Photoelectric effect

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

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

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

Summary

[ disguise ]

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

History

The first observations of the photoelectric effect were carried out by Heinrich Hertz in 1887 in his experiments on the production and reception of electromagnetic waves. His receiver consisted of a coil in which a spark could be produced as a product of the reception of electromagnetic waves. To better observe 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 electrons and the intensity of the electric spark produced in the receiver. Hertz published an article with his results without attempting to explain the observed phenomenon.

In 1897 , British physicist Joseph John Thomson was investigating cathode rays. Influenced by the works of James Clerk Maxwell , Thomson deduced that cathode rays consisted of a stream 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 electromagnetic field of variable frequency produced resonances with the atomic electric field and that if these 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. Larger increases in light intensity produced larger increases in current. Higher frequency radiation produced the emission of particles with greater kinetic energy.

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

The kinetic energy of electrons could be measured from the potential difference necessary to stop them in a cathode ray tube. Ultraviolet radiation required, for example, higher stopping potentials than longer wavelength radiation. 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 light quanta that would later be called photons. In an article titled “A heuristic point of view on the production and transformation of light” 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 produced 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 experiments 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 photons in the light ray have a characteristic energy determined by the frequency of the light. In the photoemission process, if an electron absorbs the energy of a photon and the latter has more energy than the work function, the electron is torn from the material. If the photon energy is too low, the electron cannot escape from the surface of the material. Increasing the intensity of the beam 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 release an electron from an atomic bond, or else the energy is re-emitted. If the photon’s energy is absorbed, some of it frees 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 luminous radiation, could leave the metal with kinetic energy. He tried to explain the behavior of radiation , which obeyed the intensity of the incident radiation, knowing the number of electrons that left the metal, and its frequency, which was proportional to the energy that propelled said particles.

Laws of photoelectric emission

• For a given metaland frequency of incident radiation , the number of photoelectrons emitted is directly proportional to the intensity of incident light .
• For each given metal, there exists 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 photoelectron emission occurs instantaneously, regardless of the intensity of the incident light. This fact is contrary to the theory of Classical Physicsthat would expect there to be a certain delay between the absorption of energy and the emission of the electron , less than a 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 needed to release 1 electron + kinetic energy of the emitted electron.

Algebraically it can be expressed by the following formula:

Which can also be written as follows:

Where (h) is Planck’s constant, (ƒo) is the cut-off frequency or minimum frequency of the photons for the photoelectric effect to take place, Φ is the work function, or minimum energy necessary to take an electron from the Fermi level outside the material and Ek is the maximum kinetic energy of the electrons that is experimentally observed.

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

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

Physical foundation of the phenomenon

Planck had concluded that the transfer of energy between matter and radiation in the black body occurred through energy packets. However, he did not want to admit that the radiant energy once released from matter also traveled in corpuscular form. That is to say, he continued to consider the 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 this he returned to the idea of ​​Planck’s energy quantum, postulating that:

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

When a photon hits the metal, it transfers all its energy to one of the electrons. If this energy is enough to break the electron’s bond with the metal, then the electron is released. 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 frequency of the radiation is low (as in visible light), the photons do not carry enough energy to knock off electrons, even if the intensity of the light or the time during which it hits are 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, a growth in intensity causes a greater number of electrons removed (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 time delay between the arrival of the radiation and the emission of the first electron. Since the energy is distributed uniformly over the front of the incident wave, it would take at least a few hundred seconds to transfer the necessary energy. Einstein’s theory, on the other hand, predicts that: Radiation of adequate frequency, although of extremely low intensity, produces electron emission instantaneously.

It took ten years of experimentation until the new theory was corroborated and accepted. The value of h (h₌ 6.626×10 at -34 Js, where J is Joule and s, b) was determined from photoelectric effect experiments and was found to agree perfectly with the value found by Planck from the radiation spectrum black body From that moment on, physicists accepted that, although light propagates as if it were a wave, when it interacts with matter (in the processes of absorption and emission) it behaves like a beam of particles. This surprising behavior is what has been called the dual nature of light. This shows that ideas arising from the macroscopic world are not applicable to the unimaginable world of the tiny.

Wave-Corpuscule Duality

The photoelectric effect was one of the first physical effects that revealed the wave-corpuscle duality characteristic of quantum mechanics. Light behaves like waves and can produce interference and diffraction as in Thomas Young’s double slit experiment, but it exchanges energy discretely in packets of energy, photons, whose energy depends on the frequency of electromagnetic radiation. Classical ideas about the absorption of electromagnetic radiation by an electron suggested that energy is absorbed continuously. These types of explanations were found in classic books such as Millikan’s book on Electrons or the one written by Compton and Allison on the theory and experimentation with X-rays. These ideas were quickly replaced after Albert Einstein’s quantum explanation.

Photoelectric effect today

The photoelectric effect is the basis of the production of electrical energy by solar radiation and the energy use of solar energy. The photoelectric effect is also used to manufacture cells used in the flame detectors of the boilers of large thermoelectric power plants. This effect is also the working principle of the sensors used in digital cameras. It is also used in photosensitive diodes such as those used in photovoltaic cells and in electroscopes or electrometers. Currently, the most 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 sunlight for a long time. For example, dust particles on the lunar surface become positively charged due to the impact of photons. The charged particles repel each other, rising from the surface and forming a tenuous atmosphere. Space satellites also acquire a positive electrical charge on their illuminated surfaces and a negative electrical charge on their darkened regions, so it is necessary to take these charge accumulation effects into account in their design.