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2. Electrons in molecules can be found in orbitals that extend over more than one atom. Consider
one electron that is confined in a molecular orbital that extends over 8 adjacent carbon atoms.
The electron can move freely between the 8 atoms.
a) Using the one-dimensional particle-in-the-box model, calculate the energy required to
promote an electron from the n = 2 to the n = 5 level. The length of the box is determined by
the C-C bond distance, which is 139 pm.
Note: The following information may or may not be useful.
?? = ?2ℎ2
8???2
Planck's constant = 6.626 x 10-34 J·s; Mass of Electron = 9.109 x 10-28 g;
Rydberg constant = 1.097 x 107 m-1;
b) What
c) Now imagine a straight chain of 2000 carbon atoms. Assume that the orbital extends over
the entire chain and repeat the calculation for the required energy to promote an electron
from the n = 2 to n = 5 level.
d) Would you expect the energy levels to get closer or farther apart if you increased the chain
to one million carbon atoms (i.e approaching bulk properties)? Provide a brief explanation
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