White dwarf stars represent a late stage in the evolution of stars like the Sun. They become dense enough and hot enough and that we can analyze their structure as a solid in which all Z electrons per atom are free. For a white dwarf with a mass equal to that of the Sun and a radius equal to that of the Earth, we have to calculate the Fermi energy of the electrons. We may assume that the atomic structure to be represented by iron atoms, and that .

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We will calculate first the mass of an iron atom. The molar mass of iron is

Therefore, mass of an iron atom

Atomic number of iron . Therefore, in its completely ionised state each iron atom contributes 26 free electrons.

We are given that the mass of the white dwarf star is one solar mass. That is

We are also given that the radius of the white dwarf star is equal to the radius of the earth. That is

Therefore, the number of free electrons per cubic meter in the white dwarf star will be given by

Fermi energy at absolute zero is the energy of the highest occupied state. It is a function of the number of free electrons per cubic meter, , and is given by the expression

We use and find