Themass attenuation coefficient, ormass narrow beam attenuation coefficient of a material is theattenuation coefficient normalized by the density of the material; that is, the attenuation per unit mass (rather than per unit of distance). Thus, it characterizes how easily a mass of material can be penetrated by a beam oflight,sound,particles, or otherenergy ormatter.^[1] In addition to visible light, mass attenuation coefficients can be defined for otherelectromagnetic radiation (such asX-rays),sound, or any other beam that can be attenuated. TheSI unit of mass attenuation coefficient is the square metre perkilogram (m²/kg). Other common units include cm²/g (the most common unit for X-ray mass attenuation coefficients) and L⋅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 ofabsorption cross section where the effective area is defined per unit mass instead of per particle.

Mass attenuation coefficient is defined as

${\displaystyle \frac{\mu }{{\rho }_m},}$

where

• μ is theattenuation coefficient (linear attenuation coefficient);
• ρ_m is themass density.

When using the mass attenuation coefficient, theBeer–Lambert law is written in alternative form as

${\displaystyle I=I_0{e}^{-(\mu /{\rho }_m)\lambda }}$

where

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

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

Mass absorption coefficient, andmass scattering coefficient are defined as

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

where

• μ_a is the absorption coefficient;
• μ_s is the scattering coefficient.

In chemistry, mass attenuation coefficients are often used for achemical species dissolved in asolution. 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. Theactualattenuation coefficient is computed by

${\displaystyle \mu =(\mu /\rho {)}_1{\rho }_1+(\mu /\rho {)}_2{\rho }_2+\dots ,}$

where each term in the sum is the mass attenuation coefficient and density of a different component of the solution (thesolvent 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 ascertain assumptions are fulfilled).

A closely related concept ismolar absorptivity. They are quantitatively related by

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

Tables ofphotonmass attenuation coefficients are essential inradiological physics,radiography (for medical and security purposes),dosimetry,diffraction,interferometry,crystallography, and other branches of physics. The photons can be in form ofX-rays,gamma rays, andbremsstrahlung.

The values of mass attenuation coefficients, based on proper values ofphoton cross section, are dependent upon theabsorption andscattering of theincident radiation caused by several different mechanisms such as

• Rayleigh scattering (coherent scattering);
• Compton scattering (incoherent scattering);
• photoelectric absorption;
• pair production, 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 byNational Institute of Standards and Technology (NIST):

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

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

${\displaystyle \mu =(\mu /\rho {)}_1{\rho }_1+(\mu /\rho {)}_2{\rho }_2+\dots ,}$

the spectrum can be fitted usingρ₁,ρ₂, … as adjustable parameters, sinceμ and eachμ/ρ_i are functions of wavelength. If there areN solutes or solvents, this procedure requiresat leastN measured wavelengths to create a solvable system ofsimultaneous equations, although using more wavelengths gives more reliable data.

• Absorption coefficient
• Absorption cross section
• Attenuation length
• Attenuation
• Beer–Lambert law
• Cargo scanning
• Compton edge
• Compton scattering
• Cross section
• High-energy X-rays
• Mean free path
• Molar attenuation coefficient
• Propagation constant
• Radiation length
• Scattering theory
• Transmittance

• Physical quantities
• Radiometry
• Mass-specific quantities

• Articles with short description
• Short description is different from Wikidata