Photoelectric effect

Last updated

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.

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is the portion of the spectrum that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometers (nm), or 4.00 × 10−7 to 7.00 × 10−7 m, between the infrared and the ultraviolet. This wavelength means a frequency range of roughly 430–750 terahertz (THz).

Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter.

Contents

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.

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics.

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

In physics, intensity is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2). It is used most frequently with waves, in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.

But the experimental results did not correlate with either of the two predictions made by classical theory.[ citation needed ] 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.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and 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).

Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His work is also known for its influence on the philosophy of science. He is best known to the general public for his mass–energy equivalence formula , which has been dubbed "the world's most famous equation". He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory.

The photon is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. The invariant mass of the photon is zero; it always moves at the speed of light in a vacuum.

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. [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.

A chemical element is a species of atom having the same number of protons in their atomic nuclei. For example, the atomic number of oxygen is 8, so the element oxygen consists of all atoms which have 8 protons.

The atomic number or proton number of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus. In an uncharged atom, the atomic number is also equal to the number of electrons.

Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. 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.

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.

Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.

In solid-state physics, the work function is the minimum thermodynamic work needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" means that the final electron position is far from the surface on the atomic scale, but still too close to the solid to be influenced by ambient electric fields in the vacuum. The work function is not a characteristic of a bulk material, but rather a property of the surface of the material.

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. [2] [3] [4]

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. [5]

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. [6]

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.

The maximum kinetic energy ${\displaystyle K_{\mathrm {max} }}$ of an ejected electron is given by

${\displaystyle K_{\mathrm {max} }=h\,f-\varphi ,}$

where ${\displaystyle h}$ is the Planck constant and ${\displaystyle f}$ is the frequency of the incident photon. The term ${\displaystyle \varphi }$ is the work function (sometimes denoted ${\displaystyle W}$, or ${\displaystyle \phi }$ [7] ), which gives the minimum energy required to remove an electron from the surface of the metal. The work function satisfies

${\displaystyle \varphi =h\,f_{0},}$

where ${\displaystyle f_{0}}$ is the threshold frequency for the metal. The maximum kinetic energy of an ejected electron is then

${\displaystyle K_{\mathrm {max} }=h\left(f-f_{0}\right).}$

Kinetic energy is positive, so we must have ${\displaystyle f>f_{0}}$ for the photoelectric effect to occur. [8]

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 [9]

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 ${\displaystyle K_{\mathrm {max} }}$ of the photoelectrons that are emitted. If qe is the charge on the electron and ${\displaystyle V_{0}}$ is the stopping potential, then the work done by the retarding potential in stopping the electron is ${\displaystyle q_{e}V_{0}}$, so we have

${\displaystyle q_{e}V_{0}=K_{\mathrm {max} }.}$

Recalling

${\displaystyle K_{\mathrm {max} }=h\left(f-f_{0}\right),}$

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: [10] :50–51

1. Inner photoelectric effect (see photo diode below[ clarification needed ]). 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.[ clarification needed ] The transition rules for atoms translate via the tight-binding model onto the crystal.[ clarification needed ] They are similar in geometry to plasma oscillations in that they have to be transversed.
2. Ballistic transport[ clarification needed ] 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.[ citation needed ]

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. [11] Under certain circumstances it can directly ionize gases. [11] The first of these phenomena was discovered by Heinrich Hertz and Wilhelm Hallwachs in 1887. [11] The second was announced first by Philipp Lenard in 1900. [11]

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 [12] and O. Knoblauch. [13]

19th century

In 1839, Alexandre Edmond Becquerel discovered the photovoltaic effect while studying the effect of light on electrolytic cells. [14] 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. [15]

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. [16] [17] :458 Elster and Geitel had investigated with great success the effects produced by light on electrified bodies. [18]

In 1887, Heinrich Hertz observed the photoelectric effect and the production and reception of electromagnetic waves. [11] 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 [19] 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, [20] Hoor, [21] Righi [22] and Stoletow [23] [24] [25] [26] [27] [28] [29] 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 [30] 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. [31]

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. [32] 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; [33] [34] [35] [36] [37] [38] 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.[ citation needed ]

In 1899, J. J. Thomson investigated ultraviolet light in Crookes tubes. [39] 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. [40] 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.[ citation needed ]

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", [41] and Robert Millikan was awarded the Nobel Prize in 1923 for "his work on the elementary charge of electricity and on the photoelectric effect". [42]

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. [11]

In 1902, Lenard observed that the energy of individual emitted electrons increased with the frequency (which is related to the color) of the light. [2]

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 [43] have shown that the greater part of the Lenard effect is certainly due to this 'Hertz effect'. The Lenard effect upon the gas[ clarification needed ] itself nevertheless does exist. Refound by J. J. Thomson [44] and then more decisively by Frederic Palmer, Jr., [45] [46] it was studied and showed very different characteristics than those at first attributed to it by Lenard. [11]

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. [47] By wave-particle duality the effect can be analyzed purely in terms of waves though not as conveniently. [48]

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" [49] ) 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. [3]

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, [50] [51] [52] 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. [51] [53]

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 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. [54]

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. [55]

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. [56] :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. [10] :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. [57]

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. [58] [59]

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. [60] [61] 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. [62]

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. [63] 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, 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, which is given by: [64]

${\displaystyle \sigma =\mathrm {constant} \cdot {\frac {Z^{n}}{E^{3}}}}$

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. [65]

Related Research Articles

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can also be considered forms of radiative energy; recently, with tremendous difficulty, even gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and laser interferometry. Spectroscopic data are often represented by an emission spectrum, a plot of the response of interest, as a function of wavelength or frequency.

X-ray photoelectron spectroscopy (XPS) is a surface-sensitive quantitative spectroscopic technique that measures the elemental composition at the parts per thousand range, empirical formula, chemical state and electronic state of the elements that exist within a material. Put more simply, XPS is a useful measurement technique because it not only shows what elements are within a film but also what other elements they are bonded to. This means if you have a metal oxide and you want to know if the metal is in a +1 or +2 state, using XPS will allow you to find that ratio. However at most the instrument will only probe 20 nm into a sample.

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 ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases. By calculating the total amount of radiated energy, it can be shown that a blackbody is likely to release an arbitrarily high amount of energy. This would cause all matter to instantaneously radiate all of its energy until it is near absolute zero - indicating that a new model for the behaviour of blackbodies was needed.

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify the elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.

A synchrotron light source is a source of electromagnetic radiation (EM) usually produced by a storage ring, for scientific and technical purposes. First observed in synchrotrons, synchrotron light is now produced by storage rings and other specialized particle accelerators, typically accelerating electrons. Once the high-energy electron beam has been generated, it is directed into auxiliary components such as bending magnets and insertion devices in storage rings and free electron lasers. These supply the strong magnetic fields perpendicular to the beam which are needed to convert high energy electrons into photons.

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.

Photoemission electron microscopy is a type of electron microscopy that utilizes local variations in electron emission to generate image contrast. The excitation is usually produced by ultraviolet light, synchrotron radiation or X-ray sources. PEEM measures the coefficient indirectly by collecting the emitted secondary electrons generated in the electron cascade that follows the creation of the primary core hole in the absorption process. PEEM is a surface sensitive technique because the emitted electrons originate from a shallow layer. In physics, this technique is referred to as PEEM, which goes together naturally with low-energy electron diffraction (LEED), and low-energy electron microscopy (LEEM). In biology, it is called photoelectron microscopy (PEM), which fits with photoelectron spectroscopy (PES), transmission electron microscopy (TEM), and scanning electron microscopy (SEM).

Quantum mechanics is the science of the very small. It explains the behavior of matter and its interactions with energy on the scale of atoms and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that created a shift in the original scientific paradigm: the theory of relativity and the development of quantum mechanics. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. It describes these concepts in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.

Extreme ultraviolet radiation or high-energy ultraviolet radiation is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths from 124 nm down to 10 nm, and therefore having photons with energies from 10 eV up to 124 eV. EUV is naturally generated by the solar corona and artificially by plasma and synchrotron light sources. Since UVC extends to 100 nm, there is some overlap in the terms.

Angle-resolved photoemission spectroscopy (ARPES), is a direct experimental technique to observe the distribution of the electrons in the reciprocal space of solids. The technique is a refinement of ordinary photoemission spectroscopy, studying photoemission of electrons from a sample achieved usually by illumination with soft X-rays. ARPES is one of the most direct methods of studying the electronic structure of the surface of solids.

Ultraviolet photoelectron spectroscopy (UPS) refers to the measurement of kinetic energy spectra of photoelectrons emitted by molecules which have absorbed ultraviolet photons, in order to determine molecular orbital energies in the valence region.

A gamma ray, or gamma radiation, is a penetrating electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves and so imparts the highest photon energy. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900 while studying radiation emitted by radium. In 1903, Ernest Rutherford named this radiation gamma rays based on their relatively strong penetration of matter; he had previously discovered two less penetrating types of decay radiation, which he named alpha rays and beta rays in ascending order of penetrating power.

The Planck constant, or Planck's constant, denoted is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

Laser-based angle-resolved photoemission spectroscopy is a form of angle-resolved photoemission spectroscopy that uses a laser as the light source. Photoemission spectroscopy is a powerful and sensitive experimental technique to study surface physics. It is based on the photoelectric effect originally observed by Heinrich Hertz in 1887 and later explained by Albert Einstein in 1905 that when a material is shone by light, the electrons can absorb photons and escape from the material with the kinetic energy: , where is the incident photon energy, the work function of the material. Since the kinetic energy of ejected electrons are highly associated with the internal electronic structure, by analyzing the photoelectron spectroscopy one can realize the fundamental physical and chemical properties of the material, such as the type and arrangement of local bonding, electronic structure and chemical composition.

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.

LeRoy W. Apker was an American experimental physicist. Along with his colleagues E. A. Taft and Jean Dickey, he studied the photoelectric emission of electrons from semiconductors and discovered the phenomenon of exciton-induced photoemission in potassium iodide. In 1955, he received the Oliver E. Buckley Condensed Matter Prize of the American Physical Society for his work.

Time-resolved two-photon photoelectron (2PPE) spectroscopy is a time-resolved spectroscopy technique which is used to study electronic structure and electronic excitations at surfaces. The technique utilizes femtosecond to picosecond laser pulses in order to first photoexcite an electron. After a time delay, the excited electron is photoemitted into a free electron state by a second pulse. The kinetic energy and the emission angle of the photoelectron are measured in an electron energy analyzer. To facilitate investigations on the population and relaxation pathways of the excitation, this measurement is performed at different time delays.

References

1. Serway, R. A. (1990). Physics for Scientists & Engineers (3rd ed.). Saunders. p. 1150. ISBN   0-03-030258-7.
2. Lenard, P. (1902). "Ueber die lichtelektrische Wirkung". Annalen der Physik . 313 (5): 149–198. Bibcode:1902AnP...313..149L. doi:10.1002/andp.19023130510.
3. 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.
4. 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.
5. 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.
6. 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.
7. Mee, C.; Crundell, M.; Arnold, B.; Brown, W. (2011). International A/AS Level Physics. Hodder Education. p. 241. ISBN   978-0-340-94564-3.
8. Fromhold, A. T. (1991). Quantum Mechanics for Applied Physics and Engineering. Courier Dover Publications. pp. 5–6. ISBN   978-0-486-66741-6.
9. Gautreau, R.; Savin, W. (1999). Schaum's Outline of Modern Physics (2nd ed.). McGraw-Hill. pp. 60–61. ISBN   0-07-024830-3.
10. Hüfner, S. (2003). Photoelectron Spectroscopy: Principles and Applications. Springer. ISBN   3-540-41802-4.
11. Report of the Board of Regents By Smithsonian Institution. Board of Regents, United States National Museum, Smithsonian Institution. p. 239.
12. Schmidt, G. C. (1898) Wied. Ann. Uiv. p. 708.
13. Knoblauch, O. (1899). Zeitschrift für Physikalische Chemie. xxix. p. 527.
14. Vesselinka Petrova-Koch; Rudolf Hezel; Adolf Goetzberger (2009). High-Efficient Low-Cost Photovoltaics: Recent Developments. Springer. pp. 1–. ISBN   978-3-540-79358-8.
15. 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.
16. Asimov, A. (1964) Asimov's Biographical Encyclopedia of Science and Technology , Doubleday, ISBN   0-385-04693-6.
17. 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.
18. 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.
19. Hertz, Heinrich (1887). "Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung". Annalen der Physik . 267: 983–1000. doi:10.1002/andp.18872670827.
20. Hallwachs, Wied. Ann. xxxiii. p. 301, 1888.
21. Hoor, Repertorium des Physik, xxv. p. 91, 1889.
22. Bighi, C. R. cvi. p. 1349; cvii. p. 559, 1888
23. Stoletow. C. R. cvi. pp. 1149, 1593; cvii. p. 91; cviii. p. 1241; Physikalische Revue, Bd. i., 1892.
24. 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).
25. Stoletow, A. (1888). "Sur les courants actino-electriqies au travers deTair". Comptes Rendus . CVI: 1593. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
26. Stoletow, A. (1888). "Suite des recherches actino-electriques". Comptes Rendus . CVII: 91. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
27. Stoletow, A. (1889). "Sur les phénomènes actino-électriques". Comptes Rendus . CVIII: 1241.
28. Stoletow, A. (1889). "Актино-электрические исследовaния". Journal of the Russian Physico-chemical Society (in Russian). 21: 159.
29. Stoletow, A. (1890). "Sur les courants actino-électriques dans l'air raréfié". Journal de Physique. 9: 468. doi:10.1051/jphystap:018900090046800.
30. 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.
31. Thomson, J. J. (2005). Conduction of Electricity Through Gases. Watchmaker Publishing. ISBN   978-1-929148-49-3 . Retrieved 9 July 2011.
32. Hallwachs, W. (1907). "Über die lichtelektrische Ermüdung". Annalen der Physik. 328 (8): 459–516. Bibcode:1907AnP...328..459H. doi:10.1002/andp.19073280807.
33. 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).
34. Stoletow, A. (1888). "Sur les courants actino-electriques au travers deTair". Comptes Rendus . CVI: 1593. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
35. Stoletow, A. (1888). "Suite des recherches actino-électriques". Comptes Rendus . CVII: 91. (Abstract in Beibl. Ann. d. Phys. 12, 723, 1888).
36. Stoletow, A. (1889). "Sur les phénomènes actino-électriques". Comptes Rendus . CVIII: 1241.
37. Stoletow, A. (1889). "Актино-электрические исследовaния". Journal of the Russian Physico-chemical Society (in Russian). 21: 159.
38. Stoletow, A. (1890). "Sur les courants actino-électriques dans l'air raréfié". Journal de Physique. 9: 468. doi:10.1051/jphystap:018900090046800.
39. The International Year Book. (1900). New York: Dodd, Mead & Company. p. 659.
40. 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.
41. "The Nobel Prize in Physics 1921". Nobel Foundation . Retrieved 2013-03-16.
42. "The Nobel Prize in Physics 1923". Nobel Foundation. Retrieved 2015-03-29.
43. Bloch, E. (1908). "L'ionisation de l'air par la lumière ultra-violette". Le Radium. 5 (8): 240. doi:10.1051/radium:0190800508024001.
44. 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.
45. Palmer, Frederic (1908). "Ionisation of Air by Ultra-violet Light". Nature. 77 (2008): 582. Bibcode:1908Natur..77..582P. doi:10.1038/077582b0.
46. Palmer, Frederic (1911). "Volume Ionization Produced by Light of Extremely Short Wave-Length". Physical Review. Series I. 32 (1): 1–22. Bibcode:1911PhRvI..32....1P. doi:10.1103/PhysRevSeriesI.32.1.
47. "The Nobel Prize in Physics 1921". Nobel Foundation. Retrieved 2008-10-09.
48. Lamb, Willis E.; Scully, Marlan O. (1968). "Photoelectric effect without photons, discussing classical field falling on quantized atomic electron" (PDF).
49. 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.
50. Resnick, Robert (1972) Basic Concepts in Relativity and Early Quantum Theory, Wiley, p. 137, ISBN   0-471-71702-9.
51. 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.
52. Penrose, Roger (2005) The Road to Reality: A Complete Guide to the Laws of the Universe, Knopf, p. 502, ISBN   0-679-45443-8
53. Resnick, Robert (1972) Basic Concepts in Relativity and Early Quantum Theory, Wiley, p. 138, ISBN   0-471-71702-9.
54. 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
55. Burns, R. W. (1998) Television: An International History of the Formative Years, IET, p. 358, ISBN   0-85296-914-7.
56. Tsokos, K. A. (2010). Cambridge Physics for the IB Diploma (revised ed.). Cambridge University Press. ISBN   978-0-521-13821-5.
57. 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.
58. 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.
59. "Spacecraft charging". Arizona State University.
60. Bell, Trudy E., "Moon fountains", NASA.gov, 2005-03-30.
61. Dust gets a charge in a vacuum. spacedaily.com, July 14, 2000.
62. Evans, R. D. (1955). The Atomic Nucleus. Malabar, Fla.: Krieger. p. 673. ISBN   0-89874-414-8.
63. Evans, R. D. (1955). The Atomic Nucleus. Malabar, Fla.: Krieger. p. 712. ISBN   0-89874-414-8.
64. Davisson, C. M. (1965). "Interaction of gamma-radiation with matter". In Kai Siegbahn (ed.). Alpha-, Beta- and Gamma-ray Spectroscopy: Volume 1. Amsterdam: North-Holland Publishing Company. pp. 37–78. Bibcode:1965abgs.conf...37D.
65. Knoll, Glenn F. (1999). Radiation Detection and Measurement. New York: Wiley. p. 49. ISBN   0-471-49545-X.

Applets