Question Video: Determining Work Function Using a Graph of Electron Energy Versus Photon Wavelength | Nagwa Question Video: Determining Work Function Using a Graph of Electron Energy Versus Photon Wavelength | Nagwa

# Question Video: Determining Work Function Using a Graph of Electron Energy Versus Photon Wavelength Physics • Third Year of Secondary School

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

On our graph then, this vertical axis labeled electron energy indicates maximum kinetic energy of photoelectrons. A photoelectron is an electron that’s ejected from the surface of a metal after it has absorbed an incident photon. We could say the electron is ejected after being liberated by the photon’s energy. It’s the maximum kinetic energy of photoelectrons like these that is indicated on our vertical axis. We see that this is plotted against the wavelength of incident radiation.

For all five of our curves — that is, all five of the metals indicated on this graph — the curve reaches a maximum wavelength value for which the kinetic energy of ejected electrons is zero. For each metal, it’s at this point that incoming radiation is just energetic enough to cause the release of electrons from the metal. This then is the minimum amount of energy needed for each metal for the creation of a photoelectron.

Both parts of our question ask about something called the work function of the metal. The work function is just the amount of energy we’ve been considering, the minimum energy needed to eject an electron from the surface of a metal. To answer the question of which metal has the lowest work function, we might think we would pick the metal with the lowest maximum wavelength.

Here, we must be careful though. We recall that the energy of a photon is equal to the Planck constant times the speed of light in vacuum, that’s the speed of the photon, divided by the photon’s wavelength. We know then that photon energy is inversely proportional to photon wavelength. That tells us that the metal with the lowest work function will actually be the one with the largest maximum wavelength. That, we see, is cesium. Because cesium has the largest maximum wavelength for which an incident photon will stimulate the ejection of an electron, it therefore requires the least amount of energy to eject an electron from its surface as compared to the other metals. The metal with the lowest work function is cesium.

In the next part of our question, we want to know which metal has the highest work function. Thanks to our inverse relationship between photon energy and wavelength, we know that the metal with the highest work function will correspond to the metal with the lowest maximum wavelength that will cause electron ejection. This lowest maximum wavelength is about 250 nanometers, and it corresponds to the metal selenium. Selenium therefore requires more energy to eject an electron from its surface than any of the other metals. It has the highest work function.

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