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# ⚡ Photoelectric effect

Image: 10-14 meters or 10 fermi is the size of the nucleus of an atom. Towards the end of the 19th century, it was discovered that the atom was not an indivisible element of matter.
E = hf - Φ, where E is the kinetic energy of the emitted electron, h is Planck's constant, f is the frequency of the incident light and Φ is the work function of the material which depends on the properties of the material.
The Nobel Prize in Physics was awarded to Einstein in 1921 for this explanation of the photoelectric effect.

### E = hf - Φ

The photoelectric effect is the physical phenomenon by which electrons are ejected from a material when exposed to sufficiently high frequency light. This phenomenon, known for more than a century, has been the subject of much debate among scientists. They were divided on the very nature of light. Was it a wave or a particle?

It starts in 1887. German physicist Heinrich Rudolph Hertz (1857-1894), famous for the discovery of electromagnetic waves, discovered the photoelectric effect in a fairly simple experiment.

Two metal plates are placed in the void. A potential difference is applied to these plates. The current flowing through the system is measured. As the metal plates are placed in a vacuum, the electrons have no support to pass from an electrode to each other, and therefore no current can flow through the system.

Hertz illuminates one of the plates with red light and nothing happens. He then illuminates the plate with blue light and notices that a current is beginning to flow.

The light, by striking the surface of the metal, tears electrons from it, which corresponds to the appearance of electricity since the electrons are electrically charged. But this explanation is not enough.

In 1900 another German physicist Max Planck (1858-1947) studied black body radiation and proposed a theory of light emission. Light corresponds to the activity of vibrating microscopic corpuscles, whose emitted energy E is proportional to the vibration frequency (E = hν). He calls this elementary quantity of light "quanta".

It was Albert Einstein (1879-1955) who made a major contribution to understanding the photoelectric effect. He will mix all the experimental results of Hertz, Halbwachs, Elster, Geitel and Lenard with the theoretical hypotheses of Planck. He offers a theory that light is made up of individual particles, called photons. He postulates that these photons have a quantized energy which is directly proportional to their frequency. This hypothesis helped explain the relationship between the frequency of light and the energy of electrons emitted by a material when exposed to high-energy light.

Einstein's equation for the photoelectric effect relates the kinetic energy of emitted electrons to the photon energy of incident light.

It is given by E = hf - Φ, where E is the kinetic energy of the emitted electron, h is Planck's constant, f is the frequency of the incident light and Φ is the work function of the material. Planck's constant, denoted h, is a fundamental physical constant which is used to calculate the energy of photons. It has a value of approximately 6.626 x 10^-34 joules second (J.s). The frequency of incident light, denoted f, is the number of complete light cycles per second and is measured in hertz (Hz).

The work function of the material, denoted Φ, is the minimum energy necessary to eject an electron from the material. It depends on the properties of the material itself, such as the nature of its chemical bonds, its crystal structure and its composition. The work function is a measure of how easily electrons can be ejected from a material. The larger it is, the more difficult it is to eject electrons from the material.

Einstein's equation for the photoelectric effect shows that the kinetic energy of emitted electrons is directly proportional to the photon energy of incident light minus the work function of the material. This means that if the frequency of the incident light is too low, the energy of the photons will be insufficient to eject electrons from the material, even if they are free to move. For the photoelectric effect to occur, the frequency of the incident light must exceed a threshold value determined by the work function of the material.

Einstein's equation for the photoelectric effect has important implications for understanding the nature of light and matter as well as for many areas of science and technology, including materials physics, energy solar, in medical imaging.