Online Physics Determining Fermi Energy Homework Help
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1. Choose Setup: Well Array (Square), Mouse = Set Eigenstate. Move the slider so Well Count = 10. Go to View. Choose energy, position, values/dimensions, state phasors, expectation values, uncertainties, wavefunction – probabilities+phase.
(a) Sketch an energy level diagram showing how the energies of the quantum states are distributed.
(b) How are these energies related to those for a single well? (3) How many states make up the lowest-energy band?
2. Determine how the number of non-core (or bonding) electrons per atom affects the range of occupied energies. The top occupied energy is the Fermi energy of the solid.
(Hint: imagine that the electrons are added to the solid one at a time. Each electron that is added goes into the system state of lowest possible energy consistent with Pauli’s Exclusion Principle.)
(a) If each atom contributes one electron, what is the Fermi energy, and where does this lie relative to the bands?
(b) what if each atom has two electrons?
(c) three-electrons each?
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3. Compare the conductivity of solids with one and two electrons per atom. How much energy is needed to increase the energy of one of the electrons? How likely is it that an electron may gain this amount of energy if the solid is at room temperature? Which is the better conductor?
4. Consider a solid, each atom of which has 2 non-core electrons. The potential energy well of each atom has a depth such that the band gap between bands 1 and 2 is less than 2 eV. Adjust the depth of the wells to achieve this condition.
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