Why Is the Radius of a Fermi Sphere Given by \( k_F = (3 \pi^2 n)^{1/3} \)?

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SUMMARY

The radius of a free electron Fermi sphere is defined by the equation \( k_F = (3 \pi^2 n)^{1/3} \), where \( n \) represents the concentration of electrons. This relationship is derived from principles outlined in Kittel's "Introduction to Solid State Physics" (ISSP), specifically on page 138. Understanding this equation is crucial for grasping the behavior of electrons in solid-state physics.

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[SOLVED] radius of the fermi sphere

Homework Statement


On page 249 of ISSP, Kittel says that the radius of a free electron Fermi sphere is

k_F = \left(3 \pi^2 n \right)^{1/3}

where n is the concentration of electrons.

I don't know why that is true.

EDIT: never mind; they derive that on page 138

Homework Equations


The Attempt at a Solution

 
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