16.2 and 16.4

P16.2 Semiconductors can become conductive if their temperature is raised sufficiently to populate the (empty) conduction band from the highest filled levels in the valence band. The ratio of the populations in the highest level of the conduction band to that of the lowest level in the valence band is nvalencenconduction=gvalencegconductioneE/kBT where E is the band gap, which is 1.12eV for Si and 5.5eV for diamond. Assume for simplicity that the ratio of the degeneracies is one and that the semiconductor becomes suf. ficiently conductive when nvalencenconduction=5.5107 At what temperatures will silicon and diamond become suffi. ciently conductive? Given that diamond sublimates near 3000. K, could you heat diamond enough to make it conductive and not sublimate it? P16.4 Calculate the energy levels of the -network in hexi triene, C6H8, using the particle in the box model. To calculate the box length, assume that the molecule is linear and use the values 135 and 154pm for C=C and CC bonds. What is the wavelength of light required to induce a transition from the ground state to the first excited state? How does this cortit pare with the experimentally observed value of 240nm ? What does the comparison made suggest to you about estimating the length of the -network by adding bond lengths for this molecule