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as m rseher um/FIIE/‘EIEZE7E/Ehem3322testlsnlnf n @3 There we no Ielﬂed
documents a Ihis lime, Problem 2 — 6 marks The “4n+2 rule” is a well—knewn m e in organic chemistry: the planar, aromatic form
of carbocyclic systems of the type (CH)m (cg. benzene in the case of m=ﬁ) are particularly stable for values of in given by
m=4n+2 (n=l,2,3,..i) (6) In other words, m=6, 10, 14, If the 11 electrons in these systems are treated as free
electrons on a ring, explain how the 4n+2 rule logically follows. Hint: closedshell systems,
that is, in which all energy levels are fully occupied, have enhanced stability in atoms and
molecules. Answer: 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, 1.4, .. . electrons, i.e. 4n+2. Information about ‘chem3322_lest1_soln" 3 Type: Notes (hemﬁﬂzz wk In(2[ll] 17 5) duwslnternelEuplnrer m/FIIE/‘E182574/Ehem3322hwkﬁsulnf There we no relied
documents a Ihis lime, Problem 4 — 6 mar1m The 1r electrons in benzene can be apprmcimated as particles on a ring. Calculate the
diameter of this “electron ring" if it is assumed that a. trensitiun occurring at 260.0 nm
oorreeponds 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. Make
sure you EhDW the details of your npprcudmution because there are different Ways to do this. Answer: Using E = Pm and c = Ay‘ the photon of wavelenmh 260 um gives an energy to the
molecule of E : 7.64 x 10"“ J. The energy promotes the n : 3 to n : 4 transition. 2 e 2 2
“2:121:12 (5}
Using the mean of an electron. since this is what is doing the transition, we get R = 2.36 A.
The carboncarbon bond length in benzene is 1.39 A. Assuming that the Circumference
nfthe frielectmn “ring” in benzene is six times this distance, we get a. diameter of 2.65 A. So
we see that our simple model of the particle—on»arring estimates the diameter to be about twice as big as it actually is. Information about ‘chem3322_hwk3_snln" ...
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 Spring '08
 Dieckmann,G
 Physical chemistry, pH

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