# Homework Help: Photoelectric effect and copper

1. Mar 26, 2005

### Pengwuino

So i have this problem.

An isolated copper sphere of radius 5.00cm, initially uncharged, is illuminated by ultraviolet light of wavelength 200nm. What charge will the photoelectric effect induce on the sphere? The work function for copper is 4.70 eV.

Can someone help me conceptualize whats going on here so i can start figuring out this problem?

2. Mar 26, 2005

### Staff: Mentor

If the 200nm photons have sufficient energy (do they?), they will eject electrons from the surface. For each ejected electron, the charge on the sphere increases by +e. To estimate the induced charge, you need to know how many photons hit the sphere.

3. Mar 26, 2005

### ZapperZ

Staff Emeritus
Each time an electron leaves the sphere, the sphere becomes charged. This produces an extra potential barrier for the next electron to escape the sphere. This manifests itself via an INCREASE in the effective work function of the material. So the electron now has a larger work function to over come.

At some point, you will have extracted a large enough number of electrons that the work function is now equal to the photon energy. When this happens, no more electrons will leave the material. This will be your steady-state charge value for your sphere. The thing to do is figure out how much of an increase in the work function for this to occur (this should be simple since you know the original work function and the photon energy), and then connect that into the electrostatic potential right at the surface of the sphere and figure out what charge would produce such a potential.

A very good question!

Zz.

4. Mar 26, 2005

### Staff: Mentor

And a very good answer, Zapper! (I was debating whether to go into that level of detail. But on further thought, I guess that was the whole point of the exercise. D'oh! :uhh: )

5. Mar 26, 2005

### Pengwuino

This is the first chapter on quantum physics ive seen in college so i think that detail is too much. They've only given the impression that a metal has a work function related to it but never stated it could change (yet obviously)

6. Mar 26, 2005

### ZapperZ

Staff Emeritus
Well then maybe you should have revealed exactly WHAT you do know or else the rest of us will be just wasting our time explaining this using stuff that just flies over your head.

1. You have to know what a photoelectric effect is, and what a work function is in relation to the photon energy. This is covered in intro physics.

2. Find the difference between the photon energy and the work function. This is the EXTRA energy given to the photoemission process that enables the electrons to escape. This is what will decrease as the electrons escape. I described this earlier as an increase in effective work function.

3. Once you know the difference, in units of eV, then using the definition of what an "eV" is (again, something one learns in intro physics), one will know that this is an energy transfered to/from an electron in a potential of V. You then know that if this potential is on the surface of the sphere, NO electrons will leave the sphere since this is equivalent to a effective work function that is equal to the photon energy.

4. Use your knowledge from E&M of a potential from a charged sphere to figure out what charge "q" you would need to produce such an electrostatic potential.

Zz.

P.S. the work function of the material doesn't change. It is the EFFECTIVE work function that I said can increase.