The kinetic energy of an ejected electron is the energy a photoelectron carries after leaving a metal surface, equal to the incident photon's energy minus the material's work function (KE_max = hf − W). It depends on light's frequency, not its intensity, which is core evidence that light comes in photons.
When light hits a photoactive metal and an electron pops out, that electron leaves with some kinetic energy. The accounting is pure energy conservation. One photon delivers energy hf to one electron. The metal charges an exit fee called the work function (W or φ), the minimum energy needed to free the electron. Whatever is left over becomes the electron's kinetic energy, so the fastest electrons obey KE_max = hf − W.
Here is the part the AP exam loves. This kinetic energy depends only on the frequency of the light, not on how bright it is. Cranking up intensity sends more photons, which ejects more electrons, but each electron still gets one photon's worth of energy. If the frequency is below the threshold frequency (where hf = W), no electrons come out at all, no matter how intense the light. Classical wave theory predicted the opposite, so this result is direct evidence that light behaves as a collection of photons.
This term 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. The CED's essential knowledge is explicit that the energy of emitted electrons does not depend on the number of incident photons, and that emission requires a minimum threshold frequency. The kinetic energy of the ejected electron is where all of that comes together in one equation. It is the measurable quantity that proved Einstein's photon model and earned him the Nobel Prize, and it is the quantity you will calculate, graph, and reason about on the exam. A plot of KE_max versus frequency is a straight line with slope h and x-intercept at the threshold frequency, which makes it one of the cleanest graph-interpretation setups in all of AP Physics 2.
Keep studying AP® Physics 2 Unit 15
Maximum kinetic energy (Unit 15)
KE_max is the specific value of this term for electrons that escape with zero internal energy loss. Real electrons can lose some energy on the way out of the metal, so KE_max = hf − W is a ceiling, not what every electron gets.
Threshold frequency (Unit 15)
The threshold frequency is just the frequency where the ejected electron's kinetic energy hits zero, meaning hf exactly pays the work function with nothing left over. Below it, no emission happens at any intensity.
De Broglie wavelength (Unit 15)
Once the electron is out, its kinetic energy sets its de Broglie wavelength. More kinetic energy means more momentum, which means a shorter wavelength. Exam questions chain these two ideas together, so practice going from hf − W straight to λ = h/p.
Electric potential energy and stopping potential (Unit 10)
Experimenters measure KE_max by applying a reverse voltage that just barely stops the electrons. That stopping potential satisfies qV_stop = KE_max, which is the same energy-charge-voltage relationship you learned with electric potential. It also explains why this whole topic runs on electron-volts.
Multiple-choice questions hit this concept from three angles. First, straight calculation, like finding a work function when you know the photon energy and the electron's maximum speed (watch for setups comparing two metals where one ejects electrons at twice the speed of the other, since KE scales with v², not v). Second, conceptual trend questions, like what happens to the kinetic energy of ejected electrons as photon frequency increases (it increases linearly) versus as intensity increases (it doesn't change). Third, stopping-potential comparisons, like predicting how V_stop changes when you swap to a metal with work function 1.5φ under the same light. No released FRQ has used this exact phrase verbatim, but the photoelectric effect is standard FRQ territory, where you may need to interpret or sketch a KE_max versus frequency graph and explain why intensity changes the number of electrons but not their energy.
Photon energy is what the light delivers; the ejected electron's kinetic energy is what's left after the work function is paid. They are never equal for a real metal because W > 0. If a question gives you hf and asks for the electron's KE, you must subtract W. Forgetting that subtraction is the single most common photoelectric mistake.
The maximum kinetic energy of an ejected electron is the photon's energy minus the work function, KE_max = hf − W.
Kinetic energy of photoelectrons depends on the light's frequency, not its intensity; brighter light ejects more electrons but does not make them faster.
If the photon frequency is below the threshold frequency, no electrons are ejected regardless of intensity, because one photon can't pay the work function.
A graph of KE_max versus frequency is a straight line whose slope is Planck's constant h and whose x-intercept is the threshold frequency.
Stopping potential measures KE_max through qV_stop = KE_max, linking this topic back to electric potential energy.
The fact that electron energy is independent of the number of photons is the CED's stated evidence that light is a collection of photons, not a classical wave.
It's the energy a photoelectron has after leaving the metal, given by KE_max = hf − W, where hf is the photon energy and W is the work function. It's the leftover energy after the electron pays the cost of escaping the surface.
No. Intensity controls how many photons arrive, so it controls how many electrons are ejected, not how energetic each one is. Only increasing the frequency of the light increases the kinetic energy of the ejected electrons.
The photon energy hf is the total delivered; the electron's kinetic energy is hf minus the work function W. For example, a 5.0 eV photon hitting a metal with W = 3.0 eV ejects electrons with at most 2.0 eV of kinetic energy.
It increases linearly. Each extra bit of photon energy above the work function goes straight into the electron's kinetic energy, which is why a KE_max vs. frequency graph is a straight line with slope h.
Rearrange the photoelectric equation to W = hf − KE_max. If you're given electron speed instead, compute KE = ½mv² first; in comparison problems, remember doubling the speed quadruples the kinetic energy.
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