# Photoelectric Effect: Electrons from Matter and Light The photoelectric effect occurs when matter emits electrons upon absorbing electromagnetic energy. Buena Vista Images / Getty Images

The photoelectric effect occurs when matter emits electrons upon exposure to electromagnetic radiation, such as photons of light. Here's a closer look at what the photoelectric effect is and how it works.

## Overview of the Photoelectric Effect

The photoelectric effect is studied in part because it can be an introduction to wave-particle duality and quantum mechanics.

When a surface is exposed to sufficiently energetic electromagnetic energy, light will be absorbed and electrons will be emitted. The threshold frequency is different for different materials. It is visible light for alkali metals, near-ultraviolet light for other metals, and extreme-ultraviolet radiation for nonmetals. The photoelectric effect occurs with photons having energies from a few electronvolts to over 1 MeV. At the high photon energies comparable to the electron rest energy of 511 keV, Compton scattering may occur pair production may take place at energies over 1.022 MeV.

Einstein proposed that light consisted of quanta, which we call photons. He suggested that the energy in each quantum of light was equal to the frequency multiplied by a constant (Planck's constant) and that a photon with a frequency over a certain threshold would have sufficient energy to eject a single electron, producing the photoelectric effect. It turns out that light does not need to be quantized in order to explain the photoelectric effect, but some textbooks persist in saying that the photoelectric effect demonstrates the particle nature of light.

## Einstein's Equations for the Photoelectric Effect

Einstein's interpretation of the photoelectric effect results in equations which are valid for visible and ultraviolet light:

energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron

hν = W + E

where
h is Planck's constant
ν is the frequency of the incident photon
W is the work function, which is the minimum energy required to remove an electron from the surface of a given metal: hν0
E is the maximum kinetic energy of ejected electrons: 1/2 mv2
ν0 is the threshold frequency for the photoelectric effect
m is the rest mass of the ejected electron
v is the speed of the ejected electron

No electron will be emitted if the incident photon's energy is less than the work function.

Applying Einstein's special theory of relativity, the relationship between energy (E) and momentum (p) of a particle is

E = [(pc)2 + (mc2)2](1/2)

where m is the rest mass of the particle and c is the velocity of light in a vacuum.

## Key Features of the Photoelectric Effect

• The rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light, for a given frequency of incident radiation and metal.
• The time between the incidence and emission of a photoelectron is very small, less than 10–9 second.
• For a given metal, there is a minimum frequency of incident radiation below which the photoelectric effect will not occur, so no photoelectrons can be emitted (threshold frequency).
• Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron depends on the frequency of the incident radiation but is independent of its intensity.
• If the incident light is linearly polarized, then the directional distribution of emitted electrons will peak in the direction of polarization (the direction of the electric field).

## Comparing the Photoelectric Effect With Other Interactions

When light and matter interact, several processes are possible, depending on the energy of incident radiation. The photoelectric effect results from low energy light. Mid-energy can produce Thomson scattering and Compton scattering. High energy light can cause pair production.