We consider a conduction electron in a cubical crystal of a conducting material. Such an electron is free to move throughout the volume of the crystal but cannot escape to the outside. It is trapped in a three-dimensional infinite well. The electron can move in three dimensions, so that its total energy is given by

in which , , each take on the values 1, 2, . . . . We have to calculate the energies of the lowest five distinct states for a conducting electron moving in a cubical crystal of edge length .

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The total energy of an electron moving in a cubical crystal of edge length L is given by the equation

in which , , each take on the values 1, 2, . . . ..

Therefore, the lowest energy five distinct states will have the quantum numbers

It is given that .

We note that

Therefore, the energies of the lowest five distinct states will be

,

and

.