Why does the plasma frequency of alkali metals decrease with increasing atomic numbers? Why do the plasma frequencies of the group I alkali metals, Li to Cs, decrease with increasing atomic numbers? I have tried to look at the basic expression for plasma frequency, 
$$\omega_p = 4\pi e^2n/\epsilon_l m,$$
but this does not in any way relate to the atomic number $Z$. What am I doing wrong?
 A: Your expression for the plasma frequency is correct. The material parameters enter through the electron density $n$, dielectric function $\epsilon$ and effective mass $m^*$. In an alkali metal solid, each atom contributes one electron to the conduction band (the other electrons are in filled bands, and don't contribute to the plasma oscillation). By plugging in the density and atomic masses of the alkali metals, and setting the dielectric function as vacuum permeability and setting $m^*$ as the electron mass, the calculated plasma frequency matches reasonably with experimental values. The decreasing trend of plasma frequency of alkali metals is due to the increase in atomic volume, leading to smaller free electron densities. See the table below:

Experimental values taken from P. Allippi et. al. Phys. Rev. B. 55, 20 (1997).
The small discrepancy can be resolved by plugging in the effective masses for the alkali metals. See the reference below:
Optical Properties of Solids
By Anthony Mark Fox, Department of Physics and Astronomy Mark Fox
