Mass attenuation coefficient

Encyclopedia

The

or substance absorbs or scatters

light at a given wavelength

, per unit mass. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation

(such as X-ray

s), sound

, or any other beam that attenuates.

The mass attenuation coefficient is also called

The mass extinction coefficient should not be confused with the

.

. The Beer-Lambert law is normally written

where

When discussing the mass attenuation coefficient, this equation is rewritten

where is the density

, is the mass attenuation coefficient and is the area density known also as mass thickness.

In accordance with the above, the mass attenuation coefficient is equal to the attenuation coefficient divided by the density.

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

is computed by

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:×(Molar mass

) = (Molar absorptivity).

has units of inverse-length, while density has units of mass per volume. Since the mass attenuation coefficient is the ratio of these two, we find that it has units of (length-squared) per mass. The SI unit is m

(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):

the spectrum can be fitted using as adjustable parameters. (Remember, and each are functions of wavelength.)

If there are N solutes or solvents, this procedure requires

, although using more wavelengths gives more reliable data.

When a narrow (collimated) beam of light passes through a substance, the beam will lose intensity due to two processes: The light can be absorbed by the substance, or the light can be scattered

(i.e., the photon

s can change direction) by the substance. Just looking at the narrow beam itself, the two processes cannot be distinguished. However, if you set up a detector to measure light leaving in different directions, or conversely try using a non-narrow beam, you can measure how much of the lost intensity was scattered, and how much was absorbed.

In this context, the "mass absorption coefficient" measures how quickly the beam would lose intensity due to the absorption

**mass attenuation coefficient**is a measurement of how strongly a chemical speciesChemical species

Chemical species are atoms, molecules, molecular fragments, ions, etc., being subjected to a chemical process or to a measurement. Generally, a chemical species can be defined as an ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a...

or substance absorbs or scatters

Scattering

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

light at a given wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

, per unit mass. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation

Electromagnetic radiation

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

(such as X-ray

X-ray

X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s), sound

Sound

Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

, or any other beam that attenuates.

The mass attenuation coefficient is also called

**mass absorption coefficient**or**mass extinction coefficient**. Although all three terms are usually used interchangeably, they can occasionally have a subtle distinction, as explained below.The mass extinction coefficient should not be confused with the

*different*definition of "extinction coefficient" used more commonly in physics, namely the imaginary part of the complex index of refraction (which is unitless). In fact, they have a straightforward but nontrivial relationship; see Mathematical descriptions of opacityMathematical descriptions of opacity

When an electromagnetic wave travels through a medium in which it gets absorbed , 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 absorbed...

.

## Defining equations

The defining equation for the mass attenuation coefficient is essentially a different way to write the Beer-Lambert lawBeer-Lambert law

In optics, the Beer–Lambert law, also known as Beer's law or the Lambert–Beer law or the Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is travelling.-Equations:The law states that there is a logarithmic dependence between the...

. The Beer-Lambert law is normally written

where

*I*_{0}is the original intensity of the beam,*I*is the intensity of the beam at distance into the substance,*e*is Euler's numberE (mathematical constant)The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...

, about 2.718, is the attenuation coefficientAttenuation coefficientThe attenuation coefficient is a quantity that characterizes how easily a material or medium 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" as it passes through the medium, and a small...

.

When discussing the mass attenuation coefficient, this equation is rewritten

where is the density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, is the mass attenuation coefficient and is the area density known also as mass thickness.

In accordance with the above, the mass attenuation coefficient is equal to the attenuation coefficient divided by the density.

### In solutions

In chemistry, mass attenuation coefficients are often used for a chemical speciesChemical species

Chemical species are atoms, molecules, molecular fragments, ions, etc., being subjected to a chemical process or to a measurement. Generally, a chemical species can be defined as an ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a...

dissolved in a solution

Solution

In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...

. 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 coefficientAttenuation coefficient

The attenuation coefficient is a quantity that characterizes how easily a material or medium 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" as it passes through the medium, and a small...

is computed by

where each term in the sum is the mass attenuation coefficient and density of a different component of the solution (the solvent

Solvent

A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...

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

Molar absorptivity

The molar absorption coefficient, molar extinction coefficient, or molar absorptivity, is a measurement of how strongly a chemical species absorbs light at a given wavelength...

. They are quantitatively related by:×(Molar mass

Molar mass

Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

) = (Molar absorptivity).

### Units

The attenuation coefficientAttenuation coefficient

The attenuation coefficient is a quantity that characterizes how easily a material or medium 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" as it passes through the medium, and a small...

has units of inverse-length, while density has units of mass per volume. Since the mass attenuation coefficient is the ratio of these two, we find that it has units of (length-squared) per mass. The SI unit is m

^{2}kg^{-1}. Other common units include cm^{2}g^{-1}(the most common unit for X-ray mass attenuation coefficients) and mL×g^{-1}cm^{-1}(sometimes used in solution chemistry).## Mass attenuation coefficients for X-rays

Tables of photonPhoton

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...

**mass attenuation coefficients**are essential in radiological physics, radiographyRadiography

Radiography is the use of X-rays to view a non-uniformly composed material such as the human body. By using the physical properties of the ray an image can be developed which displays areas of different density and composition....

(for medical and security purposes), dosimetry

Dosimetry

Radiation dosimetry is the measurement and calculation of the absorbed dose in matter and tissue resulting from the exposure to indirect and direct ionizing radiation...

, diffraction

Diffraction

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

, interferometry

Interferometry

Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...

, crystallography

Crystallography

Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

and other branches of physics. The photons can be in form of x-ray

X-ray

X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

, gamma-ray, and bremsstrahlung

Bremsstrahlung

Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

.

The values of mass attenuation coefficients are dependent upon the absorption

Absorption (electromagnetic radiation)

In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

and scattering

Scattering

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

of the incident

Incident

Incident may refer to:* A property of a graph *Incident , a cultural festival of The National Institute of Technology in Surathkal, Karnataka, India...

radiation caused by several different mechanisms such as:

- Rayleigh ScatteringRayleigh scatteringRayleigh scattering, named after the British physicist Lord Rayleigh, is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. The particles may be individual atoms or molecules. It can occur when light travels through...

(coherent scattering) - Compton ScatteringCompton scatteringIn physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...

(incoherent scattering) - Photoelectric AbsorptionPhotoelectric effectIn the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...
- Pair ProductionPair productionPair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...

- electron-positron production in the fields of the nucleus and atomic electrons

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

National Institute of Standards and Technology

The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

(NIST):

- XAAMDI database
- XCOM database
- FFAST database

## 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 formulathe spectrum can be fitted using as adjustable parameters. (Remember, and each 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 equationsSimultaneous equations

In mathematics, simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations...

, although using more wavelengths gives more reliable data.

## Attenuation versus absorption

The terms "mass attenuation coefficient", "mass absorption coefficient", and "mass extinction coefficient" are almost always used interchangeably. However, in certain situations they are distinguished, as follows.When a narrow (collimated) beam of light passes through a substance, the beam will lose intensity due to two processes: The light can be absorbed by the substance, or the light can be scattered

Scattering

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

(i.e., the 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 can change direction) by the substance. Just looking at the narrow beam itself, the two processes cannot be distinguished. However, if you set up a detector to measure light leaving in different directions, or conversely try using a non-narrow beam, you can measure how much of the lost intensity was scattered, and how much was absorbed.

In this context, the "mass absorption coefficient" measures how quickly the beam would lose intensity due to the absorption

*alone*, while "mass attenuation coeffient" measures the*total*loss of narrow-beam intensity, including scattering as well. The "mass extinction coefficient" can be either.## See also

- Scattering theoryScattering theoryIn mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Prosaically, 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...
- Mean Free PathMean free pathIn physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
- Scattering cross-sectionScattering cross-sectionThe scattering cross-section, σscat, is a hypothetical area which describes the likelihood of light being scattered by a particle. In general, the scattering cross-section is different from the geometrical cross-section of a particle, and it depends upon the wavelength of light and the...
- Absorption cross sectionAbsorption cross sectionAbsorption cross section is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc...
- Absorption coefficient
- Beer-Lambert lawBeer-Lambert lawIn optics, the Beer–Lambert law, also known as Beer's law or the Lambert–Beer law or the Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is travelling.-Equations:The law states that there is a logarithmic dependence between the...
- Compton edgeCompton edgeIn spectrophotometry, the Compton edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. When a gamma-ray scatters off the scintillator but escapes, only a fraction of its energy is registered by the detector. This leads to a spectrum of...
- Compton scatteringCompton scatteringIn physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...
- Propagation constantPropagation constantThe propagation constant of an electromagnetic wave is a measure of the change undergone by the amplitude of the wave as it propagates in a given direction. The quantity being measured can be the voltage or current in a circuit or a field vector such as electric field strength or flux density...
- TransmittanceTransmittanceIn optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample. A related term is absorptance, or absorption factor, which is the fraction of radiation absorbed by a sample at a specified wavelength...
- AttenuationAttenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
- Attenuation lengthAttenuation lengthIn physics, the attenuation length or absorption length is the distance \lambda into a material when the probability has dropped to 1/e that a particle has not been absorbed...
- Radiation lengthRadiation lengthIn physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic-interacting particles with it.-Definition:High-energy electrons predominantly lose energy in matter...
- High energy X-raysHigh energy X-raysHigh energy X-rays or HEX-rays are very hard X-rays, with typical energies of 80 keV - 1000 keV , about one order of magnitude higher than conventional X-rays . They are produced at modern synchrotron radiation sources such as the beamline ID15 at the European Synchrotron Radiation Facility...
- Cargo ScanningCargo scanningCargo scanning or non-intrusive inspection refers to non-destructive methods of inspecting and identifying goods in transportation systems. It is often used for scanning of intermodal freight shipping containers...