The photoelectric effect describes the emission of electrons from a metal surface when light of high enough frequency shines on it. This topic is important because it shows that light transfers energy in discrete packets called photons. A cheat sheet helps students connect frequency, wavelength, energy, work function, and electron kinetic energy in one place.
It also supports quick problem solving for AP Physics, honors physics, and introductory modern physics.
Key Facts
- Photon energy is given by , where is Planck’s constant and is the light frequency.
- Using wavelength, photon energy can be written as , where is the speed of light and is wavelength.
- The work function is the minimum energy needed to remove one electron from a metal surface.
- Einstein’s photoelectric equation is , where is the maximum kinetic energy of emitted electrons.
- The threshold frequency is , and no electrons are emitted when .
- The stopping potential satisfies , so .
- Increasing light intensity increases the number of emitted electrons if , but it does not increase .
- A graph of versus has slope and vertical intercept .
Vocabulary
- Photon
- A photon is a discrete packet of electromagnetic energy with energy .
- Work function
- The work function is the minimum energy required to remove an electron from a metal surface.
- Threshold frequency
- The threshold frequency is the minimum light frequency needed to eject electrons, given by .
- Photoelectron
- A photoelectron is an electron emitted from a material after absorbing energy from a photon.
- Stopping potential
- The stopping potential is the voltage needed to reduce the maximum photoelectron kinetic energy to .
- Maximum kinetic energy
- The maximum kinetic energy is the greatest kinetic energy of emitted electrons, equal to .
Common Mistakes to Avoid
- Using intensity instead of frequency to decide whether electrons are emitted is wrong because emission requires , regardless of brightness.
- Forgetting the work function is wrong because only the leftover photon energy becomes kinetic energy, so .
- Mixing joules and electronvolts is wrong because formulas must use consistent units, with .
- Assuming longer wavelength means greater photon energy is wrong because , so energy decreases as wavelength increases.
- Using the total number of emitted electrons to find is wrong because electron count depends mainly on intensity, while depends on frequency.
Practice Questions
- 1 A metal has work function . What is the maximum kinetic energy of electrons emitted by light with photon energy ?
- 2 Find the threshold frequency for a metal with using .
- 3 Light of wavelength shines on a metal with . Find in using .
- 4 If light is below the threshold frequency, explain why increasing the intensity still does not cause photoelectrons to be emitted.
Understanding Photoelectric Effect Reference
The key evidence came from observations that classical wave theory could not explain. If light acted only as a spread out wave, brighter light should eventually give each electron more energy. Experiments showed a different pattern.
Very dim light could release electrons immediately when its frequency was high enough. Very bright low frequency light could fail completely. This means an electron does not slowly collect energy from the whole beam.
It receives energy in one interaction with one photon. The interaction happens extremely quickly, so there is no measurable waiting time for energy to build up.
A metal holds some of its electrons near the surface, but they are still bound by electrical forces inside the material. The work function measures the energy barrier at that surface. Different metals have different barriers because their atoms and electron arrangements differ.
A photon must first supply enough energy to clear this barrier. Any energy left after escape becomes motion of the electron. Electrons do not all leave with exactly the same kinetic energy.
Some begin deeper in the metal or lose energy through collisions before reaching the surface. This is why physics problems focus on the maximum kinetic energy. It represents electrons that escape with the smallest possible energy loss.
Stopping potential gives an experimental way to measure that maximum energy. In a photoelectric tube, emitted electrons travel toward a collecting electrode. A reverse voltage can be applied to push them back.
As the reverse voltage increases, fewer electrons reach the collector. At one particular voltage, even the fastest electrons are stopped and the current falls to zero. This measurement turns electron energy into a voltage that can be read directly.
When students use this idea, they need to keep energy units consistent. Photon energies are often expressed in electron volts, while Planck's constant may be given in joule seconds. One electron volt is the energy gained by one electron moving through one volt.
Graphs reveal the model especially clearly. For a fixed metal, changing the light frequency changes the maximum electron energy in a straight line pattern. The slope is a universal constant, not a property of the metal.
The point where the line reaches zero kinetic energy identifies the threshold frequency. Changing the metal shifts the line because the surface barrier changes. Intensity produces a different kind of change.
Above threshold, greater intensity means more photons arrive each second, so more electrons can be released. It does not make each photon more energetic. This distinction appears in solar cells, light sensors, camera detectors, and laboratory phototubes.
In problems, first decide whether the frequency clears the threshold. Only then calculate the energy left for electron motion or the voltage needed to stop it.