EE372 Assignment 4
due Oct. 13, 2010 in class
You should read sections 3.7 to 3.9 of the textbook and then answer the following questions.
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 3D square well
energies are a good first approximation for the quantized energies of the electron inside a
nanoparticle.
a) Use the formula for the electron’s energy in the infinite 3D 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
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 Fall '10
 Johanson/Kasap
 ground state, ﬁrst excited state, rmean, inﬁnite 3D square

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