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TFM

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## Homework Statement

Starting from the expression for g(E) derived in the lectures, show that for a solid of volume V containing N free electrons which obey Fermi-Dirac Statistics, [tex] E_F, k_F, and v_F [/tex] can be expressed as:

[tex] E_F = \left( \frac{N}{V} \right)^{1/3}(3\pi^2)^{2/3}\left( \frac{(h/2\pi)^2}{2m} \right) [/tex]

[tex] k_F = \left( \frac{N}{V} \right)^{1/3}(3\pi^2)^{1/3} [/tex]

[tex] E_F = \left( \frac{N}{V} \right)^{1/3}(3\pi^2)^{1/3}\left( \frac{(h/2\pi)^2}{m} \right) [/tex]

Calculate approximate values of these three parameters and of (N/V), [tex] T_F [/tex] and of [tex] \lambda_F [/tex] for Na metal. Compare the values of [tex] T_F, \lambda_F v_F[/tex] with Room Temperature, the interatomic spacing in Na and the velocity of light, respectively.

For Na: AW = 23, [tex] \rho \pprox [/tex] 1 gram.cm-3

Hint:

[tex] \int^?_?g(E)de = ? [/tex]

## Homework Equations

## The Attempt at a Solution

Hi

Now I know that

[tex] g(E) = \left( \frac{V}{2\pi^2} \right)\left( \frac{2m}{\hbar^2} \right)^{3/2}E^{1/2} [/tex]

Now I think that if I remember rightly,

[tex] \int^?_?g(E)de = ? [/tex]

is the number of states?