Waves and Light: The Photoelectric Effect

The Photoelectric Effect

The photoelectric effect is the phenomenon in which electrons are emitted from the surface of a metal when light of sufficient frequency illuminates the surface.
This effect played a critical role in the development of quantum mechanics, as it supports the particle theory of light.
The photoelectric effect cannot be explained by classical wave theories of light, which predict that the energy of ejected electrons should increase with the intensity of light. However, experiments show that the energy of the electrons is instead dependent on the frequency of the incoming light.

The Threshold Frequency, often denoted ‘f0’, is the minimum frequency of incoming light needed for the photoelectric effect to occur.
The Work Function, usually denoted by the Greek letter phi (Φ), is the minimum energy required to remove an electron from a metal surface.
Each metal has a unique work function, which is typically given in electronvolt (eV) units.
The threshold frequency is directly related to the work function via the Plank-Einstein relation: Φ = h f0 - where ‘h’ is Planck’s constant.

Albert Einstein proposed that light is composed of packets of energy called photons to explain the photoelectric effect.
He suggested that an electron absorbs a whole photon and obtains its energy. If the photon energy is equal to or greater than the work function, the electron can escape the metal.
The excess energy, after the work function has been overcome, is converted into kinetic energy of the emitted photoelectron.
Mathematically this can be represented as: Energy of Photon = Work function + Kinetic energy of the ejected electron. Which simplifies to: hf = Φ + Ekmax.

Stopping Potential is defined as the minimum voltage needed to stop the most energetic electrons from reaching the other side of a circuit in a photoelectric effect experiment.
By measuring the stopping potential, it is possible to determine the maximum kinetic energy of the photoelectrons.
If ‘Vs’ is the stopping potential, then the maximum kinetic energy of the photoelectrons can be given as eVs, where e is the charge of the electron.

The photoelectric effect is utilised in many practical applications including photocells, which convert light energy into electrical energy.
In photomultipliers, the photoelectric effect is used to amplify the initial current produced by the incident light, enhancing the sensitivity of this device.
Solar cells operate on the photoelectric effect principle to convert sunlight into electricity.