of side lengths a and b , where b = 2 a . Write down the quantum numbers corresponding to the first 5 energy levels of this system. Note
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chem3322_hwk3_soln - Chem 3322 homework#3 solutions out of...

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