pset 2 - University of California, Berkeley EE230 - Solid...

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University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor pset 2.fm PROBLEM SET 2 (Due Thurs., Feb. 28, 2008) 1. [Kittel, 4.6] Consider point ions of mass M and charge q immersed in a uniform sea of con- duction electrons. The ions are imagined to be in stable equilibrium when at regular lattice points. If one ion is displaced a small distance r from its equilibrium position, the restoring force is largely due to the electric charge within the sphere of radius r centered at the equi- librium position. Take the number density of ions (or of conduction electrons) as 3/4 π R 3 , which defines R. a) Show that the frequency of a single ion set into oscillation is ω = (e 2 /MR 3 ) 1/2 . b) Estimate the value of this frequency for sodium metal. Calculate the corresponding wave- length of light that will excite this oscillation. c) From the above and some simple reasoning, estimate the velocity of sound in sodium. Find a literature value for the sound velocity in sodium for comparison.
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This note was uploaded on 08/01/2008 for the course EE 230 taught by Professor Bokor during the Spring '08 term at University of California, Berkeley.

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pset 2 - University of California, Berkeley EE230 - Solid...

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