Dr Sreepriya ---please have a look at the following useful links:

https://www.researchgate.net/post/How-do-I-calculate-the-resonance-and-plasma-frequency-of-bulk-metals

How do you find the frequency of plasma?

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.

What is effective mass approximation?

Primarily, the effective mass approximation was extensively used to describe electronic motion in the presence of slowly varying perturbations [38]. ... Assuming that the many-body interactions among electrons are negligible, the motion of the electrons can be described by the one-electron Hamiltonian.

https://www.iue.tuwien.ac.at/phd/milovanovic/diss_htmlse4.html

Regards--

A handy formula for the plasma frequency is (neglecting the contribution of the ions): f_p = 9000*sqrt(n), where the electron density n has to be taken in /cm³.

For the effective mass, it depends on what exactly you are after. In solid state physics you will find different expressions for the effective mass in different circumstances. This is because the effective mass is basically the mass with which a particle reacts to an external force via F = ma. However, in the most general form you will need to take into account the dispersion relation. For an electron this would yield: m = (h/2Pi)² * [d²E/dk²]^(-1), where E is the energy and k is the wavenumber.

Milton, Graeme W; Willis, John R (2007-03-08). "On modifications of Newton's second law and linear continuum elastodynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 463 (2079): 855–880. doi:10.1098/rspa.2006.1795