How to Determine Electron Concentration in Metals?

[jg370]

Homework Statement

To determine the Fermi Energy for metals such as sodium, copper, gold, ect one needs the Electron Concentration per cubic meter.

Homework Equations

How is this number determined?

The Attempt at a Solution

My textbook does not give me this information and searching the Internet povides me with information that mostly related to semiconductor material and other exotic topics.

Thank you for your kind attention

jg370

 

[Jhero]

3

Dear jg3703,

Thank you for your question about determining the Fermi Energy for metals. The Fermi Energy is an important concept in solid state physics, and is often used to describe the behavior of electrons in metals. To determine the Fermi Energy for a metal, one needs to first calculate the Electron Concentration per cubic meter, as you mentioned.

The Electron Concentration per cubic meter, also known as the electron density, is the number of electrons per unit volume in a metal. This value can be calculated using the Avogadro constant and the atomic weight of the metal. For example, for sodium, the electron concentration would be approximately 5.9 x 10^28 electrons per cubic meter.

Once the Electron Concentration per cubic meter is known, the Fermi Energy can be calculated using the following equation:

E_F = (h^2 / 8m) * (3π^2 * n)^(2/3)

where E_F is the Fermi Energy, h is Planck's constant, m is the effective mass of an electron in the metal, and n is the electron concentration.

The effective mass of an electron in a metal is a property that takes into account the interactions between electrons and the surrounding lattice of atoms. It can be found in tables or calculated using band structure calculations.

I hope this helps answer your question. If you have any further inquiries, please do not hesitate to ask.