======================================================================
= Photoelectric effect =
======================================================================
Introduction
======================================================================
The photoelectric effect is the emission of electrons or other free
carriers when light hits a material. Electrons emitted in this manner
can be called 'photoelectrons'. This phenomenon is commonly studied in
electronic physics and in fields of chemistry such as quantum
chemistry and electrochemistry.
According to classical electromagnetic theory, the photoelectric
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 induces changes in the kinetic energy of the electrons emitted
from the metal. According to this theory, a sufficiently dim light is
expected to show a time lag between the initial shining of its light
and the subsequent emission of an electron.
But the experimental results did not correlate with either of the two
predictions made by classical theory. Instead, experiments showed that
electrons are dislodged only by the impingement of light when it
reached or exceeded a threshold frequency. 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.
Because a low-frequency beam at a high intensity could not build up
the energy required to produce photoelectrons like it would have if
light's energy were continuous like a wave, Einstein proposed that a
beam of light is not a wave propagating through space, but rather a
collection of discrete wave packets (photons).
Emission of conduction electrons from typical metals usually requires
a few electron-volts, corresponding to short-wavelength visible or
ultraviolet light. Emissions can be induced with 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. 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. 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 which is
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 innermost
electrons. The movement of an outer electron to occupy the vacancy
then result in the emission of a photon.
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.
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'.
Experimental observations of photoelectric emission
=====================================================
The theory of the source of 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.
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.
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. Diagram of the maximum kinetic energy as a function of the
frequency of light on zinc
The maximum kinetic energy K_\mathrm{max} of an ejected electron is
given by
:K_\mathrm{max} = h\,f - \varphi,
where h is the Planck constant and f is the frequency of the incident
photon. The term \varphi is the work function (sometimes denoted W, or
\phi), which gives the minimum energy required to remove an electron
from the surface of the metal. The work function satisfies
:\varphi = h\,f_0,
where f_0 is the threshold frequency for the metal. The maximum
kinetic energy of an ejected electron is then
:K_\mathrm{max} = h \left(f - f_0\right).
Kinetic energy is positive, so we must have f > f_0 for the
photoelectric effect to occur.
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
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 K_\mathrm{max}
of the photoelectrons that are emitted. If 'qe' is the charge on the
electron and V_0 is the stopping potential, then the work done by the
retarding potential in stopping the electron is q_eV_0, so we have
:q_eV_0 = K_\mathrm{max}.
Recalling
:K_\mathrm{max} = h \left(f - f_0\right),
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:
#Inner photoelectric effect (see photo diode below). The hole left
behind can give rise to the 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 transversed.
#Ballistic transport of half of the electrons to the surface. Some
electrons are scattered.
#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. Under certain circumstances it can directly ionize
gases. The first of these phenomena was discovered by Heinrich Hertz
and Wilhelm Hallwachs in 1887. The second was announced first by
Philipp Lenard in 1900.
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 and O. Knoblauch.
19th century
==============
In 1839, Alexandre Edmond Becquerel discovered the photovoltaic effect
while studying the effect of light on electrolytic cells. 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.
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. Elster and Geitel had
investigated with great success the effects produced by light on
electrified bodies.
In 1887, Heinrich Hertz observed the photoelectric effect and the
production and reception of electromagnetic waves. 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 inside 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
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, Hoor, Righi and Stoletow 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 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.
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. 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; 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. 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. 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.
During the years 1886-1902, Wilhelm Hallwachs and Philipp Lenard
investigated the phenomenon of photoelectric emission in detail.
Hallwachs connected a zinc plate to an electroscope. He allowed
ultraviolet light to fall on the zinc plate and observed that the zinc
plate became uncharged if initially negatively charged, positively
charged if initially uncharged, and more positively charged if
initially positively charged. From these observations he concluded
that some negatively charged particles were emitted by the zinc plate
when exposed to ultraviolet light. A few years later, Lenard observed
that when ultraviolet radiation is allowed to fall on the emitter
plate of an evacuated glass tube enclosing two electrodes, a current
flows in the circuit. As soon as ultraviolet radiation is stopped, the
current also stops. This initiated the concept of photoelectric
emission.
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 was a key step in 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", and Robert Millikan was awarded the Nobel Prize in 1923 for
"his work on the elementary charge of electricity and on the
photoelectric effect".
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.
In 1902, Lenard observed that the energy of individual emitted
electrons increased with the frequency (which is related to the color)
of the light.
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 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 and then more decisively by Frederic
Palmer, Jr., it was studied and showed very different characteristics
than those at first attributed to it by Lenard.
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. By wave-particle
duality the effect can be analyzed purely in terms of waves though not
as conveniently.
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'") 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': at 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.
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, 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.
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
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.
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.
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.
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.
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.
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.
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 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.
Moon dust
===========
Light from the sun hitting lunar dust causes it to become positively
charged from the photoelectric effect. The charged dust then repels
itself and lifts off the surface of the Moon by electrostatic
levitation. 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 an interaction mechanism between photons
and atoms.
At the high photon energies comparable to the electron rest energy of
, Compton scattering, another process, may take place. Above twice
this () pair production may take place. 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, even if
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, �. 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, which is given by:
: \sigma = \mathrm{constant} \cdot \frac{Z^n}{E^3}
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.
See also
======================================================================
*Anomalous photovoltaic effect
*Dember effect
*Photo-Dember effect
*Photomagnetic effect
*Photochemistry
*Timeline of mechanics and physics
External links
======================================================================
*Astronomy Cast
"
http://www.astronomycast.com/2014/02/ep-335-photoelectric-effect/".
AstronomyCast.
*Nave, R., "'[
http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html
Wave-Particle Duality]'". HyperPhysics.
*"'[
https://web.archive.org/web/20081019151010/http://www.colorado.edu/physics/2
000/quantumzone/photoelectric.html
Photoelectric effect]'". Physics 2000. University of Colorado,
Boulder, Colorado. (page not found)
*ACEPT W3 Group,
"'[
https://web.archive.org/web/20081213000603/http://acept.la.asu.edu/PiN/rdg/ph
otoelectric/photoelectric.shtml
The Photoelectric Effect]'". Department of Physics and Astronomy,
Arizona State University, Tempe, AZ.
*Haberkern, Thomas, and N Deepak "'[
http://www.faqs.org/docs/qp/
Grains of Mystique: Quantum Physics for the Layman]'".
[
http://www.faqs.org/docs/qp/chap03.html Einstein Demystifies
Photoelectric Effect], Chapter 3.
*Department of Physics,
"'[
http://www.phy.davidson.edu/ModernPhysicsLabs/hovere.html The
Photoelectric effect]'". Physics 320 Laboratory, Davidson College,
Davidson.
*Fowler, Michael,
"'[
http://www.phys.virginia.edu/classes/252/photoelectric_effect.html
The Photoelectric Effect]'". Physics 252, University of Virginia.
*Go to
"'[
https://web.archive.org/web/20141121114532/http://www.esfm2005.ipn.mx/ESFM_Im
ages/paper1.pdf
Concerning an Heuristic Point of View Toward the Emission and
Transformation of Light]'" to read an English translation of
Einstein's 1905 paper. (Retrieved: 2014 Apr 11)
*
http://www.chemistryexplained.com/Ru-Sp/Solar-Cells.html
*Photo-electric transducers:
http://sensorse.com/page4en.html
'Applets'
*"'[
https://iwant2study.org/ospsg/index.php/interactive-resources/physics/06-qua
ntum-physics/344-photoelectriceffectwee3
HTML 5 JavaScript simulator]'" Open Source Physics project
*"'[
http://phet.colorado.edu/new/simulations/sims.php?sim=Photoelectric_Effect
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*Fendt, Walter, "'[
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License
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Original Article:
http://en.wikipedia.org/wiki/Photoelectric_effect
