Photoelectric effect

Photoelectric effect . It is the emission of electrons from a metal when an electromagnetic radiation (visible or ultraviolet light, in general) is impinged on it.

The photoelectric effect was discovered and described by Heinrich Hertz in 1887 , when observing that the arc that jumps between two electrodes connected to high voltage reaches greater distances when it is illuminated with ultraviolet light than when it is left in the dark.

The theoretical explanation was made by Albert Einstein , who published in 1905 the revolutionary article “Heuristics of light generation and conversion”, basing his formulation of photoelectricity on an extension of Max Planck’s work on quanta . Later Robert Andrews Millikan spent ten years experimenting to prove that Einstein’s theory was not correct, to finally conclude that it was.

Summary

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  • 1 History
  • 2 Explanation
  • 3 Laws of photoelectric emission
  • 4 Mathematical formulation
  • 5 Physical basis of the phenomenon
  • 6 Wave-Corpuscle Duality
  • 7 Photoelectric effect today
  • 8 Sources

History

The first observations of the photoelectric effect were made by Heinrich Hertz in 1887 in his experiments on the production and reception of electromagnetic waves. Its receiver consisted of a coil in which a spark could be produced as a result of receiving electromagnetic waves. To get a better look at the spark, Hertz enclosed his receiver in a black box.

However, the maximum spark length was reduced in this case compared to previous spark observations. In effect, the absorption of ultraviolet light facilitated the jump of the electrons and the intensity of the electrical spark produced in the receiver. Hertz published an article with his results without trying to explain the observed phenomenon.

In 1897 , British physicist Joseph John Thomson investigated cathode rays. Influenced by the works of James Clerk Maxwell , Thomson deduced that cathode rays consisted of a flow of negatively charged particles, which he called corpuscles and are now known as electrons.

Thomson used a metal plate enclosed in a vacuum tube as a cathode, exposing it to light of different wavelengths. Thomson thought that the variable frequency electromagnetic field produced resonances with the atomic electric field and that if they reached a sufficient amplitude, the emission of a subatomic “corpuscle” of electric charge could occur, and therefore the passage of electric current .

The intensity of this electric current varied with the intensity of the light. Greater increases in light intensity produced greater increases in current. The higher frequency radiation produced the emission of particles with higher kinetic energy.

In 1902 Philipp von Lenard made observations of the photoelectric effect in which the variation of energy of the electrons with the frequency of the incident light was revealed .

The kinetic energy of the electrons could be measured from the potential difference necessary to brake them in a cathode ray tube. Ultraviolet radiation, for example, required higher braking potentials than radiation with a longer wavelength. Lenard’s experiments yielded only qualitative data given the difficulties of the instrumental equipment with which he worked.

In 1905 Albert Einstein proposed a mathematical description of this phenomenon that seemed to work correctly and in which the emission of electrons was produced by the absorption of quanta of light that would later be called photons. In an article entitled “A heuristic view of light production and transformation” he showed how the idea of ​​discrete light particles could explain the photoelectric effect and the presence of a characteristic frequency for each material below which it is not had no effect. For this explanation of the photoelectric effect Einstein would receive the Nobel Prize in Physics in 1921 .

Einstein’s work predicted that the energy with which electrons escaped from the material increased linearly with the frequency of the incident light. Surprisingly this aspect had not been observed in previous experiences on the photoelectric effect. The experimental demonstration of this aspect was carried out in 1915 by the American physicist Robert Andrews Millikan .

Heinrich Hertz Max Planck Joseph John Thomson Albert Einstein

Explanation

The light ray photons have a characteristic energy determined by the frequency of light. In the photoemission process, if an electron absorbs the energy of a photon and the photon has more energy than the work function, the electron is ripped from the material. If the energy of the photon is too low, the electron cannot escape from the surface of the material. Increasing the beam intensity does not change the energy of the constituent photons, it only changes the number of photons. Consequently, the energy of the emitted electrons does not depend on the intensity of the light, but on the energy of the individual photons.

Electrons can absorb energy from photons when they are irradiated, but following an “all or nothing” principle. All the energy of a photon must be absorbed and used to free an electron from an atomic bond, or else the energy is re-emitted. If the photon’s energy is absorbed, one part releases the electron from the atom and the rest contributes to the kinetic energy of the electron as a free particle.

Einstein did not intend to study the causes of the effect in which the electrons of certain metals , due to light radiation, could leave the metal with kinetic energy. He was trying to explain the behavior of the radiation , which was due to the intensity of the incident radiation, by knowing the amount of electrons leaving the metal, and the frequency of it, which was proportional to the energy that was driving these particles.

Photoelectric emission laws

  • For metal and frequency of radiation incident given, the amount of photoelectrons emitted is directly proportional to the intensity of light incident.
  • For each given metal, there is a certain minimum frequency of incident radiation below which no photoelectron can be emitted. This frequency is called the cutoff frequency, also known as the “Threshold Frequency”.
  • Above the cutoff frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light, but depends on the frequency of the incident light.
  • The emission of the photoelectron is carried out instantaneously, regardless of the intensity of the incident light. This fact is opposed to the theory of Classical Physics that would expect a certain delay between the absorption of energy and the emission of the electron , less than one nanosecond.

Mathematical formulation

To analyze the photoelectric effect quantitatively using the method derived by Einstein, it is necessary to pose the following equations:

  • Energy of an absorbed photon = Energy necessary to release 1 electron + kinetic energy of the emitted electron.

Algebraically it can be expressed by the following formula:

It can also be written as follows:

Where (h) is the Planck constant, (ƒo) is the frequency of cutting or minimum frequency of photons to take place the photoelectric effect, Φ is the work function, or minimum energy required to keep electron from the Fermi level outside the material and Ek is the maximum kinetic energy of the electrons that is observed experimentally.

If the photon energy (hƒ) is not greater than the work function (Φ), no electron will be emitted.

In some materials this equation describes the behavior of the photoelectric effect only roughly. This is so because the state of the surfaces is not perfect (non-uniform contamination of the external surface).

Physical basis of the phenomenon

Planck had concluded that the transfer of energy between matter and radiation in the black body occurred through energy packages. However, he did not want to admit that the radiant energy once detached from matter also traveled in a corpuscular way. In other words, he continued to consider radiation that propagates as a classical wave.

In 1905 , Albert Einstein went a step further by fully explaining the characteristics of the photoelectric effect. To do so, he took up Planck’s idea of ​​the quantum of energy, postulating that:

Electromagnetic radiation is made up of energy packets or photons. Each photon carries an energy (E = vh), where (v) is the frequency of radiation and (h) is Planck’s constant.

When a photon hits the metal, it transfers all of its energy to one of the electrons. If this energy is enough to break the bond of the electron with the metal, then the electron falls off. If the photon carries more energy than necessary, this excess is transformed into kinetic energy of the electron:

This theory perfectly explains the following observed facts:

  • If the radiation frequency is low (as in visible light), the photons do not carry enough energy to start electrons, even if the intensity of the light or the time during which it affects is increased. For each type of material there is a minimum frequency below which the photoelectric effect does not occur.
  • If the frequency of the radiation is sufficient for the photoelectric effect to occur, an increase in intensity causes the number of electrons to be removed to be greater (therefore the current will be greater), but does not affect the speed of the electrons. Increasing the intensity of light is equivalent to increasing the number of photons, but without increasing the energy carried by each one.
  • According to classical theory, there would be a delay time between the arrival of radiation and the emission of the first electron. Since the energy is evenly distributed over the front of the incident wave, it would take at least a few hundred seconds for the necessary wave to transfer the necessary energy. Einstein’s theory, by contrast, predicts that: Radiation of adequate frequency, albeit of extremely low intensity, produces instantaneous electron emission.

Ten years of experimentation passed before the new theory was corroborated and accepted. The value of h (h₌ 6.626×10 at -34 Js, where J is Joule and s, second) was determined from photoelectric effect experiences and was found to be in perfect agreement with the value found by Planck from the radiation spectrum black-bodied. From then on, physicists accepted that, although light propagates like a wave, when interacting with matter (in the processes of absorption and emission) it behaves like a particle beam. This amazing behavior is what has been called the dual nature of light. This shows that the ideas emerged from the macroscopic world are not applicable to the unimaginable world of the tiny.

Wave-Corpuscle Duality

The photoelectric effect was one of the first physical effects that revealed the characteristic wave-corpuscle duality of quantum mechanics. Light behaves like waves and can produce interferences and diffraction as in Thomas Young’s double slit experiment, but it exchanges energy in discrete energy packages, photons, whose energy depends on the frequency of electromagnetic radiation. Classic ideas about the absorption of electromagnetic radiation by an electron suggested that energy is absorbed continuously. Explanations of this kind were found in classic books like Millikan’s book on Electrons or Compton and Allison’s on X-ray theory and experimentation.

Photoelectric effect today

The photoelectric effect is the basis for the production of electrical energy by solar radiation and the energy use of solar energy. The photoelectric effect is also used for the manufacture of cells used in the flame detectors of the boilers of large thermoelectric plants. This effect is also the operating principle of the sensors used in digital cameras. It is also used in light-sensitive diodes such as those used in photovoltaic cells and in electroscopes or electrometers. Currently, the most widely used photosensitive materials are, apart from those derived from copper (now in less use), silicon, which produces higher electrical currents.

The photoelectric effect also manifests itself in bodies exposed to prolonged sunlight. For example, dust particles on the lunar surface acquire a positive charge due to the impact of photons. The charged particles repel each other rising from the surface and forming a faint atmosphere. Space satellites also acquire a positive electric charge on their illuminated surfaces and a negative one in darkened regions, so these charge accumulation effects need to be taken into account in their design.

 

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