ENGRI_111_MIDTERM_2007

ENGRI_111_MIDTERM_2007 - ENGRI 111 MIDTERM EXAM SOLUTIONS...

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ENGRI 111 MIDTERM EXAM SOLUTIONS Friday October 19, 2007 in class Time Length: 50 minutes, Total Points: 100 1. Bonding and Band Structure (33 points): Titanium (Ti) is a conductive metal but TiO 2 is a semiconductor with a bandgap of 3.2 eV. a) Based on what you know in general about the band structures of metals and the band structures of semiconductors, describe the differences and similarities between the band structures of Ti and the band structure of TiO 2 . Use words and schematic diagrams. (10 points) In the band structure of a metal, the valence band is not entirely full, or if valence band is full then conduction band is not full. In the band structure of a semiconductor, the valence band is full. The conduction band is nearly empty or empty. Band gap present between conduction and valence bands. b) Just on the basis of the size of its bandgap, explain whether you expect TiO 2 to be more conductive or less conductive than Si at room temperature? (4 points) Si has a smaller bandgap so it is easier to excite electrons into the conduction band (1.1 eV bandgap of Si). c) Explain if the changes in the band structure in going from TiO 2 to Ti are consistent with a chemist’s understanding of a reduction process. (3 points) Electrons are removed from the valence band in the simple band picture. In reduction, electrons are generally added. However since the band picture is of Ti and TiO 2 but not Partially Filled Valence Band Empty Conduction band Filled Valence Band Empty Conduction band Band Gap Band Gap
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of O 2 , it appears that in the band picture electrons have been removed, this is not consistent with the chemist’s picture. d) TiO
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This note was uploaded on 03/07/2010 for the course MS&E 111 at Cornell.

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ENGRI_111_MIDTERM_2007 - ENGRI 111 MIDTERM EXAM SOLUTIONS...

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