Photoelectric effect

Photoelectric effect
In the photoelectric effect, electrons are emitted from matter (metals and non-metallic solids, liquids or gases) as a
consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible
or ultraviolet radiation. Electrons emitted in this manner may be referred to as photoelectrons.[1][2] First observed by
Heinrich Hertz in 1887,[2][3] the phenomenon is also known as the Hertz effect,[4][5] although the latter term has
fallen out of general use. Hertz observed and then showed that electrodes illuminated with ultraviolet light create
electric sparks more easily.
The photoelectric effect requires photons with energies from a few electronvolts to over 1 MeV in high atomic
number elements. 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 waveparticle 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.

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. Increasing the intensity of the light beam increases the number of
photons in the light beam, and thus increases the number of electrons excited, but does not increase the energy that
each electron possesses. The energy of the emitted electrons does not depend on the intensity of the incoming light,
but only on the energy or frequency of the individual photons. It is an interaction between the incident photon and
the outermost electron.
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, 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. The number of electrons also
changes because the probability that each photon results in an emitted electron is a function of photon energy.
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. Increase in intensity of incident beam (keeping the frequency fixed)
increases the magnitude of the photoelectric current, though stopping voltage remains the same.
The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 109
second.

Photoelectric effect

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
The maximum kinetic energy

where

of an ejected electron is given by

is the Planck constant and

function (sometimes denoted

is the frequency of the incident photon. The term =

is the work

), which gives the minimum energy required to remove a delocalised 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.[11]

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 positive potential on 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 depends on the intensity of illumination, but not its wavelength.
If we apply a negative potential to plate Q with respect to plate P and gradually increase it, the photoelectric current
decreases until it is zero, at a certain negative potential on plate Q. The minimum negative potential given to plate Q
at which the photoelectric current becomes zero is called stopping potential or cut off potential.[12]
i. For the given frequency of incident radiation, the stopping potential is independent of its intensity.
ii. For a given frequency of the incident radiation, the stopping potential Vo is related to the maximum kinetic energy
of the photoelectron that is just stopped from reaching plate Q. If
is the mass and
is the maximum velocity
of photoelectron emitted, then

If e is the charge on the electron and

stopping the electron

is the stopping potential, then the work done by the retarding potential in

, which gives

The above relation shows that the maximum velocity of the emitted photoelectron is independent of the intensity of
the incident light. Hence,

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.

Photoelectric effect

Three-step model
In the X-ray regime, the photoelectric effect in crystalline material is often decomposed into three steps:[13]
1. Inner photoelectric effect (see photodiode 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 transversal.
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.

History
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.[14] Under certain circumstances it can directly ionize gases.[14]
The first of these phenomena was discovered by Hertz and Hallwachs in 1887.[14] The second was announced first
by Philipp Lenard in 1900.[14]
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[15] and O.
Knoblauch.[16]

19th century
In 1839, Alexandre Edmond Becquerel discovered the photovoltaic effect while studying the effect of light on
electrolytic cells.[17] 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.[18]
Johann Elster (18541920) and Hans Geitel (18551923), students in Heidelberg, developed the first practical
photoelectric cells that could be used to measure the intensity of light.[19] Elster and Geitel had investigated with
great success the effects produced by light on electrified bodies.[20]

Photoelectric effect

In 1887, Heinrich Hertz observed the photoelectric effect and the

production and reception of electromagnetic waves.[14] 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 substituted quartz for glass, as
quartz does not absorb UV radiation. Hertz concluded his months
of investigation and reported the results obtained. He did not
further pursue investigation of this effect.
[21]

Heinrich Rudolf Hertz,

from Oliver Heaviside: Sage in Solitude

The discovery by Hertz

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,[22] Hoor,[23] Righi[24] and
Stoletow.[25][26][27][28][29][30][31] 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[32] 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.[33]
With regard to the Hertz effect, the researches 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.[34]
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 photoeffect was performed by Aleksandr
Stoletov with results published in 6 works; 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 photoeffect. Using this setup, he
discovered the direct proportionality between the intensity of light and the induced photo electric current (the first
law of photoeffect 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.[35] Influenced by the work of James Clerk
Maxwell, Thomson deduced that cathode rays consisted of negatively charged particles, 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. 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

Photoelectric effect
detected. The amount of this current varied with the intensity and colour 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 made very great positive and small negative ions, 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.[14]
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 James Clerk Maxwell's wave
theory of light, which was thought to predict 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
Hungarian physicist Philipp Lenard
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 oxidised 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[36] 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[37] and then more decisively by Frederic Palmer, Jr.,[38][39] it was studied and showed very different
characteristics than those at first attributed to it by Lenard.[14]
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.[40] By wave-particle duality the effect can be analyzed purely in terms of waves though not as
conveniently.[41]

Photoelectric effect

Albert Einstein's mathematical description of how the

photoelectric effect was caused by absorption of quanta of light
(now called photons), 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. Einstein's explanation of the photoelectric effect won
him the Nobel Prize in Physics in 1921.[42]
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"[43]) 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
Einstein, in 1905, when he wrote the Annus Mirabilis
light actually consisted of discrete energy packets, Einstein wrote
papers
an equation for the photoelectric effect that agreed with
experimental results. It explained why the energy of
photoelectrons were dependent only on the frequency of the incident light and not on its intensity: a low-intensity,
high-frequency source could supply a few high energy photons, whereas a high-intensity, 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 propel the then-emerging concept of the dualistic nature of light, that 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,[44][45][46]
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.[45][47]

Uses and effects

Photomultipliers
These are extremely light-sensitive vacuum tubes with a photocathode coated onto part (an end or side) of the inside
of the envelope. The photocathode contains combinations of materials such as caesium, 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

Photoelectric effect
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.[48]

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.[49]

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. The 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
The gold leaf electroscope.
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.[50]

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.[51]
Photoelectron spectroscopy is done in a high-vacuum environment, since the electrons would be scattered by gas
molecules if they were present. The light source can be a laser, a discharge tube, or a synchrotron radiation
source.[52]
The concentric hemispherical analyser (CHA) 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.

Photoelectric effect

Spacecraft
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 in shadow develop a negative charge from nearby plasma, and the
imbalance can discharge through delicate electrical components. The static charge created by the photoelectric effect
is self-limiting, though, because a more highly charged object gives up its electrons less easily.[53]

Moon dust
Light from the sun hitting lunar dust causes it to become charged through the photoelectric effect. The charged dust
then repels itself and lifts off the surface of the Moon by electrostatic levitation.[54][55] 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 up to kilometers high, 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 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.[56]
At the high photon energies comparable to the electron rest energy of 511keV, Compton scattering, another process,
may take place. Above twice this (1.022MeV) pair production may take place.[57] Compton scattering and pair
production are an example 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 nuclear (gamma ray) energies).
The probability of the photoelectric effect occurring is measured by the cross section of interaction, . 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:[58]

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

Photoelectric effect
materials make good gamma-ray shields, which is the principal reason that lead (Z = 82) is a preferred and
ubiquitous gamma radiation shield.[59]

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[23] Hoor, Repertorium des Physik, xxv. p. 91, 1889.
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723, 1888).
[28] A. Stoletow (1888). "Suite des recherches actino-electriques". Comptes Rendus CVII: 91. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
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1895.

Photoelectric effect
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External links
Physics: Applications of the Photoelectric Effect (http://www.howstuffworks.com/
17448-physics-applications-of-the-photoelectric-effect-video.htm) at HowStuffWorks
Nave, R., " Wave-Particle Duality (http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html)". HyperPhysics.
" Photoelectric effect (http://www.colorado.edu/physics/2000/quantumzone/photoelectric.html)". Physics
2000. University of Colorado, Boulder, Colorado.
ACEPT W3 Group, " The Photoelectric Effect (http://acept.la.asu.edu/PiN/rdg/photoelectric/photoelectric.
shtml)". Department of Physics and Astronomy, Arizona State University, Tempe, AZ.
Haberkern, Thomas, and N Deepak " Grains of Mystique: Quantum Physics for the Layman (http://www.faqs.
org/docs/qp/)". Einstein Demystifies Photoelectric Effect (http://www.faqs.org/docs/qp/chap03.html),
Chapter 3.

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Photoelectric effect
Department of Physics, " The Photoelectric effect (http://www.phy.davidson.edu/ModernPhysicsLabs/hovere.
html)". Physics 320 Laboratory, Davidson College, Davidson.
Fowler, Michael, " The Photoelectric Effect (http://www.phys.virginia.edu/classes/252/photoelectric_effect.
html)". Physics 252, University of Virginia.
Applets
" Photoelectric Effect (http://phet.colorado.edu/new/simulations/sims.php?sim=Photoelectric_Effect)". The
Physics Education Technology (PhET) project. (Java)
Fendt, Walter, " The Photoelectric Effect (http://www.walter-fendt.de/ph14e/photoeffect.htm)". (Java)
" Applet: Photo Effect (http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm)". Open Source
Distributed Learning Content Management and Assessment System. (Java)

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Article Sources and Contributors

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