Consider a three-dimensional infinite-well, modeled as a cube of dimensions Lx L× L. The length L is such, that the ground state energy of one electron confined in this box is 0.50eV. (a) Write down the 4 lowest energy states and their corresponding degeneracy. (b) If 15 (total) electrons are placed in the box, find the Fermi energy of the system. (c) What is the total energy of the 15-electron system?
Consider a three-dimensional infinite-well, modeled as a cube of dimensions Lx L× L. The length L is such, that the ground state energy of one electron confined in this box is 0.50eV. (a) Write down the 4 lowest energy states and their corresponding degeneracy. (b) If 15 (total) electrons are placed in the box, find the Fermi energy of the system. (c) What is the total energy of the 15-electron system?
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Transcribed Image Text:Consider a three-dimensional infinite-well, modeled as a cube of
dimensions Lx L× L. The length L is such, that the ground state
energy of one electron confined in this box is 0.50eV.
(a) Write down the 4 lowest energy states and their corresponding
degeneracy.
(b) If 15 (total) electrons are placed in the box, find the Fermi energy
of the system.
(c) What is the total energy of the 15-electron system?
(d) How much energy would be required to lift an electron from the
Fermi energy of part (b) to the first excited state ?
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