# Mass attenuation coefficient

The mass attenuation coefficient, mass extinction coefficient, or mass narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter.[1] In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation (such as X-rays), sound, or any other beam that attenuates. The SI unit of mass attenuation coefficient is the square metre per kilogram (m2/kg). Other common units include cm2/g (the most common unit for X-ray mass attenuation coefficients) and mL⋅g−1⋅cm−1 (sometimes used in solution chemistry). "Mass extinction coefficient" is an old term for this quantity.[1]

The mass attenuation coefficient can be thought of as a variant of absorption cross section where the effective area is defined per unit mass instead of per particle.

## Mathematical definitions

Mass attenuation coefficient is defined as

${\displaystyle {\frac {\mu }{\rho _{m}}},}$

where

When using the mass attenuation coefficient, the Beer-Lambert law is written in alternative form as

${\displaystyle I=I_{0}\,e^{-(\mu /\rho _{m})\lambda }}$

where

${\displaystyle \lambda =\rho _{m}\ell }$ is the area density known also as mass thickness, and ${\displaystyle \ell }$ is the length, over which the attenuation takes place.

### Mass absorption and scattering coefficients

When a narrow (collimated) beam passes through a volume, the beam will lose intensity to two processes: absorption and scattering.

Mass absorption coefficient, and mass scattering coefficient are defined as

${\displaystyle {\frac {\mu _{\mathrm {a} }}{\rho _{m}}},\quad {\frac {\mu _{\mathrm {s} }}{\rho _{m}}},}$

where

• μa is the absorption coefficient;
• μs is the scattering coefficient.

### In solutions

In chemistry, mass attenuation coefficients are often used for a chemical species dissolved in a solution. In that case, the mass attenuation coefficient is defined by the same equation, except that the "density" is the density of only that one chemical species, and the "attenuation" is the attenuation due to only that one chemical species. The actual attenuation coefficient is computed by

${\displaystyle \mu =(\mu /\rho _{1})\rho _{1}+(\mu /\rho _{2})\rho _{2}+\ldots ,}$

where each term in the sum is the mass attenuation coefficient and density of a different component of the solution (the solvent must also be included). This is a convenient concept because the mass attenuation coefficient of a species is approximately independent of its concentration (as long as certain assumptions are fulfilled).

A closely related concept is molar absorptivity. They are quantitatively related by

(mass attenuation coefficient) × (molar mass) = (molar absorptivity).

## X-rays

Mass attenuation coefficient of iron with contributing sources of attenuation: Coherent scattering, Incoherent scattering, Photoelectric Absorption, and two types of Pair Production. The discontinuity of photoelectric absorption values are due to K-edge. Graph data came from NIST's XCOM database.
Mass attenuation coefficient values shown for all elements with atomic number Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to absorption edges which were also shown.

Tables of photon mass attenuation coefficients are essential in radiological physics, radiography (for medical and security purposes), dosimetry, diffraction, interferometry, crystallography and other branches of physics. The photons can be in form of X-ray, gamma-ray, and bremsstrahlung.

The values of mass attenuation coefficients are dependent upon the absorption and scattering of the incident radiation caused by several different mechanisms such as

The actual values have been thoroughly examined and are available to the general public through three databases run by National Institute of Standards and Technology (NIST):

1. XAAMDI database;[2]
2. XCOM database;[3]
3. FFAST database.[4]

## Calculating the composition of a solution

If several known chemicals are dissolved in a single solution, the concentrations of each can be calculated using a light absorption analysis. First, the mass attenuation coefficients of each individual solute or solvent, ideally across a broad spectrum of wavelengths, must be measured or looked up. Second, the attenuation coefficient of the actual solution must be measured. Finally, using the formula

${\displaystyle \mu =(\mu /\rho _{1})\rho _{1}+(\mu /\rho _{2})\rho _{2}+\ldots ,}$

the spectrum can be fitted using ρ1, ρ2, … as adjustable parameters, since μ and each μ/ρi are functions of wavelength. If there are N solutes or solvents, this procedure requires at least N measured wavelengths to create a solvable system of simultaneous equations, although using more wavelengths gives more reliable data.

## References

1. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Attenuation coefficient".
2. ^ Hubbell, J. H.; Seltzer, S. M. "Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients". National Institute of Standards and Technology (NIST). Retrieved 2 Nov 2007.
3. ^ M.J.Berger; J.H. Hubbell; S.M. Seltzer; J. Chang; J.S. Coursey; R. Sukumar; D.S. Zucker. "XCOM: Photon Cross Sections Database". National Institute of Standards and Technology (NIST). Retrieved 2 Nov 2007.
4. ^ Chantler, C.T.; Olsen, K.; Dragoset, R.A.; Chang, J.; Kishore, A.R.; Kotochigova, S.A.; Zucker, D.S. "X-Ray Form Factor, Attenuation and Scattering Tables (version 2.1)". National Institute of Standards and Technology (NIST). Retrieved 2 Nov 2007.

In physics, absorption of electromagnetic radiation is the way in which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed into internal energy of the absorber, for example thermal energy. The reduction in intensity of a light wave propagating through a medium by absorption of a part of its photons is often called attenuation. Usually, the absorption of waves does not depend on their intensity (linear absorption), although in certain conditions (usually, in optics), the medium changes its transparency dependently on the intensity of waves going through, and saturable absorption (or nonlinear absorption) occurs.

Attenuation (disambiguation)

Attenuation is the gradual loss in intensity of any kind of flux through a medium, including:

Acoustic attenuation, the loss of sound energy in a viscous medium

Anelastic attenuation factor, a way to describe attenuation of seismic energy in the EarthAttenuation (or verb attenuate) may also refer to:

Attenuation (botany)

Attenuation (brewing), the percent of sugar converted to alcohol and carbon dioxide by the yeast in brewing

Attenuation coefficient, a basic quantity used in calculations of the penetration of materials by quantum particles or other energy beams

Mass attenuation coefficient, a measurement of how strongly a chemical species or substance absorbs or scatters light at a given wavelength, per unit mass

Regression attenuation or Regression dilution, a cause of statistical bias

The process of producing an attenuated vaccine by reducing the virulence of a pathogen

Attenuation constant, the real part of the propagation constant

Attenuator (genetics), form of regulation in prokaryotic cells.

Attenuation coefficient

For "attenuation coefficient" as it applies to electromagnetic theory and telecommunications see Attenuation constant. For the "mass attenuation coefficient", see Mass attenuation coefficient.Attenuation coefficient or narrow beam attenuation coefficient of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. A large attenuation coefficient means that the beam is quickly "attenuated" (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent to the beam. The SI unit of attenuation coefficient is the reciprocal metre (m−1). Extinction coefficient is an old term for this quantity but is still used in meteorology and climatology. Most commonly, the quantity measures the number of downward e-foldings of the original intensity that will be had as the energy passes through a unit (e.g. one meter) thickness of material, so that an attenuation coefficient of 1 m-1 means that after passing through 1 metre, the radiation will be reduced by a factor of e, and for material with a coefficient of 2 m-1, it will be reduced twice by e, or e2. Other measures may use a different factor than e, such as the decadic attenuation coefficient below.

Extinction (disambiguation)

Extinction is in biology and palaeontology, the end of a species or other taxon.

Extinction may also refer to:

Extinction (peerage), in the United Kingdom, happens when all possible heirs of a peer have died out

High energy X-ray imaging technology

High energy X-ray imaging technology (HEXITEC) is a family of spectroscopic, single photon counting, pixel detectors developed for high energy X-ray and Ύ-ray spectroscopy applications.The HEXITEC consortium was formed in 2006 funded by the Engineering and Physical Sciences Research Council, UK. The consortium is led by the University of Manchester; other members include the Science and Technology Facilities Council, the University of Surrey, Durham University and University of London, Birkbeck. In 2010 the consortium expanded to include the Royal Surrey County Hospital and the University College London. The vision of the consortium was to "develop a UK-based capability in high energy X-ray imaging technology".

Index of physics articles (M)

The index of physics articles is split into multiple pages due to its size.

Iron

Iron is a chemical element with symbol Fe (from Latin: ferrum) and atomic number 26. It is a metal in the first transition series. It is by mass the most common element on Earth, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust. Its abundance in rocky planets like Earth is due to its abundant production by fusion in high-mass stars, where it is the last element to be produced with release of energy before the violent collapse of a supernova, which scatters the iron into space.

Like the other group 8 elements, ruthenium and osmium, iron exists in a wide range of oxidation states, −2 to +7, although +2 and +3 are the most common. Elemental iron occurs in meteoroids and other low oxygen environments, but is reactive to oxygen and water. Fresh iron surfaces appear lustrous silvery-gray, but oxidize in normal air to give hydrated iron oxides, commonly known as rust. Unlike the metals that form passivating oxide layers, iron oxides occupy more volume than the metal and thus flake off, exposing fresh surfaces for corrosion.

Iron metal has been used since ancient times, although copper alloys, which have lower melting temperatures, were used even earlier in human history. Pure iron is relatively soft, but is unobtainable by smelting because it is significantly hardened and strengthened by impurities, in particular carbon, from the smelting process. A certain proportion of carbon (between 0.002% and 2.1%) produces steel, which may be up to 1000 times harder than pure iron. Crude iron metal is produced in blast furnaces, where ore is reduced by coke to pig iron, which has a high carbon content. Further refinement with oxygen reduces the carbon content to the correct proportion to make steel. Steels and iron alloys formed with other metals (alloy steels) are by far the most common industrial metals because they have a great range of desirable properties and iron-bearing rock is abundant.

Iron chemical compounds have many uses. Iron oxide mixed with aluminium powder can be ignited to create a thermite reaction, used in welding and purifying ores. Iron forms binary compounds with the halogens and the chalcogens. Among its organometallic compounds is ferrocene, the first sandwich compound discovered.

Iron plays an important role in biology, forming complexes with molecular oxygen in hemoglobin and myoglobin; these two compounds are common oxygen transport proteins in vertebrates. Iron is also the metal at the active site of many important redox enzymes dealing with cellular respiration and oxidation and reduction in plants and animals. In adult human males are some 3.8 grams of iron, and 2.3 grams in females, for whom iron is distributed in hemoglobin and throughout the body. Iron is a critical element in the metabolism of hundreds of proteins and enzymes involved in diverse body functions, such as oxygen transport, DNA synthesis, and cell growth.

Mathematical descriptions of opacity

When an electromagnetic wave travels through a medium in which it gets attenuated (this is called an "opaque" or "attenuating" medium), it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:

attenuation coefficient;

penetration depth and skin depth;

complex angular wavenumber and propagation constant;

complex refractive index;

complex electric permittivity;

Mean free path

In physics, the mean free path is the average distance travelled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.

The following table lists some typical values for air at different pressures at room temperature.

Molar attenuation coefficient

The molar attenuation coefficient is a measurement of how strongly a chemical species attenuates light at a given wavelength. It is an intrinsic property of the species. The SI unit of molar attenuation coefficient is the square metre per mole (m2/mol), but in practice, it is usually taken as the M−1⋅cm−1 or the L⋅mol−1⋅cm−1. In older literature, the cm2/mol is sometimes used with corresponding values 1,000 times larger. In practice these units are the same, with the difference being expression of volume in either cm3 or in L. The molar attenuation coefficient is also known as the molar extinction coefficient and molar absorptivity, but the use of these alternative terms has been discouraged by the IUPAC.

Nucleic acid quantitation

In molecular biology, quantitation of nucleic acids is commonly performed to determine the average concentrations of DNA or RNA present in a mixture, as well as their purity. Reactions that use nucleic acids often require particular amounts and purity for optimum performance. To date, there are two main approaches used by scientists to quantitate, or establish the concentration, of nucleic acids (such as DNA or RNA) in a solution. These are spectrophotometric quantification and UV fluorescence tagging in presence of a DNA dye.

Opacity (optics)

Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through). When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted (also see refraction). Reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Both mirrors and carbon black are opaque. Opacity depends on the frequency of the light being considered. For instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. More extreme frequency-dependence is visible in the absorption lines of cold gases. Opacity can be quantified in many ways; for example, see the article mathematical descriptions of opacity.

Different processes can lead to opacity including absorption, reflection, and scattering.

Refractive index

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as

${\displaystyle n={\frac {c}{v}},}$

where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water.

The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle.

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index. As a result, the energy (E = h f) of the photon, and therefore the perceived color of the refracted light to a human eye which depends on photon energy, is not affected by the refraction or the refractive index of the medium.

While the refractive index affects wavelength, it depends on photon frequency, color and energy so the resulting difference in the bending angle causes white light to split into its constituent colors. This is called dispersion. It can be observed in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction.

The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.

Scattering theory

In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future". The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object.

Since its early statement for radiolocation, the problem has found vast number of applications, such as echolocation, geophysical survey, nondestructive testing, medical imaging and quantum field theory, to name just a few.

X-ray image intensifier

An x-ray image intensifier (XRII) is an image intensifier that converts x-rays into visible light at higher intensity than mere fluorescent screens do. Such intensifiers are used in x-ray imaging systems (such as fluoroscopes ) to allow low-intensity x-rays to be converted to a conveniently bright visible light output. The device contains a low absorbency/scatter input window, typically aluminum, input fluorescent screen, photocathode, electron optics, output fluorescent screen and output window. These parts are all mounted in a high vacuum environment within glass or more recently, metal/ceramic. By its intensifying effect, It allows the viewer to more easily see the structure of the object being imaged than fluorescent screens alone, whose images are dim. The XRII requires lower absorbed doses due to more efficient conversion of x-ray quanta to visible light. This device was originally introduced in 1948.

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