Number of electrons in the conduction band of various metals

[fluidistic]

Homework Statement

Calculate the number $n_0$ of electrons per volume unit in the conduction band for the lithium, copper and aluminium. Compare this result with the number of electrons of valence per volume unit of these metals.

Homework Equations

None given, no ressource either.
Currently checking out this: http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html#c6 but I don't see how this can help me for that problem.

The Attempt at a Solution

Basically stuck at start, I've checked out in 3 books (Brehm's, Serway's and Alonso&Finn's) +the Internet about this and couldn't find how to start the problem.
What I imagine is that since they are 3 good conductors, the conduction band must be somehow filled so that I expect the number of electrons per volume unit in the conduction band to be "high" or about the same order of magnitude than the number of electrons per volume unit in the valance band.
I don't really know how to show this mathematically though. I guess I'll have to check out the electrical configuration of the lithium to start with. From memory it's $1s^22s^1$. And this is where I'm stuck, I don't know what to do next.
Thanks for any help, even if it's redirecting me to books/websites!

 

[mark726]

Thank you for your question. Calculating the number of electrons per volume unit in the conduction band for lithium, copper, and aluminum can be done using the following equation:

n_0 = (2/π) * (2m/h^2)^(3/2) * √(E_c - E_f)

where n_0 is the number of electrons per unit volume, m is the effective mass of the electron in the conduction band, h is Planck's constant, and E_c and E_f are the energies of the conduction band and the Fermi level, respectively.

To calculate the number of electrons per volume unit in the conduction band, you will need to find the values for m, E_c, and E_f for each of the metals. These values can be found in tables or obtained from a reliable source.

Once you have these values, you can plug them into the equation and calculate the number of electrons per volume unit in the conduction band for each metal. Then, you can compare these values with the number of electrons per volume unit in the valence band, which can be calculated using a similar equation:

n_v = (2/π) * (2m/h^2)^(3/2) * √(E_v - E_f)

where n_v is the number of electrons per unit volume in the valence band, m is the effective mass of the electron in the valence band, h is Planck's constant, and E_v and E_f are the energies of the valence band and the Fermi level, respectively.

By comparing these two values for each metal, you can see how the number of electrons in the conduction band compares to the number of electrons in the valence band. I hope this helps and good luck with your calculations!