# Density of states and fermi energy

I am trying to find the fermi energy and density of states. From the equation:

K_F^3=3*(pi)^2*n

and

n=NAvagadrosdensity/m

what is the big N here?

## 1 Answer

Your first equation is $k_F$ in the Sommerfeld model, so long as the variable $n$ is the electron density, $n = N/V$, where $V$ is the volume of the system and $N$ is the total number of electons in the system. I'm not quite sure what you meant to write for $n$, but it probably works out to the electron density.

• So if i know the atomic weight, density and volume of a material, how would i go about finding n, or N? – pythonman11 May 13 '15 at 13:38
• Well, if you knew the volume of a material, you would have V. To get N, you would need to know the number of electrons in the material, so you would need to look up the material on the periodic table to get that information and estimate how many of those atoms there are by dividing the total mass (which you have as density * volume) by the atomic mass of the appropriate atomic species. Now you have the number of atoms, and the number of electrons per atom, so you can get the total number of electrons in the material, N. – danielsmw May 13 '15 at 14:51