# Regarding calculation of Plasma frequency and static dielectric constant

#### sami6108

Hello:

I want to calculate the plasma frequency of Au, Ag, Cu and Al. But wondering what is the most precise way to calculate the plasma frequency.If any one can help me with that it will be really appreciated.

I know that Plasma Energy = √(n*e^2/(m*ε°)) = plank constant * ωp

Here, where n is the conduction electron density, e is the elementary charge, m is the electron mass, ε° the permittivity of free space and ωp the plasmon frequency.

But I do not have precise data or table of the conduction electron density. If any one know any link or table please provide me the source.

My other question "Is the plasma energy equal to the Band gap of the metal"? If so then how to measure "Static dielectric constant" if we measure the plasma frequency or wave length from the following equation?

Plasma Energy = Energy Band Gap = plank constant * ωp

If any one can reply that will be a big help for me. Any kind of reply will be highly appreciated.

Thanks,

Sami

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#### DrDu

Science Advisor
Calculation of the plasma frequency from the conduction electron density is only approximate.
To really calculate it precisely you need to use some electronic structure programs.
The conduction electron density can be estimated from the number of conduction electrons (valence electrons) per atom. That is 1 for Cu, Ag, Au and 3 for Al.

The plasma frequency isn't related to the band gap.

#### sami6108

Thanks man for the reply. I am working on it. But for the copper I have found from a website the free electron density (I am assuming this is the conduction electron density) is 8.4 * 10^ 28 / m^3 which gives a plasma wavelength around 115 nm but it should be around 500 nm mark. Wondering what went wrong, m I missing something or free electron density data is wrong?

#### DrDu

Science Advisor
500 nm would be in the visible which I don't believe. I'd buy more the 115 nm.
Note that copper and gold have some absorptions in the visible range (from d orbitals to the conduction band) due to which their reflectivity decreases in the visible range, but that is unrelated to the position of the plasma frequency.

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