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Unformatted text preview: EE372 Assignment 4 Solutions 1. Nanoparticles A hot research topic at the moment are nanoparticles, very small grains of various semi- conductors. An electron that is inside a nanoparticle is equivalent to an electron inside a three dimensional square well. The potential outside the well is not infinite but instead is roughly the work function of the material. However, the first few infinite 3-D square well energies are a good first approximation for the quantized energies of the electron inside a nanoparticle. a) Use the formula for the electrons energy in the infinite 3-D square well to derive a formula for the energy difference between the first excited state and the ground state. b) The nanoparticles can be induced to give off light by exciting the electron. The formula derived in part (a) gives the energy of the photon emitted when the electron goes from the first excited state to the ground state. Calculate the dimension a required so that the photons emitted are red (1.8 eV), green (2.4 eV), or blue (3.5 eV). Such nanoparticles might someday be used in colour displays. Answer: a) The energy of an electron in an infinite 3D square well is E n 1 n 2 n 3 = h 2 2 2 ma 2 n 2 1 + n 2 2 + n 2 3 The ground state energy is E 111 and the first excited state energy is E 211 . So the energy difference is E = 3 h 2 2 2 ma 2 b) The size required to emit light with energy...
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This note was uploaded on 01/20/2011 for the course EE 372 taught by Professor Johanson/kasap during the Fall '10 term at University of Saskatchewan- Management Area.
- Fall '10