# Question Video: Determining Work Function Using a Graph of Electron Energy versus Photon Energy Physics • 9th Grade

The graph shows the maximum kinetic energy of photoelectrons when different metals are illuminated with light of different frequencies. Which metal has the lowest work function? Which metal has the highest work function?

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### Video Transcript

The graph shows the maximum kinetic energy of photoelectrons when different metals are illuminated with light of different frequencies. Which metal has the lowest work function? Which metal has the highest work function?

Looking at our graph, we see that the maximum kinetic energy of electrons ejected from metal surfaces is plotted against photon energy. The idea is that we have metal of some type, whether cesium, calcium, aluminum, beryllium, or platinum, and photons of various frequencies are incident on that metal. If an incident photon has enough energy, then when it’s absorbed by the metal, it will cause the ejection of an electron from that surface. The minimum amount of energy required for a photon to cause that electron ejection is called the work function of the metal.

We can think of the work function as an energy barrier that an electron must overcome in order to leave the surface. According to our graph, the work function varies for our different metals. Something important about the work function is that it’s the very minimum amount of energy required to eject an electron from a surface.

In identifying the work functions of the metals on our graph, we want to look for the energies at which these metals will emit an electron, but one with zero kinetic energy. These energies occur where our five lines meet the horizontal axis. It’s these photon energies which, if transferred to these five different types of metals, would just barely eject an electron from that surface. The electron would no longer be part of the metal, but it wouldn’t be moving.

The first part of our question asks, which metal has the lowest work function? This is the metal that will require the least amount of photon energy to eject an electron. Of our five metals, we see that cesium has the lowest work function. The curve for this metal intersects the horizontal axis at a smaller value than any of the other metals. So cesium has the lowest work function of all the metals.

And now we want to know which metal has the highest work function. This will be the metal whose curve intersects the horizontal axis at the highest value. And we see that this corresponds to platinum. The lowest work function of our metals then belongs to cesium with a value of about 2.1 electron volts, while platinum has the highest work function with a value of about 6.3 electron volts.