Photoelectric effect

The photoelectric effect is the emission of electrons or other free carriers when light falls on a material. Electrons emitted in this manner can be called photoelectrons. This phenomenon is commonly studied in electronic physics, as well as in fields of chemistry, such as quantum chemistry or electrochemistry.

According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron. From this perspective, an alteration in the intensity of light would induce changes in the kinetic energy of the electrons emitted from the metal. Furthermore, according to this theory, a sufficiently dim light would be expected to show a time lag between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by classical theory.

Instead, electrons are dislodged only by the impingement of photons when those photons reach or exceed a threshold frequency (energy). Below that threshold, no electrons are emitted from the material regardless of the light intensity or the length of time of exposure to the light. (Rarely, an electron will escape by absorbing two or more quanta. However, this is extremely rare because by the time it absorbs enough quanta to escape, the electron will probably have emitted the rest of the quanta.) To make sense of the fact that light can eject electrons even if its intensity is low, Albert Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy . This shed light on Max Planck's previous discovery of the Planck relation (E = ) linking energy (E) and frequency (ν) as arising from quantization of energy. The factor h is known as the Planck constant.[1][2]

In 1887, Heinrich Hertz[2][3] discovered that electrodes illuminated with ultraviolet light create electric sparks more easily. In 1900, while studying black-body radiation, the German physicist Max Planck suggested that the energy carried by electromagnetic waves could only be released in "packets" of energy. In 1905, Albert Einstein published a paper advancing the hypothesis that light energy is carried in discrete quantized packets to explain experimental data from the photoelectric effect. This model contributed to the development of quantum mechanics. In 1914, Millikan's experiment supported Einstein's model of the photoelectric effect. Einstein was awarded the Nobel Prize in 1921 for "his discovery of the law of the photoelectric effect",[4] and Robert Millikan was awarded the Nobel Prize in 1923 for "his work on the elementary charge of electricity and on the photoelectric effect".[5]

The photoelectric effect requires photons with energies approaching zero (in the case of negative electron affinity) to over 1 MeV for core electrons in elements with a high atomic number. Emission of conduction electrons from typical metals usually requires a few electron-volts, corresponding to short-wavelength visible or ultraviolet light. Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave–particle duality.[1] Other phenomena where light affects the movement of electric charges include the photoconductive effect (also known as photoconductivity or photoresistivity), the photovoltaic effect, and the photoelectrochemical effect.

Photoemission can occur from any material, but it is most easily observable from metals or other conductors because the process produces a charge imbalance, and if this charge imbalance is not neutralized by current flow (enabled by conductivity), the potential barrier to emission increases until the emission current ceases. It is also usual to have the emitting surface in a vacuum, since gases impede the flow of photoelectrons and make them difficult to observe. Additionally, the energy barrier to photoemission is usually increased by thin oxide layers on metal surfaces if the metal has been exposed to oxygen, so most practical experiments and devices based on the photoelectric effect use clean metal surfaces in a vacuum.

When the photoelectron is emitted into a solid rather than into a vacuum, the term internal photoemission is often used, and emission into a vacuum distinguished as external photoemission.

Versuch zum Fotoeffekt
Schematic of experimental apparatus to demonstrate the photoelectric effect. The filter passes light of certain wavelengths from the lamp at left. The light strikes the curved electrode, and electrons are emitted. The adjustable voltage can be increased until the current stops flowing. This "stopping voltage" is a function only of the electrode material and the frequency of the incident light, and is not affected by the intensity of the light.

Emission mechanism

The photons of a light beam have a characteristic energy proportional to the frequency of the light. In the photoemission process, if an electron within some material absorbs the energy of one photon and acquires more energy than the work function (the electron binding energy) of the material, it is ejected. If the photon energy is too low, the electron is unable to escape the material. Since an increase in the intensity of low-frequency light will only increase the number of low-energy photons sent over a given interval of time, this change in intensity will not create any single photon with enough energy to dislodge an electron. Thus, the energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy (equivalent frequency) of the individual photons. It is an interaction between the incident photon and the outermost electrons.

Electrons can absorb energy from photons when irradiated, but they usually follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or else the energy is re-emitted. If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.[6][7][8]

Experimental observations of photoelectric emission

The theory of the photoelectric effect must explain the experimental observations of the emission of electrons from an illuminated metal surface.

For a given metal surface, there exists a certain minimum frequency of incident radiation below which no photoelectrons are emitted. This frequency is called the threshold frequency. Increasing the frequency of the incident beam, keeping the number of incident photons fixed (this would result in a proportionate increase in energy) increases the maximum kinetic energy of the photoelectrons emitted. Thus the stopping voltage increases (see the experimental setup in the figure). The number of electrons also changes because of the probability that each photon results in an emitted electron are a function of photon energy. If the intensity of the incident radiation of a given frequency is increased, there is no effect on the kinetic energy of each photoelectron.

Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron depends on the frequency of the incident light, but is independent of the intensity of the incident light so long as the latter is not too high.[9]

For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light. An increase in the intensity of the incident beam (keeping the frequency fixed) increases the magnitude of the photoelectric current, although the stopping voltage remains the same.

The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10−9 second.

The direction of distribution of emitted electrons peaks in the direction of polarization (the direction of the electric field) of the incident light, if it is linearly polarized.[10]

Mathematical description

In 1905, Einstein proposed an explanation of the photoelectric effect using a concept first put forward by Max Planck that light waves consist of tiny bundles or packets of energy known as photons or quanta.

Photoelectric effect diagram
Diagram of the maximum kinetic energy as a function of the frequency of light on zinc

The maximum kinetic energy of an ejected electron is given by

where is the Planck constant and is the frequency of the incident photon. The term is the work function (sometimes denoted , or [11]), which gives the minimum energy required to remove an electron from the surface of the metal. The work function satisfies

where is the threshold frequency for the metal. The maximum kinetic energy of an ejected electron is then

Kinetic energy is positive, so we must have for the photoelectric effect to occur.[12]

Stopping potential

The relation between current and applied voltage illustrates the nature of the photoelectric effect. For discussion, a light source illuminates a plate P, and another plate electrode Q collects any emitted electrons. We vary the potential between P and Q and measure the current flowing in the external circuit between the two plates.

If the frequency and the intensity of the incident radiation are fixed, the photoelectric current increases gradually with an increase in the positive potential on the collector electrode until all the photoelectrons emitted are collected. The photoelectric current attains a saturation value and does not increase further for any increase in the positive potential. The saturation current increases with the increase of the light intensity. It also increases with greater frequencies due to a greater probability of electron emission when collisions happen with higher energy photons.

If we apply a negative potential to the collector plate Q with respect to the plate P and gradually increase it, the photoelectric current decreases, becoming zero at a certain negative potential. The negative potential on the collector at which the photoelectric current becomes zero is called the stopping potential or cut off potential[13]

i. For a given frequency of incident radiation, the stopping potential is independent of its intensity.

ii. For a given frequency of incident radiation, the stopping potential is determined by the maximum kinetic energy of the photoelectrons that are emitted. If qe is the charge on the electron and is the stopping potential, then the work done by the retarding potential in stopping the electron is , so we have


we see that the stopping voltage varies linearly with frequency of light, but depends on the type of material. For any particular material, there is a threshold frequency that must be exceeded, independent of light intensity, to observe any electron emission.

Three-step model

In the X-ray regime, the photoelectric effect in crystalline material is often decomposed into three steps:[14]:50–51

  1. Inner photoelectric effect (see photo diode below). The hole left behind can give rise to Auger effect, which is visible even when the electron does not leave the material. In molecular solids phonons are excited in this step and may be visible as lines in the final electron energy. The inner photoeffect has to be dipole allowed. The transition rules for atoms translate via the tight-binding model onto the crystal. They are similar in geometry to plasma oscillations in that they have to be transversl.
  2. Ballistic transport of half of the electrons to the surface. Some electrons are scattered.
  3. Electrons escape from the material at the surface.

In the three-step model, an electron can take multiple paths through these three steps. All paths can interfere in the sense of the path integral formulation. For surface states and molecules the three-step model does still make some sense as even most atoms have multiple electrons which can scatter the one electron leaving.


When a surface is exposed to electromagnetic radiation above a certain threshold frequency (typically visible light for alkali metals, near ultraviolet for other metals, and extreme ultraviolet for non-metals), the radiation is absorbed and electrons are emitted. Light, and especially ultra-violet light, discharges negatively electrified bodies with the production of rays of the same nature as cathode rays.[15] Under certain circumstances it can directly ionize gases.[15] The first of these phenomena was discovered by Hertz and Hallwachs in 1887.[15] The second was announced first by Philipp Lenard in 1900.[15]

The ultra-violet light to produce these effects may be obtained from an arc lamp, or by burning magnesium, or by sparking with an induction coil between zinc or cadmium terminals, the light from which is very rich in ultra-violet rays. Sunlight is not rich in ultra-violet rays, as these have been absorbed by the atmosphere, and it does not produce nearly so large an effect as the arc-light. Many substances besides metals discharge negative electricity under the action of ultraviolet light: lists of these substances will be found in papers by G. C. Schmidt[16] and O. Knoblauch.[17]

19th century .

In 1839, Alexandre Edmond Becquerel discovered the photovoltaic effect while studying the effect of light on electrolytic cells.[18] Though not equivalent to the photoelectric effect, his work on photovoltaics was instrumental in showing a strong relationship between light and electronic properties of materials. In 1873, Willoughby Smith discovered photoconductivity in selenium while testing the metal for its high resistance properties in conjunction with his work involving submarine telegraph cables.[19]

Johann Elster (1854–1920) and Hans Geitel (1855–1923), students in Heidelberg, developed the first practical photoelectric cells that could be used to measure the intensity of light.[20][21]:458 Elster and Geitel had investigated with great success the effects produced by light on electrified bodies.[22]

In 1887, Heinrich Hertz observed the photoelectric effect and the production and reception of electromagnetic waves.[15] He published these observations in the journal Annalen der Physik. His receiver consisted of a coil with a spark gap, where a spark would be seen upon detection of electromagnetic waves. He placed the apparatus in a darkened box to see the spark better. However, he noticed that the maximum spark length was reduced when in the box. A glass panel placed between the source of electromagnetic waves and the receiver absorbed ultraviolet radiation that assisted the electrons in jumping across the gap. When removed, the spark length would increase. He observed no decrease in spark length when he replaced the glass with quartz, as quartz does not absorb UV radiation. Hertz concluded his months of investigation and reported the results obtained. He did not further pursue the investigation of this effect.

The discovery by Hertz[23] in 1887 that the incidence of ultra-violet light on a spark gap facilitated the passage of the spark, led immediately to a series of investigations by Hallwachs,[24] Hoor,[25] Righi[26] and Stoletow[27][28][29][30][31][32][33] on the effect of light, and especially of ultra-violet light, on charged bodies. It was proved by these investigations that a newly cleaned surface of zinc, if charged with negative electricity, rapidly loses this charge however small it may be when ultra-violet light falls upon the surface; while if the surface is uncharged to begin with, it acquires a positive charge when exposed to the light, the negative electrification going out into the gas by which the metal is surrounded; this positive electrification can be much increased by directing a strong airblast against the surface. If however the zinc surface is positively electrified it suffers no loss of charge when exposed to the light: this result has been questioned, but a very careful examination of the phenomenon by Elster and Geitel[34] has shown that the loss observed under certain circumstances is due to the discharge by the light reflected from the zinc surface of negative electrification on neighbouring conductors induced by the positive charge, the negative electricity under the influence of the electric field moving up to the positively electrified surface.[35]

With regard to the Hertz effect, the researchers from the start showed a great complexity of the phenomenon of photoelectric fatigue — that is, the progressive diminution of the effect observed upon fresh metallic surfaces. According to an important research by Wilhelm Hallwachs, ozone played an important part in the phenomenon.[36] However, other elements enter such as oxidation, the humidity, the mode of polish of the surface, etc. It was at the time not even sure that the fatigue is absent in a vacuum.

In the period from February 1888 and until 1891, a detailed analysis of photo effect was performed by Aleksandr Stoletov with results published in 6 works;[37][38][39][40][41][42] four of them in Comptes Rendus, one review in Physikalische Revue (translated from Russian), and the last work in Journal de Physique. First, in these works Stoletov invented a new experimental setup which was more suitable for a quantitative analysis of photo effect. Using this setup, he discovered the direct proportionality between the intensity of light and the induced photo electric current (the first law of photo effect or Stoletov's law). One of his other findings resulted from measurements of the dependence of the intensity of the electric photo current on the gas pressure, where he found the existence of an optimal gas pressure Pm corresponding to a maximum photocurrent; this property was used for a creation of solar cells.

In 1899, J. J. Thomson investigated ultraviolet light in Crookes tubes.[43] Thomson deduced that the ejected particles were the same as those previously found in the cathode ray, later called electrons, which he called "corpuscles". In the research, Thomson enclosed a metal plate (a cathode) in a vacuum tube, and exposed it to high-frequency radiation.[44] It was thought that the oscillating electromagnetic fields caused the atoms' field to resonate and, after reaching a certain amplitude, caused a subatomic "corpuscle" to be emitted, and current to be detected. The amount of this current varied with the intensity and color of the radiation. Larger radiation intensity or frequency would produce more current.

20th century

The discovery of the ionization of gases by ultra-violet light was made by Philipp Lenard in 1900. As the effect was produced across several centimeters of air and yielded a greater number of positive ions than negative, it was natural to interpret the phenomenon, as did J. J. Thomson, as a Hertz effect upon the solid or liquid particles present in the gas.[15]

In 1902, Lenard observed that the energy of individual emitted electrons increased with the frequency (which is related to the color) of the light.[6]

This appeared to be at odds with Maxwell's wave theory of light, which predicted that the electron energy would be proportional to the intensity of the radiation.

Lenard observed the variation in electron energy with light frequency using a powerful electric arc lamp which enabled him to investigate large changes in intensity, and that had sufficient power to enable him to investigate the variation of potential with light frequency. His experiment directly measured potentials, not electron kinetic energy: he found the electron energy by relating it to the maximum stopping potential (voltage) in a phototube. He found that the calculated maximum electron kinetic energy is determined by the frequency of the light. For example, an increase in frequency results in an increase in the maximum kinetic energy calculated for an electron upon liberation – ultraviolet radiation would require a higher applied stopping potential to stop current in a phototube than blue light. However, Lenard's results were qualitative rather than quantitative because of the difficulty in performing the experiments: the experiments needed to be done on freshly cut metal so that the pure metal was observed, but it oxidized in a matter of minutes even in the partial vacuums he used. The current emitted by the surface was determined by the light's intensity, or brightness: doubling the intensity of the light doubled the number of electrons emitted from the surface.

The researches of Langevin and those of Eugene Bloch[45] have shown that the greater part of the Lenard effect is certainly due to this 'Hertz effect'. The Lenard effect upon the gas itself nevertheless does exist. Refound by J. J. Thomson[46] and then more decisively by Frederic Palmer, Jr.,[47][48] it was studied and showed very different characteristics than those at first attributed to it by Lenard.[15]

In 1905, Albert Einstein solved this apparent paradox by describing light as composed of discrete quanta, now called photons, rather than continuous waves. Based upon Max Planck's theory of black-body radiation, Einstein theorized that the energy in each quantum of light was equal to the frequency multiplied by a constant, later called Planck's constant. A photon above a threshold frequency has the required energy to eject a single electron, creating the observed effect. This discovery led to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921.[49] By wave-particle duality the effect can be analyzed purely in terms of waves though not as conveniently.[50]

Albert Einstein's mathematical description of how the photoelectric effect was caused by absorption of quanta of light was in one of his 1905 papers, named "On a Heuristic Viewpoint Concerning the Production and Transformation of Light". This paper proposed the simple description of "light quanta", or photons, and showed how they explained such phenomena as the photoelectric effect. His simple explanation in terms of absorption of discrete quanta of light explained the features of the phenomenon and the characteristic frequency.

The idea of light quanta began with Max Planck's published law of black-body radiation ("On the Law of Distribution of Energy in the Normal Spectrum"[51]) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck's constant. By assuming that light actually consisted of discrete energy packets, Einstein wrote an equation for the photoelectric effect that agreed with experimental results. It explained why the energy of photoelectrons was dependent only on the frequency of the incident light and not on its intensity: a low-intensity, the high-frequency source could supply a few high energy photons, whereas a high-intensity, the low-frequency source would supply no photons of sufficient individual energy to dislodge any electrons. This was an enormous theoretical leap, but the concept was strongly resisted at first because it contradicted the wave theory of light that followed naturally from James Clerk Maxwell's equations for electromagnetic behavior, and more generally, the assumption of infinite divisibility of energy in physical systems. Even after experiments showed that Einstein's equations for the photoelectric effect were accurate, resistance to the idea of photons continued since it appeared to contradict Maxwell's equations, which were well understood and verified.

Einstein's work predicted that the energy of individual ejected electrons increases linearly with the frequency of the light. Perhaps surprisingly, the precise relationship had not at that time been tested. By 1905 it was known that the energy of photoelectrons increases with increasing frequency of incident light and is independent of the intensity of the light. However, the manner of the increase was not experimentally determined until 1914 when Robert Andrews Millikan showed that Einstein's prediction was correct.[7]

The photoelectric effect helped to propel the then-emerging concept of wave–particle duality in the nature of light. Light simultaneously possesses the characteristics of both waves and particles, each being manifested according to the circumstances. The effect was impossible to understand in terms of the classical wave description of light,[52][53][54] as the energy of the emitted electrons did not depend on the intensity of the incident radiation. Classical theory predicted that the electrons would 'gather up' energy over a period of time, and then be emitted.[53][55]

Uses and effects


These are extremely light-sensitive vacuum tubes with a photocathode coated onto part (an end or side) of the inside of the envelope. The photo cathode contains combinations of materials such as cesium, rubidium, and antimony specially selected to provide a low work function, so when illuminated even by very low levels of light, the photocathode readily releases electrons. By means of a series of electrodes (dynodes) at ever-higher potentials, these electrons are accelerated and substantially increased in number through secondary emission to provide a readily detectable output current. Photomultipliers are still commonly used wherever low levels of light must be detected.[56]

Image sensors

Video camera tubes in the early days of television used the photoelectric effect, for example, Philo Farnsworth's "Image dissector" used a screen charged by the photoelectric effect to transform an optical image into a scanned electronic signal.[57]

Gold-leaf electroscope

Gold leaf electroscope diagram
The gold leaf electroscope

Gold-leaf electroscopes are designed to detect static electricity. Charge placed on the metal cap spreads to the stem and the gold leaf of the electroscope. Because they then have the same charge, the stem and leaf repel each other. This will cause the leaf to bend away from the stem.

An electroscope is an important tool in illustrating the photoelectric effect. For example, if the electroscope is negatively charged throughout, there is an excess of electrons and the leaf is separated from the stem. If high-frequency light shines on the cap, the electroscope discharges, and the leaf will fall limp. This is because the frequency of the light shining on the cap is above the cap's threshold frequency. The photons in the light have enough energy to liberate electrons from the cap, reducing its negative charge. This will discharge a negatively charged electroscope and further charge a positive electroscope. However, if the electromagnetic radiation hitting the metal cap does not have a high enough frequency (its frequency is below the threshold value for the cap), then the leaf will never discharge, no matter how long one shines the low-frequency light at the cap.[58]:389–390

Photoelectron spectroscopy

Since the energy of the photoelectrons emitted is exactly the energy of the incident photon minus the material's work function or binding energy, the work function of a sample can be determined by bombarding it with a monochromatic X-ray source or UV source, and measuring the kinetic energy distribution of the electrons emitted.[14]:14–20

Photoelectron spectroscopy is usually done in a high-vacuum environment, since the electrons would be scattered by gas molecules if they were present. However, some companies are now selling products that allow photoemission in air. The light source can be a laser, a discharge tube, or a synchrotron radiation source.[59]

The concentric hemispherical analyzer is a typical electron energy analyzer and uses an electric field to change the directions of incident electrons, depending on their kinetic energies. For every element and core (atomic orbital) there will be a different binding energy. The many electrons created from each of these combinations will show up as spikes in the analyzer output, and these can be used to determine the elemental composition of the sample.


The photoelectric effect will cause spacecraft exposed to sunlight to develop a positive charge. This can be a major problem, as other parts of the spacecraft are in shadow which will result in the spacecraft developing a negative charge from nearby plasmas. The imbalance can discharge through delicate electrical components. The static charge created by the photoelectric effect is self-limiting, because a higher charged object doesn't give up its electrons as easily as a lower charged object does.[60][61]

Moon dust

Light from the sun hitting lunar dust causes it to become charged with the photoelectric effect. The charged dust then repels itself and lifts off the surface of the Moon by electrostatic levitation.[62][63] This manifests itself almost like an "atmosphere of dust", visible as a thin haze and blurring of distant features, and visible as a dim glow after the sun has set. This was first photographed by the Surveyor program probes in the 1960s. It is thought that the smallest particles are repelled kilometers from the surface and that the particles move in "fountains" as they charge and discharge.

Night vision devices

Photons hitting a thin film of alkali metal or semiconductor material such as gallium arsenide in an image intensifier tube cause the ejection of photoelectrons due to the photoelectric effect. These are accelerated by an electrostatic field where they strike a phosphor coated screen, converting the electrons back into photons. Intensification of the signal is achieved either through acceleration of the electrons or by increasing the number of electrons through secondary emissions, such as with a micro-channel plate. Sometimes a combination of both methods is used. Additional kinetic energy is required to move an electron out of the conduction band and into the vacuum level. This is known as the electron affinity of the photocathode and is another barrier to photoemission other than the forbidden band, explained by the band gap model. Some materials such as Gallium Arsenide have an effective electron affinity that is below the level of the conduction band. In these materials, electrons that move to the conduction band are all of the sufficient energy to be emitted from the material and as such, the film that absorbs photons can be quite thick. These materials are known as negative electron affinity materials.

Cross section

The photoelectric effect is one interaction mechanism between photons and atoms. It is one of 12 theoretically possible interactions.[64]

At the high photon energies comparable to the electron rest energy of 511 keV, Compton scattering, another process, may take place. Above twice this (1.022 MeV) pair production may take place.[65] Compton scattering and pair production are examples of two other competing mechanisms.

Indeed, even if the photoelectric effect is the favoured reaction for a particular single-photon bound-electron interaction, the result is also subject to statistical processes and is not guaranteed, albeit the photon has certainly disappeared and a bound electron has been excited (usually K or L shell electrons at gamma ray energies). The probability of the photoelectric effect occurring is measured by the cross-section of interaction, σ. This has been found to be a function of the atomic number of the target atom and photon energy. A crude approximation, for photon energies above the highest atomic binding energy, is given by:[66]

Here Z is atomic number and n is a number which varies between 4 and 5. (At lower photon energies a characteristic structure with edges appears, K edge, L edges, M edges, etc.) The obvious interpretation follows that the photoelectric effect rapidly decreases in significance, in the gamma-ray region of the spectrum, with increasing photon energy, and that photoelectric effect increases steeply with atomic number. The corollary is that high-Z materials make good gamma-ray shields, which is the principal reason that lead (Z = 82) is a preferred and ubiquitous gamma radiation shield.[67]

See also


  1. ^ a b Serway, R. A. (1990). Physics for Scientists & Engineers (3rd ed.). Saunders. p. 1150. ISBN 0-03-030258-7.
  2. ^ a b Sears, F. W.; Zemansky, M. W.; Young, H. D. (1983). University Physics (6th ed.). Addison-Wesley. pp. 843–844. ISBN 0-201-07195-9.
  3. ^ Hertz, H. (1887). "Ueber den Einfluss des ultravioletten Lichtes auf die electrische Entladung" [On an effect of ultra-violet light upon the electrical discharge]. Annalen der Physik. 267 (8): S. 983–1000. Bibcode:1887AnP...267..983H. doi:10.1002/andp.18872670827.
  4. ^ "The Nobel Prize in Physics 1921". Nobel Foundation. Retrieved 2013-03-16.
  5. ^ "The Nobel Prize in Physics 1923". Nobel Foundation. Retrieved 2015-03-29.
  6. ^ a b Lenard, P. (1902). "Ueber die lichtelektrische Wirkung". Annalen der Physik. 313 (5): 149–198. Bibcode:1902AnP...313..149L. doi:10.1002/andp.19023130510.
  7. ^ a b Millikan, R. (1914). "A Direct Determination of "h."". Physical Review. 4 (1): 73–75. Bibcode:1914PhRv....4R..73M. doi:10.1103/PhysRev.4.73.2.
  8. ^ Millikan, R. (1916). "A Direct Photoelectric Determination of Planck's "h"" (PDF). Physical Review. 7 (3): 355–388. Bibcode:1916PhRv....7..355M. doi:10.1103/PhysRev.7.355.
  9. ^ Zhang, Q. (1996). "Intensity dependence of the photoelectric effect induced by a circularly polarized laser beam". Physics Letters A. 216 (1–5): 125. Bibcode:1996PhLA..216..125Z. doi:10.1016/0375-9601(96)00259-9.
  10. ^ Bubb, F. (1924). "Direction of Ejection of Photo-Electrons by Polarized X-rays". Physical Review. 23 (2): 137–143. Bibcode:1924PhRv...23..137B. doi:10.1103/PhysRev.23.137.
  11. ^ Mee, C.; Crundell, M.; Arnold, B.; Brown, W. (2011). International A/AS Level Physics. Hodder Education. p. 241. ISBN 978-0-340-94564-3.
  12. ^ Fromhold, A. T. (1991). Quantum Mechanics for Applied Physics and Engineering. Courier Dover Publications. pp. 5–6. ISBN 978-0-486-66741-6.
  13. ^ Gautreau, R.; Savin, W. (1999). Schaum's Outline of Modern Physics (2nd ed.). McGraw-Hill. pp. 60–61. ISBN 0-07-024830-3.
  14. ^ a b Hüfner, S. (2003). Photoelectron Spectroscopy: Principles and Applications. Springer. ISBN 3-540-41802-4.
  15. ^ a b c d e f g Report of the Board of Regents By Smithsonian Institution. Board of Regents, United States National Museum, Smithsonian Institution. p. 239.
  16. ^ Schmidt, G. C. (1898) Wied. Ann. Uiv. p. 708.
  17. ^ Knoblauch, O. (1899). Zeitschrift für Physikalische Chemie. xxix. p. 527.
  18. ^ Vesselinka Petrova-Koch; Rudolf Hezel; Adolf Goetzberger (2009). High-Efficient Low-Cost Photovoltaics: Recent Developments. Springer. pp. 1–. ISBN 978-3-540-79358-8.
  19. ^ Smith, W. (1873). "Effect of Light on Selenium during the passage of an Electric Current". Nature. 7 (173): 303. Bibcode:1873Natur...7R.303.. doi:10.1038/007303e0.
  20. ^ Asimov, A. (1964) Asimov's Biographical Encyclopedia of Science and Technology, Doubleday, ISBN 0-385-04693-6.
  21. ^ Robert Bud; Deborah Jean Warner (1998). Instruments of Science: An Historical Encyclopedia. Science Museum, London, and National Museum of American History, Smithsonian Institution. ISBN 978-0-8153-1561-2.
  22. ^ Elster and Geitel arrange the metals in the following order with respect to their power of discharging negative electricity: rubidium, potassium, alloy of potassium and sodium, sodium, lithium, magnesium, thallium and zinc. For copper, platinum, lead, iron, cadmium, carbon, and mercury the effects with ordinary light are too small to be measurable. The order of the metals for this effect is the same as in Volta's series for contact-electricity, the most electropositive metals giving the largest photo-electric effect.
  23. ^ Hertz, Wied. Ann. xxxi. p. 983, 1887.
  24. ^ Hallwachs, Wied. Ann. xxxiii. p. 301, 1888.
  25. ^ Hoor, Repertorium des Physik, xxv. p. 91, 1889.
  26. ^ Bighi, C. R. cvi. p. 1349; cvii. p. 559, 1888
  27. ^ Stoletow. C. R. cvi. pp. 1149, 1593; cvii. p. 91; cviii. p. 1241; Physikalische Revue, Bd. i., 1892.
  28. ^ Stoletow, A. (1888). "Sur une sorte de courants electriques provoques par les rayons ultraviolets". Comptes Rendus. CVI: 1149. (Reprinted in Stoletow, M.A. (1888). "On a kind of electric current produced by ultra-violet rays". Philosophical Magazine. Series 5. 26 (160): 317. doi:10.1080/14786448808628270.; abstract in Beibl. Ann. d. Phys. 12, 605, 1888).
  29. ^ Stoletow, A. (1888). "Sur les courants actino-electriqies au travers deTair". Comptes Rendus. CVI: 1593. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
  30. ^ Stoletow, A. (1888). "Suite des recherches actino-electriques". Comptes Rendus. CVII: 91. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
  31. ^ Stoletow, A. (1889). "Sur les phénomènes actino-électriques". Comptes Rendus. CVIII: 1241.
  32. ^ Stoletow, A. (1889). "Актино-электрические исследовaния". Journal of the Russian Physico-chemical Society (in Russian). 21: 159.
  33. ^ Stoletow, A. (1890). "Sur les courants actino-électriques dans l'air raréfié". Journal de Physique. 9: 468. doi:10.1051/jphystap:018900090046800.
  34. ^ Elster and Geitel, Wied. Ann. xxxviii. pp. 40, 497, 1889; xli. p. 161, 1890; xlii. p. 564, 1891; xliii. p. 225, 1892; lii. p. 433, 1894 ; lv. p. 684, 1895.
  35. ^ Thomson, J. J. (2005). Conduction of Electricity Through Gases. Watchmaker Publishing. ISBN 978-1-929148-49-3. Retrieved 9 July 2011.
  36. ^ Hallwachs, W. (1907). "Über die lichtelektrische Ermüdung". Annalen der Physik. 328 (8): 459–516. Bibcode:1907AnP...328..459H. doi:10.1002/andp.19073280807.
  37. ^ Stoletow, A. (1888). "Sur une sorte de courants electriques provoques par les rayons ultraviolets". Comptes Rendus. CVI: 1149. (Reprinted in Stoletow, M.A. (1888). "On a kind of electric current produced by ultra-violet rays". Philosophical Magazine. Series 5. 26 (160): 317. doi:10.1080/14786448808628270.; abstract in Beibl. Ann. d. Phys. 12, 605, 1888).
  38. ^ Stoletow, A. (1888). "Sur les courants actino-electriques au travers deTair". Comptes Rendus. CVI: 1593. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
  39. ^ Stoletow, A. (1888). "Suite des recherches actino-électriques". Comptes Rendus. CVII: 91. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
  40. ^ Stoletow, A. (1889). "Sur les phénomènes actino-électriques". Comptes Rendus. CVIII: 1241.
  41. ^ Stoletow, A. (1889). "Актино-электрические исследовaния". Journal of the Russian Physico-chemical Society (in Russian). 21: 159.
  42. ^ Stoletow, A. (1890). "Sur les courants actino-électriques dans l'air raréfié". Journal de Physique. 9: 468. doi:10.1051/jphystap:018900090046800.
  43. ^ The International Year Book. (1900). New York: Dodd, Mead & Company. p. 659.
  44. ^ Buchwald, Jed; Warwick, Andrew, eds. (2004). Histories of the Electron: The Birth of Microphysics (PDF) (illustrated, reprint ed.). MIT Press. pp. 21–23. ISBN 978-0-262-52424-7.
  45. ^ Bloch, E. (1908). "L'ionisation de l'air par la lumière ultra-violette". Le Radium. 5 (8): 240. doi:10.1051/radium:0190800508024001.
  46. ^ Thomson, J. J. (1907). "On the Ionisation of Gases by Ultra-Violet Light and on the evidence as to the Structure of Light afforded by its Electrical Effects". Proc. Camb. Phil. Soc. 14: 417.
  47. ^ Palmer, Frederic (1908). "Ionisation of Air by Ultra-violet Light". Nature. 77 (2008): 582–582. Bibcode:1908Natur..77..582P. doi:10.1038/077582b0.
  48. ^ Palmer, Frederic (1911). "Volume Ionization Produced by Light of Extremely Short Wave-Length". Physical Review. Series I. 32: 1–22. Bibcode:1911PhRvI..32....1P. doi:10.1103/PhysRevSeriesI.32.1.
  49. ^ "The Nobel Prize in Physics 1921". Nobel Foundation. Retrieved 2008-10-09.
  50. ^ Lamb, Willis E.; Scully, Marlan O. (1968). "Photoelectric effect without photons, discussing classical field falling on quantized atomic electron" (PDF).
  51. ^ Planck, Max (1901). "Ueber das Gesetz der Energieverteilung im Normalspectrum (On the Law of Distribution of Energy in the Normal Spectrum)". Annalen der Physik. 4 (3): 553. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310.
  52. ^ Resnick, Robert (1972) Basic Concepts in Relativity and Early Quantum Theory, Wiley, p. 137, ISBN 0-471-71702-9.
  53. ^ a b Knight, Randall D. (2004) Physics for Scientists and Engineers With Modern Physics: A Strategic Approach, Pearson-Addison-Wesley, p. 1224, ISBN 0-8053-8685-8.
  54. ^ Penrose, Roger (2005) The Road to Reality: A Complete Guide to the Laws of the Universe, Knopf, p. 502, ISBN 0-679-45443-8
  55. ^ Resnick, Robert (1972) Basic Concepts in Relativity and Early Quantum Theory, Wiley, p. 138, ISBN 0-471-71702-9.
  56. ^ Timothy, J. Gethyn (2010) in Huber, Martin C.E. (ed.) Observing Photons in Space, ISSI Scientific Report 009, ESA Communications, pp. 365–408, ISBN 978-92-9221-938-3
  57. ^ Burns, R. W. (1998) Television: An International History of the Formative Years, IET, p. 358, ISBN 0-85296-914-7.
  58. ^ Tsokos, K. A. (2010). Cambridge Physics for the IB Diploma (revised ed.). Cambridge University Press. ISBN 978-0-521-13821-5.
  59. ^ Weaver, J. H.; Margaritondo, G. (1979). "Solid-State Photoelectron Spectroscopy with Synchrotron Radiation". Science. 206 (4415): 151–156. Bibcode:1979Sci...206..151W. doi:10.1126/science.206.4415.151. PMID 17801770.
  60. ^ Lai, Shu T. (2011). Fundamentals of Spacecraft Charging: Spacecraft Interactions with Space Plasmas (illustrated ed.). Princeton University Press. pp. 1–6. ISBN 978-0-691-12947-1.
  61. ^ "Spacecraft charging". Arizona State University.
  62. ^ Bell, Trudy E., "Moon fountains",, 2005-03-30.
  63. ^ Dust gets a charge in a vacuum., July 14, 2000.
  64. ^ Evans, R. D. (1955). The Atomic Nucleus. Malabar, Fla.: Krieger. p. 673. ISBN 0-89874-414-8.
  65. ^ Evans, R. D. (1955). The Atomic Nucleus. Malabar, Fla.: Krieger. p. 712. ISBN 0-89874-414-8.
  66. ^ Davisson, C. M. (1965). Interaction of gamma-radiation with matter. pp. 37–78. Bibcode:1965abgs.conf...37D.
  67. ^ Knoll, Glenn F. (1999). Radiation Detection and Measurement. New York: Wiley. p. 49. ISBN 0-471-49545-X.

External links


Aleksandr Stoletov

Alexander Grigorievich Stoletov (Russian: Алекса́ндр Григо́рьевич Столе́тов; 10 August 1839 – 27 May 1896) was a Russian physicist, founder of electrical engineering, and professor in Moscow University. He was the brother of general Nikolai Stoletov.

Annus Mirabilis papers

The Annus mirabilis papers (from Latin annus mīrābilis, "extraordinary year") are the papers of Albert Einstein published in the Annalen der Physik scientific journal in 1905. These four articles contributed substantially to the foundation of modern physics and changed views on space, time, mass, and energy. The annus mirabilis is often called the "miracle year" in English or Wunderjahr in German.


Cathodoluminescence is an optical and electromagnetic phenomenon in which electrons impacting on a luminescent material such as a phosphor, cause the emission of photons which may have wavelengths in the visible spectrum. A familiar example is the generation of light by an electron beam scanning the phosphor-coated inner surface of the screen of a television that uses a cathode ray tube. Cathodoluminescence is the inverse of the photoelectric effect, in which electron emission is induced by irradiation with photons.

Dember effect

In physics, the Dember effect is when the electron current from a cathode subjected to both illumination and a simultaneous electron bombardment is greater than the sum of the photoelectric current and the secondary emission current .

Einstein's awards and honors

During the year of 1922, Albert Einstein was awarded the 1921 Nobel Prize in Physics, "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect". This refers to his 1905 paper on the photoelectric effect, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light", which was well supported by the experimental evidence by that time. The presentation speech began by mentioning "his theory of relativity [which had] been the subject of lively debate in philosophical circles [and] also has astrophysical implications which are being rigorously examined at the present time". (Einstein 1923)

Heinrich Hertz

Heinrich Rudolf Hertz (; German: [ˈhaɪ̯nʁɪç ˈhɛɐ̯ts]; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves theorized by James Clerk Maxwell's electromagnetic theory of light. The unit of frequency, cycle per second, was named the "Hertz" in his honor.

History of quantum mechanics

The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ε (epsilon) such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:

where h is a numerical value called Planck's constant.

Then, Albert Einstein in 1905, in order to explain the photoelectric effect previously reported by Heinrich Hertz in 1887, postulated consistently with Max Planck's quantum hypothesis that light itself is made of individual quantum particles, which in 1926 came to be called photons by Gilbert N. Lewis. The photoelectric effect was observed upon shining light of particular wavelengths on certain materials, such as metals, which caused electrons to be ejected from those materials only if the light quantum energy was greater than the work function of the metal's surface.

The phrase "quantum mechanics" was coined (in German, Quantenmechanik) by the group of physicists including Max Born, Werner Heisenberg, and Wolfgang Pauli, at the University of Göttingen in the early 1920s, and was first used in Born's 1924 paper "Zur Quantenmechanik". In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.


A photocathode is a negatively charged electrode in a light detection device such as a photomultiplier or phototube that is coated with a photosensitive compound. When this is struck by a quantum of light (photon), the absorbed energy causes electron emission due to the photoelectric effect.


A photodiode is a semiconductor device that converts light into an electrical current. The current is generated when photons are absorbed in the photodiode. Photodiodes may contain optical filters, built-in lenses, and may have large or small surface areas. Photodiodes usually have a slower response time as their surface area increases. The common, traditional solar cell used to generate electric solar power is a large area photodiode.

Photodiodes are similar to regular semiconductor diodes except that they may be either exposed (to detect vacuum UV or X-rays) or packaged with a window or optical fiber connection to allow light to reach the sensitive part of the device. Many diodes designed for use specially as a photodiode use a PIN junction rather than a p–n junction, to increase the speed of response. A photodiode is designed to operate in reverse bias.

Photoelectrochemical process

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

Photoemission spectroscopy

Photoemission spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance. The term refers to various techniques, depending on whether the ionization energy is provided by an X-ray photon, an EUV photon, or an ultraviolet photon. Regardless of the incident photon beam, however, all photoelectron spectroscopy revolves around the general theme of surface analysis by measuring the ejected electrons.

Photomultiplier tube

Photomultiplier tubes (photomultipliers or PMTs for short), members of the class of vacuum tubes, and more specifically vacuum phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum. These detectors multiply the current produced by incident light by as much as 100 million times or 108 (i.e., 160 dB), in multiple dynode stages, enabling (for example) individual photons to be detected when the incident flux of light is low.

The combination of high gain, low noise, high frequency response or, equivalently, ultra-fast response, and large area of collection has maintained photomultipliers an essential place in low light level spectroscopy, confocal microscopy, Raman spectroscopy, fluorescence spectroscopy, nuclear and particle physics, astronomy, medical diagnostics including blood tests, medical imaging, motion picture film scanning (telecine), radar jamming, and high-end image scanners known as drum scanners. Elements of photomultiplier technology, when integrated differently, are the basis of night vision devices. Research that analyzes light scattering, such as the study of polymers in solution, often uses a laser and a PMT to collect the scattered light data.

Semiconductor devices, particularly avalanche photodiodes, are alternatives to photomultipliers; however, photomultipliers are uniquely well-suited for applications requiring low-noise, high-sensitivity detection of light that is imperfectly collimated.

Photovoltaic effect

The photovoltaic effect is the creation of voltage and electric current in a material upon exposure to light and is a physical and chemical phenomenon.The photovoltaic effect is closely related to the photoelectric effect. In either case, light is absorbed, causing excitation of an electron or other charge carrier to a higher-energy state. The main distinction is that the term photoelectric effect is now usually used when the electron is ejected out of the material (usually into a vacuum) and photovoltaic effect used when the excited charge carrier is still contained within the material. In either case, an electric potential (or voltage) is produced by the separation of charges, and the light has to have a sufficient energy to overcome the potential barrier for excitation. The physical essence of the difference is usually that photoelectric emission separates the charges by ballistic conduction and photovoltaic emission separates them by diffusion, but some "hot carrier" photovoltaic device concepts blur this distinction.

The first solar cell, consisting of a layer of selenium covered with a thin film of gold, was experimented by Charles Fritts in 1884, but it had a very poor efficiency. A demonstration of the photovoltaic effect in 1839 used an electrochemical cell. However, the most familiar form of the photovoltaic effect uses solid-state devices, mainly in photodiodes. When sunlight or other sufficiently energetic light is incident upon the photodiode, the electrons present in the valence band absorb energy and, being excited, jump to the conduction band and become free. These excited electrons diffuse, and some reach the rectifying junction (usually a diode p-n junction) where they are accelerated into the p-type semiconductor material by the built-in potential (Galvani potential). This generates a flow of electrical current electromotive force, and thus some of the light energy is converted into electric energy. The photovoltaic effect can also occur when two photons are absorbed simultaneously in a process called two-photon photovoltaic effect.

The photovoltaic effect was first observed by French physicist A. E. Becquerel in 1839. He explained his discovery in Comptes rendus de l'Académie des sciences, "the production of an electric current when two plates of platinum or gold immersed in an acid, neutral, or alkaline solution are exposed in an uneven way to solar radiation."Besides the direct excitation of free electrons, a photovoltaic effect can also arise simply due to the heating caused by absorption of the light. The heating leads to increased temperature of the semiconductor material, which is accompanied by temperature gradients. These thermal gradients in turn may generate a voltage through the Seebeck effect. Whether direct excitation or thermal effects dominate the photovoltaic effect will depend on many material parameters.

In most photovoltaic applications the radiation is sunlight, and the devices are called solar cells. In the case of a semiconductor p-n (diode) junction solar cell, illuminating the material creates an electric current because excited electrons and the remaining holes are swept in different directions by the built-in electric field of the depletion region.

Robert Andrews Millikan

Robert Andrews Millikan (March 22, 1868 – December 19, 1953) was an American experimental physicist honored with the Nobel Prize for Physics in 1923 for the measurement of the elementary electric charge and for his work on the photoelectric effect.

Millikan graduated from Oberlin College in 1891 and obtained his doctorate at Columbia University in 1895. In 1896 he became an assistant at the University of Chicago, where he became a full professor in 1910. In 1909 Millikan began a series of experiments to determine the electric charge carried by a single electron. He began by measuring the course of charged water droplets in an electric field. The results suggested that the charge on the droplets is a multiple of the elementary electric charge, but the experiment was not accurate enough to be convincing. He obtained more precise results in 1910 with his famous oil-drop experiment in which he replaced water (which tended to evaporate too quickly) with oil.

In 1914 Millikan took up with similar skill the experimental verification of the equation introduced by Albert Einstein in 1905 to describe the photoelectric effect. He used this same research to obtain an accurate value of Planck’s constant. In 1921 Millikan left the University of Chicago to become director of the Norman Bridge Laboratory of Physics at the California Institute of Technology (Caltech) in Pasadena, California. There he undertook a major study of the radiation that the physicist Victor Hess had detected coming from outer space. Millikan proved that this radiation is indeed of extraterrestrial origin, and he named it "cosmic rays." As chairman of the Executive Council of Caltech (the school's governing body at the time) from 1921 until his retirement in 1945, Millikan helped to turn the school into one of the leading research institutions in the United States. He also served on the board of trustees for Science Service, now known as Society for Science & the Public, from 1921 to 1953.

Stoletov's law

Stoletov's law (or the first law of photoeffect) for photoelectric effect establishes the direct proportionality between the intensity of electromagnetic radiation acting on a metallic surface and the photocurrent induced by this radiation. The law was discovered by Aleksandr Stoletov in 1888.

Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.

The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson–Morley experiment on Earth's drift through a luminiferous ether. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect, previously an experimental result lacking a theoretical formulation.

Timeline of solar cells

In the 19th century, it was observed that the sunlight striking certain materials generates detectable electric current - the photoelectric effect. This discovery has laid the foundation of solar cells. Solar cells have gone on to be used in many applications. They have historically been used in situations where electrical power from the grid was unavailable.

Wave–particle duality

Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote:

It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.

Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles exhibit a wave nature and vice versa. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.Although the use of the wave-particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved; see Interpretations of quantum mechanics.

Bohr regarded the "duality paradox" as a fundamental or metaphysical fact of nature. A given kind of quantum object will exhibit sometimes wave, sometimes particle, character, in respectively different physical settings. He saw such duality as one aspect of the concept of complementarity. Bohr regarded renunciation of the cause-effect relation, or complementarity, of the space-time picture, as essential to the quantum mechanical account.Werner Heisenberg considered the question further. He saw the duality as present for all quantic entities, but not quite in the usual quantum mechanical account considered by Bohr. He saw it in what is called second quantization, which generates an entirely new concept of fields which exist in ordinary space-time, causality still being visualizable. Classical field values (e.g. the electric and magnetic field strengths of Maxwell) are replaced by an entirely new kind of field value, as considered in quantum field theory. Turning the reasoning around, ordinary quantum mechanics can be deduced as a specialized consequence of quantum field theory.

Wilhelm Hallwachs

Wilhelm Ludwig Franz Hallwachs (9 July 1859 – 20 June 1922) was a German physicist.

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