9. Consider a three-dimensional infinite-well, modeled as a cube of dimensions L × 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 ?
9. Consider a three-dimensional infinite-well, modeled as a cube of dimensions L × 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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Transcribed Image Text:9. Consider a three-dimensional infinite-well, modeled as a cube of dimensions L × 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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