Dear fellows, how to determine plasma and resonance frequency of the bulk metals? Such as, gold, silver and Aluminum, etc. I need it mathematical formulation, as plasma frequency is wp = sqrt (n*e/m*epsilon_0), here how to to find free electron n and effective mass m of the bulk metal. Similarly, how to determine the resonance frequency?
Dear Abuzar Baqir
May this help you.
At a resonance frequency , called the plasma frequency(Wp), the dielectric function changes sign from negative to positive and real part of the dielectric function drops to zero then you can use the next formula:
wp2= N (qe)2 / (Eom)
where wp is the plasma frequency in radians, N is the number of electrons per unit volume, Eo is the permittivity of free space, qe is the charge of an electron and m is the mass of the electron. The following values are available:
qe = 1.6E-19 coulomb
Eo = 8.85E-12 farad-meter-1
m = 9.11E-31 kgm
A value for N, the number of electrons per unit volume for the ionosphere is available from the University of Leicester, on a web page entitled Ionospheric Physics (valid 08/19/01). It will be seen that representative values for the electron density of the ionosphere range from approximately 1E2 to 1E6 electrons per cubic centimeter. For this example, let us use a rather representative value of 1E5 electrons / cm3.
Using these values in the above equation,
wp2 = (1E11 (e-/m3) * (1.6 E-19coulomb)2) / ((8.85E-12 farad-meter-1) * (9.11E-31kg))
or
wp = 1.78E7radians
and dividing by 2 * pi for cycles/sec
wp = 2.83Mhz.
The reference is (http://carnicominstitute.org/articles/plasma1.htm) at the middle of the page.
You can find free electron concentration n from Free electron model. The Fermi energy and effective mass are in handbooks.
https://en.wikipedia.org/wiki/Free_electron_model
Dear Lev B. Matyushkin, thank you for you answer. One part of my question is not answered yet, how to determine the resonance frequency?
Dear Abuzar Baqir
May this help you.
At a resonance frequency , called the plasma frequency(Wp), the dielectric function changes sign from negative to positive and real part of the dielectric function drops to zero then you can use the next formula:
wp2= N (qe)2 / (Eom)
where wp is the plasma frequency in radians, N is the number of electrons per unit volume, Eo is the permittivity of free space, qe is the charge of an electron and m is the mass of the electron. The following values are available:
qe = 1.6E-19 coulomb
Eo = 8.85E-12 farad-meter-1
m = 9.11E-31 kgm
A value for N, the number of electrons per unit volume for the ionosphere is available from the University of Leicester, on a web page entitled Ionospheric Physics (valid 08/19/01). It will be seen that representative values for the electron density of the ionosphere range from approximately 1E2 to 1E6 electrons per cubic centimeter. For this example, let us use a rather representative value of 1E5 electrons / cm3.
Using these values in the above equation,
wp2 = (1E11 (e-/m3) * (1.6 E-19coulomb)2) / ((8.85E-12 farad-meter-1) * (9.11E-31kg))
or
wp = 1.78E7radians
and dividing by 2 * pi for cycles/sec
wp = 2.83Mhz.
The reference is (http://carnicominstitute.org/articles/plasma1.htm) at the middle of the page.
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