# University of Wisconsin Green Bay

Light (electromagnetic radiation) is incident on a silver plate. What is the threshold frequency of the light in order for electrons to be freed in the sliver? If light with twice the threshold frequency strikes the plate, what is the maximum kinetic energy of the freed electrons? What is the speed of the electron in this case? What will happen if visible light strikes the silver?

• In introduction to quantum mechanics units, you are introduced to a variety of experimental results involving light, atoms, or constituents of atoms. In most cases, when you look at interactions on these tiny scales, you have a foundations of quantum mechanics problem.

In this case, the interaction of interest is that of light (electromagnetic) energy being used to free electrons from their atoms. This is known as the photoelectric effect. The photoelectric effect is best understood through Conservation of Energy—tracking the energy of the incoming light as it is transferred to the electron—so at root this is an energy problem.

• In the photoelectric effect, the energy from incident light is absorbed by electrons—freeing them from their atoms and (if additional energy is available) giving them kinetic energy. This is one of the few cases where a picture is not particularly helpful in understanding the problem.

• Photoelectric effect problems are best understood through energy. Your book as probably provided you with this partially-solved version of the Conservation of Energy equation.

• Note that visible light (part 4 of this problem) has a maximum frequency of 7.5 x 1014 Hz, which is less than the threshold frequency for silver. In other words, visible light does not have enough energy to free an electron, so nothing happens when visible light strikes silver. Once you understand threshold frequency, scroll down to answer the remaining questions in this problem.

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Step 2

In the second question, you are told the frequency (and therefore the energy) of the incident photon, so it is straightforward to solve for the maximum kinetic energy of the electron. Note that this problem could also have been solved conceptually—you know that you have twice as much energy as is needed to free the electron, so half of the energy (4.30 eV) goes to freeing the electron and the remaining half (also 4.30 eV) is available as kinetic energy.

Now that you know the kinetic energy of the electron, it is merely a definition problem to find its speed.

• Once you recognize this problem as the photoelectric effect, you can solve it mathematically merely by plugging into KEmax = hf – φ. However, to understand the problem you need to recognize that this equation tracks energy.

Remember that in order to understand the experimental results of the photoelectric effect, we treat light as a particle rather than as a wave. In other words, we understand the interaction of light with the photoelectric material as interactions between a single photons and a single electrons. If the initial energy of a photon (hf) is at least enough to free an electron (φ) it will do so. If there is additional energy left over (if hf – φ is greater than zero), that remaining energy goes to kinetic energy of the electron.