The Photoelectric Effect

The photoelectric effect is the name given to the emission of electrons in electromagnetic radiation.

The photoelectric effect and photoelectrons

An example is for electrons to be ejected from a metallic material after being set free from an atom by light with high energy impacting that material. The electrons ejected from the material are called photoelectrons. A simple explanation of the effect and important developments of the theory are listed below.

• The light energy depends on its wavelength and frequency. Higher frequency and shorter wavelength lead to more electrons being ejected.
• The photoelectric effect was first observed by Heinrich Hertz, who could not understand why it happened. Subsequent experiments made by other scientists helped to explain the phenomenon now known as the ‘photoelectric effect’.
• Theoretical developments by Albert Einstein and Max Planck explained the phenomenon by assuming that light as radiation was composed of discrete particles with fixed amounts of energy.
• A photon only needs a minimum amount of energy, called the work function, to release an electron from the material.
• Once the minimum amount of energy is surpassed, the rest of the energy is used to push the electron out of the metal plate at a certain velocity.
• Solar cells are an application of the photoelectric effect.

Frequency energy dependence

Experiments carried out to measure how light affects the emission of electrons from the plates delivered two main results.

1. The intensity of the light had no effect on the energy of the electrons emitted.
2. The frequency of the light affects the energy of the emitted electrons. The higher the frequency, the faster the electrons were emitted.

The work function

The amount of energy needed to release an electron is called the ‘work function’ (φ), which is different for each material. The energy is specified as the product of the Planck constant ‘h’ and the light frequency ‘f’:

The Planck constant has a value of:

The work function is measured in electron volts or eV.

Albert Einstein and the photoelectric effect

The first experiments describing the photoelectric effect failed to explain why the brightness of the light did not affect the emitted electrons. The electron velocity did not change when the lights were brighter; the electrons only moved faster when higher light frequencies were used.

Albert Einstein discovered that the increase of the kinetic energy affecting the photoelectrons was proportional to an increase in the frequency of the light. If conservation must occur, then the light’s energy was proportional to its frequency, and the light was acting as a particle where its energy is equal to the product of the Planck constant ‘h’ and the light frequency ‘f’.

And if the light’s energy is carried by the photons (light’s particles), we get:

How are the photon theory of light and the photoelectric effect related?

If we connect Einstein’s explanation concerning the light and the photoelectric effect discovered by earlier experiments, we arrive at the expression that explains the photoelectric effect.

Figure 1. The photoelectric effect can be described using energy conservation between the photon energy impacting the electron at the metallic plate and the energy used to remove the electron from the metal plate or φ and the energy excess that is transformed into kinetic energy. Source: Manuel R. Camacho, StudySmarter.

An example of the photoelectric effect

You have a particle emitted from a copper plate that has a kinetic energy of 2.0 [eV]. You wish to determine the energy and the frequency of the photon that released the electron.