Consider a three-dimensional infinite well modeled as a cube of side L. The width L of the cube is such that the ground state energy of one electron confined to this box is En. (a) Calculate the four lowest energy states and evaluate their corresponding degeneracy. (b) If a total of 9 non-interacting electrons are placed in the box, find the Fermi energy of the system.
Consider a three-dimensional infinite well modeled as a cube of side L. The width L of the cube is such that the ground state energy of one electron confined to this box is En. (a) Calculate the four lowest energy states and evaluate their corresponding degeneracy. (b) If a total of 9 non-interacting electrons are placed in the box, find the Fermi energy of the system.
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Transcribed Image Text:Consider a three-dimensional infinite well modeled as a cube of side L. The width L of the cube is such that
the ground state energy of one electron confined to this box is En.
(a) Calculate the four lowest energy states and evaluate their corresponding degeneracy.
(b) If a total of 9 non-interacting electrons are placed in the box, find the Fermi energy of the system.
(c) What is the total energy of the 9-electron system?
(d) Find the lowest transition energy required to excite an electron in this system and place it in an
unoccupied energy level?
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