Maximum kinetic energy (Kmax) is the greatest kinetic energy a photoelectron can have when light ejects it from a metal, equal to the photon energy minus the work function (Kmax = hf − φ). It increases linearly with light frequency above the threshold frequency and does not depend on light intensity.
In the photoelectric effect, a photon hands its entire energy (hf) to a single electron in the metal. The electron has to pay an "exit fee," the work function φ, just to escape the surface. Whatever energy is left over becomes the electron's kinetic energy. An electron right at the surface pays only φ, so it leaves with the most energy possible. That leftover is the maximum kinetic energy, Kmax = hf − φ. Electrons that start deeper in the metal lose extra energy on the way out, so they exit with less than Kmax.
The big idea from the CED is what Kmax depends on, and what it doesn't. Kmax increases linearly with the frequency of the incident light once you're above the threshold frequency. It does NOT depend on how bright the light is. Cranking up intensity means more photons, which ejects more electrons, but each electron still gets energy from one photon at a time. That one-photon-one-electron rule is the evidence that light behaves as a collection of particles (photons), not just a wave. If light were purely a wave, brighter light should mean faster electrons, and it doesn't.
Maximum kinetic energy lives in Topic 15.5 (The Photoelectric Effect) in Unit 15: Modern Physics, supporting learning objective 15.5.A, which asks you to describe photon-matter interactions using the photoelectric effect. Kmax is the measurable quantity that makes the whole argument work. The fact that Kmax depends on frequency but not on the number of photons is exactly the essential knowledge the CED highlights as evidence for the particle model of light. If you can explain why a dim ultraviolet beam ejects faster electrons than a blazing red one, you've got the core of Unit 15's wave-particle duality story. For the full experimental setup and graphs, head up to the Topic 15.5 study guide.
Keep studying AP® Physics 2 Unit 15
Threshold frequency (Unit 15)
Threshold frequency f₀ is the frequency where Kmax hits exactly zero, because the photon energy just barely covers the work function (hf₀ = φ). Below f₀, no electrons come out no matter how intense the light is. On a Kmax vs. frequency graph, f₀ is the x-intercept and Planck's constant h is the slope.
Kinetic energy of ejected electron (Unit 15)
Kmax is the ceiling, not the only value. Ejected electrons come out with a range of kinetic energies from zero up to Kmax, because electrons starting deeper in the metal lose extra energy escaping. Only surface electrons get the full hf − φ.
Inverse relationship between de Broglie wavelength and kinetic energy (Unit 15)
Once an electron is ejected, it's a moving particle of matter, so it has a de Broglie wavelength λ = h/p. A higher Kmax means more momentum and a shorter wavelength. This is a favorite combo question because it tests both halves of wave-particle duality, photons acting like particles and electrons acting like waves.
This term gets tested constantly in Topic 15.5, almost always built around Kmax = hf − φ. Multiple-choice stems give you two of the three quantities and ask for the third, like finding Kmax from a 310 nm wavelength and a 3.2 eV work function (remember to convert wavelength to photon energy first using E = hc/λ). Another classic stem compares two metals with different work functions hit by the same frequency, where the smaller work function gives the larger Kmax. Watch for the threshold trap, like the question where a 5.0 eV photon ejects electrons with 2.3 eV but dropping the photon energy to 2.5 eV means it falls below the 2.7 eV work function and nothing comes out at all. On the free-response side, the 2018 LAQ had you analyze how Kmax varies as frequency is varied, and the 2024 Short FRQ compared photoelectric trials on two different metals at three frequencies. Be ready to interpret or sketch the Kmax vs. f graph, where the slope is h, the x-intercept is the threshold frequency, and the y-intercept is −φ.
Photon energy is what the light delivers; maximum kinetic energy is what the electron keeps after escaping. They differ by the work function (Kmax = hf − φ). A common error is setting the electron's kinetic energy equal to hf, which ignores the energy cost of leaving the metal. The two are only close when the photon energy is far above the work function, and Kmax is zero (not hf) right at the threshold frequency.
Maximum kinetic energy is the photon's energy minus the work function, written as Kmax = hf − φ.
Kmax increases linearly with the frequency of the incident light above the threshold frequency.
Kmax does not depend on light intensity, because each electron absorbs energy from only one photon; this is key evidence that light comes in particle-like packets.
At the threshold frequency, Kmax equals zero because the photon energy exactly matches the work function.
Only electrons at the metal's surface reach Kmax; electrons from deeper inside exit with less kinetic energy.
On a Kmax vs. frequency graph, the slope is Planck's constant h, the x-intercept is the threshold frequency, and the y-intercept is the negative of the work function.
It's the most kinetic energy an ejected photoelectron can have, equal to the incident photon's energy minus the metal's work function, Kmax = hf − φ. Surface electrons reach this maximum; deeper electrons come out with less.
No. Intensity only changes how many electrons are ejected, not how fast they move. Kmax depends only on the light's frequency and the metal's work function, which is the central evidence that light behaves as photons rather than a continuous wave.
Photon energy is hf, the full energy the light delivers. Maximum kinetic energy is what's left after the electron pays the work function to escape, so Kmax = hf − φ. For example, a 5.0 eV photon hitting a metal with φ = 2.7 eV gives Kmax = 2.3 eV, not 5.0 eV.
Kmax is exactly zero at the threshold frequency, because the photon energy just barely equals the work function (hf₀ = φ). Below f₀, no electrons are emitted at all, regardless of how many photons hit the surface.
The slope is Planck's constant h, and it's the same for every metal. Different metals shift the line left or right (different threshold frequencies and work functions), but the slope never changes, which is exactly what the 2018 FRQ-style graph analysis tests.
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