Consider electrons trapped in an infinitely deep square well. Suppose that 100 electrons are placed in a well of width 120 pm, two to a level with opposite spins. We have to calculate the Fermi energy of the system. (Note: The Fermi energy is the energy of the highest occupied level at the absolute zero of temperature.)

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In an infinite potential well both ends and are nodes of stationary waves. We therefore have the condition that

Therefore, the wavelengths of the stationary waves will be

We using de Broglie relation we write the momentum associated with stationary waves,

The corresponding energy of a stationary state characterized with quantum number is

As each energy state can be occupied by two electrons (spins in opposite directions), the quantum number of the highest occupied state in the well by 100 electrons will be .

Therefore, the Fermi energy of 100 electrons confined in an infinitely deep square well of width 120 pm will be

The Fermi energy is 65.3 keV.