Threshold frequency is the minimum frequency of electromagnetic radiation required to eject electrons from a particular metal surface. Below this frequency, no photoelectrons are emitted, regardless of the radiation's intensity.
In the photoelectric effect, light transfers energy in discrete packets called photons. Each photon has energy
where is the Planck constant and is the radiation frequency. One photon transfers its energy to one electron.
An electron must receive at least enough energy to overcome the metal's work function, , which is the minimum energy required to remove an electron from the surface. At the threshold frequency , the photon has exactly this energy:
Therefore,
At exactly , an emitted electron has a maximum kinetic energy of zero. Above the threshold frequency, the excess photon energy becomes the electron's maximum kinetic energy:
For example, if , then
| Incident radiation | Result |
|---|---|
| No photoelectrons are emitted, even at high intensity. | |
| Electrons are just emitted with . | |
| Photoelectrons are emitted with . |
Increasing the frequency above raises the maximum kinetic energy and therefore the stopping potential, because every photon carries more energy. Increasing intensity at a fixed frequency above instead increases the number of photons arriving per second, so more electrons can be emitted and the photoelectric current increases. It does not increase . The immediate emission of electrons also supports the photon model: electrons do not gradually accumulate energy from a continuous wave.
A common misconception is that increasing intensity can compensate for a frequency below . It cannot: greater intensity supplies more photons, but each photon still has insufficient energy.
This is HL-only content in E.2 Quantum physics. In calculations, convert the work function from electronvolts to joules when using in , show the equation and substitution, and distinguish the effects of increasing frequency from those of increasing intensity.
