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Emission spectrum

Emission spectrum

Overview
The emission spectrum of a chemical element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

 or chemical compound
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

 is the spectrum of frequencies of electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 emitted by the element's atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s or the compound's molecules when they are returned to a lower energy state.

Each element's emission spectrum is unique. Therefore, spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 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.

In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emission of a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

, resulting in the production of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

.
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Encyclopedia
The emission spectrum of a chemical element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

 or chemical compound
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

 is the spectrum of frequencies of electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 emitted by the element's atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s or the compound's molecules when they are returned to a lower energy state.

Each element's emission spectrum is unique. Therefore, spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 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.

Emission (light)


In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emission of a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

, resulting in the production of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

. The frequency of light emitted is a function of the energy of the transition. Since energy must be conserved, the energy difference between the two states equals the energy carried off by the photon. The energy states of the transitions can lead to emissions over a very large range of frequencies. For example, visible light is emitted by the coupling of electronic states in atoms and molecules (then the phenomenon is called fluorescence
Fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation of a different wavelength. It is a form of luminescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation...

 or phosphorescence
Phosphorescence
Phosphorescence is a specific type of photoluminescence related to fluorescence. Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. The slower time scales of the re-emission are associated with "forbidden" energy state transitions in quantum...

). On the other hand, nuclear shell transitions can emit high energy gamma rays, while nuclear spin transitions emit low energy radiowaves
Radiowaves
Radiowaves is the final studio album by Norwegian rock band Seigmen. It is sung entirely in English. The album came in two editions: a limited edition black jewel case, and a transparent jewel case.-Track listing:# "Performance Alpha" - 4:42...

.

The emittance
Beam emittance
The beam emittance of a particle accelerator is the extent occupied by the particles of the beam in space and momentum phase space as it travels. A low emittance particle beam is a beam where the particles are confined to a small distance and have nearly the same momentum...

 of an object quantifies how much light is emitted by it. This may be related to other properties of the object through the Stefan–Boltzmann law.
For most substances, the amount of emission varies with the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and the spectroscopic composition
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 of the object, leading to the appearance of color temperature
Color temperature
Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, and other fields. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of...

 and emission lines. Precise measurements at many wavelengths allow the identification of a substance via emission spectroscopy.

Emission of radiation is typically described using semi-classical quantum mechanics: the particle's energy levels and spacings are determined from quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, and light is treated as an oscillating electric field that can drive a transition if it is in resonance with the system's natural frequency. The quantum mechanics problem is treated using time-dependent perturbation theory
Perturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...

 and leads to the general result known as Fermi's golden rule
Fermi's golden rule
In quantum physics, Fermi's golden rule is a way to calculate the transition rate from one energy eigenstate of a quantum system into a continuum of energy eigenstates, due to a perturbation....

. The description has been superseded by quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

, although the semi-classical version continues to be more useful in most cases.

Origins


When the electrons in the atom are excited, for example by being heated, the additional energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 pushes the electrons to higher energy orbitals. When the electrons fall back down and leave the excited state, energy is re-emitted in the form of a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

. The wavelength (or equivalently, frequency) of the photon is determined by the difference in energy between the two states. These emitted photons form the element's emission spectrum.

The fact that only certain colors appear in an element's atomic emission spectrum means that only certain frequencies of light are emitted. Each of these frequencies are related to energy by the formula:
where E is the energy of the photon, ν is its frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

, and h is Planck's constant.
This concludes that only photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s having certain energies are emitted by the atom. The principle of the atomic emission spectrum explains the varied colors in neon sign
Neon sign
Neon signs are made using electrified, luminous tube lights that contain rarefied neon or other gases. They are the most common use for neon lighting, which was first demonstrated in a modern form in December, 1910 by Georges Claude at the Paris Motor Show. While they are used worldwide, neon signs...

s, as well as chemical flame test
Flame test
A flame test is a procedure used in chemistry to detect the presence of certain metal ions, based on each element's characteristic emission spectrum. The color of flames in general also depends on temperature; see flame color....

 results mentioned above.

The frequencies of light that an atom can emit are dependent on states the electrons can be in. When excited, an electron moves to a higher energy level/orbital. When the electron falls back to its ground level the light is emitted.

Radiation from molecules


As well as the electronic transitions discussed above, the energy of a molecule can also change via rotational
Rotational transition
A rotational transition is an abrupt change in angular momentum in quantum physics. Like all other properties of a quantum particle, angular momentum is quantized, meaning it can only equal certain discrete values, which correspond to different rotational energy states. When a particle loses...

, vibrational, and vibronic
Vibronic transition
A vibronic transition denotes the simultaneous change of vibrational and electronic quantum number in a molecule. According to the separability of electronic and nuclear motion in the Born-Oppenheimer approximation, the vibrational transition and electronic transition may be described separately...

 (combined vibrational and electronic) transitions. These energy transitions often lead to closely spaced groups of many different spectral lines, known as spectral bands
Spectral bands
Spectral bands are part of optical spectra of polyatomic systems, including condensed materials, large molecules etc. Each line corresponding to one level in atom splits in molecules. When the number of atoms is large, one gets continuum of energy levels, so called "spectral bands". They are often...

. Unresolved band spectra may appear as a spectral continuum.

Molecular emission is the mechanism behind the sulfur lamp
Sulfur lamp
The sulfur lamp is a highly efficient full-spectrum electrodeless lighting system whose light is generated by sulfur plasma that has been excited by microwave radiation. The technology was developed in the early 1990s, but, although it appeared initially to be very promising, sulfur lighting was...

 and the deuterium arc lamp
Deuterium arc lamp
A deuterium arc lamp is a low-pressure gas-discharge light source often used in spectroscopy when a continuous spectrum in the ultraviolet region is needed.-Principle of operation:...

.

Emission spectroscopy


Light consists of electromagnetic radiation of different wavelengths. Therefore, when the elements or their compounds are heated either on a flame or by an electric arc they emit energy in form of light. Analysis of this light, with the help of a spectroscope gives us a discontinuous spectrum. A spectroscope or a spectrometer is an instrument which is used for separating the components of light, which have different wavelengths. The spectrum appears in a series of lines called the line spectrum. This line spectrum is also called the Atomic Spectrum because it originates in the element. Each element has a different atomic spectrum. The production of line spectra by the atoms of an element indicate that an atom can radiate only a certain amount of energy. This leads to the conclusion that electrons cannot have just any amount of energy but only a certain amount of energy.

The emission spectrum can be used to determine the composition of a material, since it is different for each element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

 of the periodic table
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...

. One example is astronomical spectroscopy
Astronomical spectroscopy
Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...

: identifying the composition of star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s by analysing the received light.
The emission spectrum characteristics of some elements are plainly visible to the naked eye when these elements are heated. For example, when platinum wire is dipped into a strontium
Strontium
Strontium is a chemical element with the symbol Sr and the atomic number 38. An alkaline earth metal, strontium is a soft silver-white or yellowish metallic element that is highly reactive chemically. The metal turns yellow when exposed to air. It occurs naturally in the minerals celestine and...

 nitrate solution and then inserted into a flame, the strontium atoms emit a red color. Similarly, when copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

 is inserted into a flame, the flame becomes green. These definite characteristics allow elements to be identified by their atomic emission spectrum. Not all lights emitted by the spectrum are viewable to the naked eye, it also includes ultra violet rays and infra red lighting,
an emission is formed when an excited gas is viewed directly through a spectroscope.


Emission spectroscopy is a spectroscopic
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 technique which examines the wavelengths of photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s emitted by atoms or molecules during their transition from an excited state
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....

 to a lower energy state. Each element emits a characteristic set of discrete wavelengths according to its electronic structure, by observing these wavelengths the elemental composition of the sample can be determined. Emission spectroscopy developed in the late 19th century and efforts in theoretical explanation of atomic emission spectra eventually led to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

.

There are many ways in which atoms can be brought to an excited state. Interaction with electromagnetic radiation is used in fluorescence spectroscopy
Fluorescence spectroscopy
Fluorescence spectroscopy aka fluorometry or spectrofluorometry, is a type of electromagnetic spectroscopy which analyzes fluorescence from a sample. It involves using a beam of light, usually ultraviolet light, that excites the electrons in molecules of certain compounds and causes them to emit...

, protons or other heavier particles in Particle-Induced X-ray Emission and electrons or X-ray photons in Energy-dispersive X-ray spectroscopy
Energy-dispersive X-ray spectroscopy
Energy-dispersive X-ray spectroscopy is an analytical technique used for the elemental analysis or chemical characterization of a sample. It relies on the investigation of an interaction of a some source of X-ray excitation and a sample...

 or X-ray fluorescence
X-ray fluorescence
X-ray fluorescence is the emission of characteristic "secondary" X-rays from a material that has been excited by bombarding with high-energy X-rays or gamma rays...

. The simplest method is to heat the sample to a high temperature, after which the excitations are produced by collisions between the sample atoms. This method is used in flame emission spectroscopy, and it was also the method used by Anders Jonas Ångström
Anders Jonas Ångström
Anders Jonas Ångström was a Swedish physicist and one of the founders of the science of spectroscopy.-Biography:...

 when he discovered the phenomenon of discrete emission lines in 1850s.

Although the emission lines are caused by a transition between quantized energy states and may at first look very sharp, they do have a finite width, i.e. they are composed of more than one wavelength of light. This spectral line broadening has many different causes.

Emission spectroscopy is often referred to as optical emission spectroscopy, due to the light nature of what is being emitted.

History


Emission lines from hot gases were first discovered by Ångström
Anders Jonas Ångström
Anders Jonas Ångström was a Swedish physicist and one of the founders of the science of spectroscopy.-Biography:...

, and the technique was further developed by David Alter
David Alter
David Alter was a prominent American inventor and scientist of the 19th century. He was born in Westmoreland County, Pennsylvania and graduated from the Reformed Medical School in New York City. He had German and Swiss ancestry.-Inventions:Dr...

, Gustav Kirchhoff
Gustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...

 and Robert Bunsen
Robert Bunsen
Robert Wilhelm Eberhard Bunsen was a German chemist. He investigated emission spectra of heated elements, and discovered caesium and rubidium with Gustav Kirchhoff. Bunsen developed several gas-analytical methods, was a pioneer in photochemistry, and did early work in the field of organoarsenic...

.

See spectrum analysis
Spectrum analysis
Spectrum, also known as emission spectrochemical analysis, is the original scientific method of charting and analyzing the chemical properties of matter and gases by looking at the bands in their optical spectrum...

 for details.

Experimental technique in flame emission spectroscopy


The solution containing the relevant substance to be analysed is drawn into the burner and dispersed into the flame as a fine spray. The solvent evaporates first, leaving finely divided solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

 particles which move to the hottest region of the flame where gaseous atoms and ions are produced. Here electrons are excited as described above. It is common for a monochromator
Monochromator
A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input...

 to be used to allow for easy detection.

On a simple level, flame emission spectroscopy can be observed using just a Flame
Flame
A flame is the visible , gaseous part of a fire. It is caused by a highly exothermic reaction taking place in a thin zone...

 and samples of metal salts. This method of Qualitative analysis is called a Flame test
Flame test
A flame test is a procedure used in chemistry to detect the presence of certain metal ions, based on each element's characteristic emission spectrum. The color of flames in general also depends on temperature; see flame color....

. For example, Sodium
Sodium
Sodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...

 salts placed in the flame will glow yellow from Sodium ions, while Strontium
Strontium
Strontium is a chemical element with the symbol Sr and the atomic number 38. An alkaline earth metal, strontium is a soft silver-white or yellowish metallic element that is highly reactive chemically. The metal turns yellow when exposed to air. It occurs naturally in the minerals celestine and...

 (used in road flares) ions color it red. Copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

 wire will create a blue colored flame, however in the presence of Chloride
Chloride
The chloride ion is formed when the element chlorine, a halogen, picks up one electron to form an anion Cl−. The salts of hydrochloric acid HCl contain chloride ions and can also be called chlorides. The chloride ion, and its salts such as sodium chloride, are very soluble in water...

 gives green (molecular contribution by CuCl).

Emission coefficient


Emission coefficient is a coefficient
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of an expression ; it is usually a number, but in any case does not involve any variables of the expression...

 in the power output per unit time of an electromagnetic
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 source, a calculated value in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

. It is also used as a measure of environmental
Natural environment
The natural environment encompasses all living and non-living things occurring naturally on Earth or some region thereof. It is an environment that encompasses the interaction of all living species....

 emissions (by mass) per MWh of electricity generated
Electricity generation
Electricity generation is the process of generating electric energy from other forms of energy.The fundamental principles of electricity generation were discovered during the 1820s and early 1830s by the British scientist Michael Faraday...

, see: Emission factor
Emission factor
An emission intensity is the average emission rate of a given pollutant from a given source relative to the intensity of a specific activity; for example grams of carbon dioxide released per megajoule of energy produced, or the ratio of greenhouse gas emissions produced to GDP...

.

Scattering of light


In Thomson scattering
Thomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering...

 a charged particle emits radiation under incident light. The particle may be an ordinary atomic electron, so emission coefficients have practical applications.

If X dV dΩ dλ is the energy scattered by a volume element dV into solid angle dΩ between wavelengths λ and λ+dλ per unit time then the Emission coefficient
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of an expression ; it is usually a number, but in any case does not involve any variables of the expression...

 is X.

The values of X in Thomson scattering can be predicted
Thomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering...

 from incident flux, the density of the charged particles and their Thomson differential cross section (area/solid angle).

Spontaneous Emission


A warm body emitting photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s has a monochromatic emission coefficient relating to its temperature and total power radiation. This is sometimes called the second "Einstein coefficient", and can be deduced from quantum mechanical theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

.

Energy spectrum


An energy spectrum is a distribution energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 among a large assemblage of particles. It is a statistical representation of the wave energy as a function of the wave frequency, and an empirical estimator of the spectral function. For any given value of energy, it determines how many of the particles have that much energy.

The particles may be atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s, photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s or a flux of elementary particles.

The Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

 and a set of boundary conditions form an eigenvalue problem. A possible value (E) is called an eigenenergy. A non-zero solution of the wave function is called an eigenenergy state, or simply an eigenstate. The set of eigenvalues {Ej} is called the energy spectrum of the particle.

The electromagnetic spectrum can also be represented as the distribution of electromagnetic radiation according to energy. The relationship among the wavelength (usually denoted by Greek ""), the frequency (usually denoted by Greek ""), and the energy E are:


where c is the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

 and h is Planck's Constant.

An example of an energy spectrum in the physical domain is ocean waves breaking on the shore. For any given interval of time it can be observed that some of the waves are larger than others. Plotting the number of waves against the amplitude (height) for the interval will yield the energy spectrum of the set.

Optical Spectroscopy and Astrophysics Application


Energy spectra are often used in astrophysical spectroscopy.

The quantity plotted, energy units, is the wavelength times the energy per unit wavelength and thus accurately represents the amount of energy at any wavelength. The energy per unit wavelength and the energy per unit frequency peak at significantly different wavelengths due the reciprocal relation between frequency and wavelength. Using energy units avoids this problem, since (wavelength * flux per unit wavelength) = (frequency * flux per unit frequency).


Some modern spectrophotometers, such as the Perkin Elmer 950, include an energy scan option. This is additionally useful in cases where a reference cell is not practical or when absorbance / transmittance is off-scale.

See also

  • Atomic spectral line
    Atomic spectral line
    In physics, atomic spectral lines are of two types:* An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength...

  • Rydberg formula
    Rydberg formula
    The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on November 5, 1888.-History:...

  • Fraunhofer lines
    Fraunhofer lines
    In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer . The lines were originally observed as dark features in the optical spectrum of the Sun....

  • Isotopic shift
    Isotopic shift
    The isotopic shift is the shift in atomic spectra which occurs when one nuclear isotope is replaced by another. If the spectra have also hyperfine structure the shift refers to the center of gravity of the spectra. There are two effects which contribute to this shift:*The mass difference. This...

  • Isomeric shift
    Isomeric shift
    The isomeric shift is the shift on atomic spectral lines and gamma spectral lines, which occurs as a consequence of replacement of one nuclear isomer by another. It is usually called isomeric shift on atomic spectral lines and Mössbauer isomeric shift respectively...


Links related to emission spectroscopy

  • Electromagnetic spectroscopy
  • Absorption spectroscopy
    Absorption spectroscopy
    Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a...

  • Astronomical spectroscopy
    Astronomical spectroscopy
    Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...


Links related to emission coefficient

  • The Diode
    Diode
    In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

     equation includes the emission coefficient
  • Plasma
    Plasma (physics)
    In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

     physics.
  • An emission coefficient is also given for ballistic secondary electron
    Electron
    The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

     emission
    Thermionic emission
    Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the binding potential, also known as work function of the metal. The charge carriers can be electrons or ions, and...

    .
  • Luminous coefficient

External links