Amount of electrons in a material? Is there a way to calculate the amount of electrons in a plate of a certain material and certain dimensions?
What I want to know is how many electrons are available to remove from a plate when light of appropriate wavelength hits the plate(photoelectric effect).
 A: Yes. In the free electron model (of a metal), it is possible to define an electron density in the conduction band. See the table in this link for example. 
But to a first approximation you can consider the density of atoms in the material (mass density upon molar volume times Avogadro number) times the valency of the metal under question as the electron density. 
A: As an addition to the answer by @SuperfastJellyfish, consider this.
Your charge of $18.1\times10^{28}$ electrons is approximately equal to $3\times10^{10}$ Coulomb. If we have that charge removed to a distance of $1 m$ (and the opposite positive charge is left on the aluminium), the force on the removed electrons is given by $$F = K_e  q^2 / r^2$$ where $K_e$ is the Coulomb constant ($8.99\times10^9$), $q$ is the charge, and $r=1$.
This force is approximately $9\times10^{30}$N. 
Hence you will not be able to remove that many electrons. The attractive force will cause the electrons (and whatever equipment is used to remove them) to smash back into the aluminium. If you did remove them, the two plates would move towards each other with an acceleration be of the order of $10^{36}g$. You would prefer not to be close by!
