Imagine that we take all the people in the world... we give all the money of a certain denomination to one person. For example, I would have all of the pennies, and you might get all of the nickels. We keep doing this so that everyone has one certain denomination of money. Now, imagine that some of our friends (say an infinite amount) are being held captive by some evil person. He will let any captive go, if that captive can pay $.85. The great thing is that we can throw our money at them. The only problem is that if I start throwing pennies; I have to get 85 pennies to one person out of an infinite number of people. That is very unlikely, but if the guy who has the $1 bills starts throwing them, anyone who gets one of the bills can buy his freedom and have $.15 in change. The rate at which the guy with the dollar bills throws them only affects the rate at which the prisoners can escape.
How does this relate to the Photoelectric effect?
Well, way back when, physicists noticed that when certain metals were bombarded with photons, they would emit electrons. Basically, the electrons are like the prisoners; they require a certain amount of energy to leave the metal. The energy of the photons is dependent on the frequency of the photon. Because of this, there is a threshold frequency that photons have to have cause electrons to go flying. This amount of energy is different for each metal and is called the work function for the metal.
If an electron get the necessary energy to be ejected, then the rest of the energy that the photon gave it is changed to Kinetic Energy. So we can say that K.E. = hf - Work Function. Where hf is Wavelength times frequency. Note that increasing the intensity increases the number of electrons ejected, not their kinetic energy.
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