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The Photoelectric Effect
Modern Physics
When light falls on a metal, it can knock electrons out of the surface, but only if the light's frequency is high enough. This photoelectric effect proved that light comes in packets.
What the effect is
The photoelectric effect is the emission of electrons from a metal surface when light shines on it. Experiments in the late nineteenth century found three puzzling facts. First, no electrons are emitted if the light's frequency is below a threshold, however bright the light is. Second, above the threshold, electrons are emitted immediately, with no delay. Third, increasing the brightness increases the number of electrons but not their maximum energy, while increasing the frequency does increase their energy. A wave picture of light could not explain any of this, because a wave would spread its energy over the whole surface and take time to build up.
Einstein's photon explanation
Einstein explained the effect in 1905 by treating light as a stream of particles called photons, each carrying energy E = hf. One photon gives all its energy to one electron. Part of that energy, the work function phi, is needed to escape the metal, and the rest becomes the electron's kinetic energy: KE_max = hf - phi. If hf is less than phi, no electron can escape, which explains the threshold frequency f0 = phi/h. Brighter light means more photons and therefore more electrons, but each photon still carries the same energy, so the maximum kinetic energy is unchanged. This work won Einstein the Nobel Prize in 1921.
Where you see it
Solar cells use the photoelectric effect in a different form: photons free charge carriers inside a semiconductor, producing a current that powers homes and satellites. Photomultiplier tubes and light sensors in cameras, smoke alarms and automatic doors detect light by the current it produces. The effect also sets the basis for spectroscopy, where the energies of emitted electrons reveal the properties of a material. The photoelectric effect remains the clearest classroom demonstration that light behaves as particles, and it opened the door to quantum mechanics.
Worked example: fastest electrons from a metal
Light of photon energy 3.5 eV falls on a metal with work function phi = 2.0 eV. Use maximum kinetic energy KE_max = h f - phi. Here h f = 3.5 eV, so KE_max = 3.5 - 2.0 = 1.5 eV. Convert to joules: 1 eV = 1.60 x 10^-19 J. KE_max = 1.5 x 1.60 x 10^-19 = 2.40 x 10^-19 J. So the fastest electrons leave with 1.5 eV, or 2.40 x 10^-19 J, of kinetic energy.
Common mistakes
- Thinking intensity controls electron energy: intensity controls how many electrons are ejected, while frequency controls how energetic each one is.
- Forgetting the work function: an electron needs at least phi of energy to escape, and only the excess becomes kinetic energy.
- Expecting a delay: emission is immediate when the frequency is above threshold, because a single photon gives all its energy to one electron.
Practice questions
- Photons of 4.0 eV hit a metal with work function 2.5 eV. What is the maximum kinetic energy of the electrons?
Show answer
KE_max = 4.0 - 2.5 = 1.5 eV.
- What happens if the photon energy is 1.5 eV for the same metal?
Show answer
No electrons are emitted, because 1.5 eV is below the 2.5 eV work function.
- What is the threshold frequency for a metal with work function 2.0 eV?
Show answer
f0 = phi/h = (2.0 x 1.60 x 10^-19)/(6.63 x 10^-34) = 4.83 x 10^14 Hz.
Frequently asked questions
Can very bright low-frequency light eject electrons?
No. Below the threshold frequency, no electrons are emitted however bright the light is, because each photon carries too little energy.
Does brighter light make the electrons faster?
Yes, it increases the number of electrons emitted per second, and therefore the current, but not the maximum energy of each electron.