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 Eo. (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?

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 Eo. (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?