Quick Fermi Energy QuestionFree electrons?

[Master J]

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!

 

[kiv_vik]

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.