Dannyinjapan said:
How can matter from the Earth just jump up and replenish the missing matter from a piece of metal?
When an object is "grounded", it means it's in contact with a much larger body that has many electrons that can be easily carried from one point to another. How do they get from one point to the other? By the electric force, of course.
Imagine that I have a much smaller conductor, like a little metal sphere, that
isn't grounded, so there are no electrons available to it from outside. If I shine light of the appropriate energy on it, some of its electrons will be removed and it the sphere will now have more positive charges than negative charges. Now the interesting thing about a conductor is that this net positive charge will be now be distributed "uniformly" on its surface, such that the surface is all at the same potential. Why? Well, if it's not distributed this way, then the charges on one part of the sphere will be pulling on the charges on another part of the sphere. Since charge is free to move, this force will result in motion of charge. The charge will keep moving around until it has reached some sort of balance where the net force on any charge in the sphere is zero. Not surprisingly, this balance occurs when the charge is uniformly distributed on the sphere (this just follows from symmetry).
What if this conductor is much larger, like the earth? The effects are basically the same; that is, the charge will still distribute to make an equipotential, but this time the excess charge will be
much more spread out. In the case we're discussing, you're effectively removing a charge of a few electrons from a conductor the size of the Earth (assuming the experiment is grounded). If this charge were to distribute uniformly on the surface of the earth, the net overdensity of charge (just from the electrons you removed) in one square meter would be
Q=\frac{Nq_e}{4\pi R_e^2}
where N is the number of electrons removed, q
e is the charge of the electron, and R
e is the radius of the earth. For 100 electrons, this equates to ~10
-36 Coulombs! You won't get a strong force from that.
In practice, the Earth isn't quite as ideal a conductor as this, but the idea is the same. Removing such a small amount of charge from a conductor as large as that will result in the charge being effectively "replenished" at the point where the charge was removed. Charge is still conserved, however, and if you did enough photoelectric experiments (billions of billions!), the charge difference on the Earth might become noticable, but such things make no practical difference.
It's also worth noting that the Earth
does carry a noticable amount of charge on its surface and the potential difference between the surface and upper atmosphere is quite large. This is because lightning storms (tens of thousands per day) will periodically deposit large numbers of electrons on the surface. So, another way to look at why your experiment makes no difference to the Earth's charge is to consider how it compares to tens of thousands of bolts of lightning.
