Calculating Fermi Energy in Graphite Using Free Electron Model

[fluidistic]

Homework Statement

Graphite has a structure of parallel planes weakly interacting with each others such that for many effects it can be considered as two dimensional. Each plane has a hexagonal (honeycomb) structure with a single C atom by site which gives 1 electron of conduction. Assume that the model of free electrons can be applied to all conduction electrons, find the Fermi energy.

Homework Equations

Not really sure. Are there some missing data?

The Attempt at a Solution

What boggles me is that there's no volume given nor electron density. I don't think I can calculate the latter either, because even though I know there is 1 atom per elementary unit, I do not know the distance between atoms (not sure it even makes sense in a honeycomb structure). Thus I don't really know how to tackle the problem.
I know that $E_F= \frac{\hbar ^2 \pi n }{m}$. I know that n is the density of electron for an area unit but that number is an unknown in the problem.
I'd like some tip to start the problem, thank you!

 

[mark726]

Thank you for bringing up some important points regarding the problem. As you correctly mentioned, there are indeed some missing data that are crucial for solving this problem. In order to calculate the Fermi energy, we would need to know the electron density, which is the number of electrons per unit volume. In this case, since we are dealing with a two-dimensional structure, we would need to know the electron density per unit area.

Unfortunately, the problem does not provide us with this information. However, we can make some assumptions and estimate the electron density based on the given information. For example, we know that there is 1 electron per atom, and each atom is located at a site in the hexagonal structure. We also know that the hexagonal structure has a lattice constant (a) of approximately 0.142 nm.

Using this information, we can estimate the electron density by assuming that each atom occupies an area of approximately a^2/2 (since the hexagonal structure can be divided into two triangles). This would give us an electron density of approximately 7.0 x 10^14 electrons/cm^2.

With this estimated value for the electron density, we can now calculate the Fermi energy using the formula you mentioned, E_F = (hbar^2 * pi * n)/m. The mass of an electron (m) is approximately 9.1 x 10^-31 kg.

I hope this helps you get started on the problem. Please let me know if you have any further questions. Good luck!