How Many Electron States in the Irreducible Part of 1BZ?

[malawi_glenn]

Homework Statement

How many electron states are there in the irreducable part of 1BZ (one irreducable part is 1/48 of 1BZ).

Homework Equations

Volume of 1Bz:
\Omega = \dfrac{(2 \pi)^3}{V}

Volume of ordinary cell:
V = a^3

Density of states, I assume that the temperature is so low that fermi-dirac function does not play big part, hence max energy = fermi energy.

D(\epsilon ) = \dfrac{V}{2 \pi ^2} \left( \dfrac{2m}{\hbar ^2} \right)^{3/2} \sqrt{\epsilon }

The Attempt at a Solution

total number of states:
\int_0^{\epsilon _{F}} D(\epsilon ) d \epsilon

just gives me N = N

:S

What do I do wrong? My plan was first to calculate the number of states i ordinary space, then convert into reciprocal space...

 

[malawi_glenn]

Never mind, I will ask my teacher tomorrow.

 

[malawi_glenn]

First Brillouin zone, A very common short notation for it...

And I realized that there is N number of k-values in 1 BZ, so that there is N/24 in the irreducible 1 BZ, since there is two electron states per k-value due to pauli principle.