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Before we look into more details of the photoelectric effect, we need to go over the main tool we will be using to analyze the behavior of the electron. This is a potential energy graph.

• S: Can you remind me again what is potential energy?
• M: Sure, first lets remember the Potetial Energy when we looked at the skateboarder. That was "gravitational potential energy" and the further you were away from Earth, the bigger the potential energy (the "potential to have motion, or... fall!"). There is a potential energy for each force. Right now, the only force you have studied is the electric force which, as you remember, is the charge q times the electric field (not energy) F=qE.
• S: Yes, I remember both those things.
• M: Ok, well another way to think about the force is in term of electric potential energy U. The electric potential energy can be graphed just like the skate park from week 2. This potential energy is everywhere in space (just like the electric field) and you can find the force on a particle by simply looking at the slope of the potential energy. The steeper the slope, the stronger the electric force.

If you are in area where the potential energy is changing quickly, you will find a big force in the direction of lower energy. If you are in area where the potential energy is constant, you will not feel any force.

Total Energy for Electrons

The total energy of an electron and proton under the effect of an electric force with electric potential energy is, like before, just its potential energy + kinetic energy.

E_{tot} = K+U

Turning Points

Turning points are simply places in space where a particle has no more kinetic energy and must either stop or turn back. To find turning points, you can just draw a horizontal line on the energy graph at the value of the total energy. The turning points are where the total energy is equal to the potential energy (see Fig "Turning Points")

Again: Turning points are places where the object must have a velocity of zero and thus stop momentarily. This occurs when kinetic energy is zero which occurs when the total energy is all in the form of potential energy.

Sometimes a particle could be in one region of space and it may not have enough energy to access some other regions. We call this being "trapped" in one well, because it cannot escape to the nearby well. (see Fig. "Trapped Region").