Quick Fermi Energy QuestionFree electrons?

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SUMMARY

The discussion centers on the derivation of the Fermi energy expression for a solid, specifically the formula Ef = h^2/2m . (3.pi^2.N/V)^2/3. It clarifies that the term N/V refers to the density of free electrons, as the Fermi energy pertains to the highest occupied energy level at absolute zero, which includes only free valence electrons and not bound electrons. The distinction is made that bound electrons do not contribute to metallic properties, aligning with the principles of the Landau Fermi Liquid theory, which models valence electrons as a gas of quasi-particles that behave similarly to free electrons.

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Quick Fermi Energy Question..Free electrons??

A quick question on the Fermi energy.

From a 3D cubic well, one can derive an expression for the Fermi energy of a solid:

Ef = h^2/2m . (3.pi^2.N/V)^2/3


Now, I have come across an expression where N/V, electrons per volume, is replaced by density over mass, times no of FREE electrons. Why is it the FREE electrons tho?? I thought the fermi energy was the highest occupied energy of the electrons at 0 K, which would include the bound electrons (in the ion core say) and the free valence electrons?

Perhaps this is because the formula above is derived from a free electron gas?

Hope someone can enlighten me on this, Cheers!
 
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The valence electrons in a metal maybe modeled as a gas of electrons. Fermi energy or surface is relevant to the description of the valence electrons only. Bound electrons take no part in the metallic properties (usually).

It so happens that the effective excitations (quasi-particles) due to the interaction of the valence/free electrons resembles the original free electrons in the electron-gas model. This result is known as the Landau Fermi Liquid theory. So one can substitute these interacting electrons with the free ones. Only the mass of these new "electrons" also called quasi-particles is different from the original free electrons.

Hope I've not left you in more confusion. Should wiki/google "Fermi Liquid" theory.
 

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