# What is Linear and Mass Attenuation Coefficient – X-rays – Definition

Linear and Mass Attenuation Coefficient – X-rays. The linear attenuation coefficient increases as the atomic number of the absorber increases. The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). Radiation Dosimetry

X-rays, also known as X-radiation, refers to electromagnetic radiation (no rest mass, no charge) of high energies. X-rays are high-energy photons with short wavelengths and thus very high frequency. The radiation frequency is key parameter of all photons, because it determines the energy of a photon. Photons are categorized according to the energies from low-energy radio waves and infrared radiation, through visible light, to high-energy X-rays and gamma rays.

Most X-rays have a wavelength ranging from 0.01 to 10 nanometers (3×1016 Hz to 3×1019 Hz), corresponding to energies in the range 100 eV to 100 keV. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays. The distinction between X-rays and gamma rays is not so simple and has changed in recent decades.  According to the currently valid definition, X-rays are emitted by electrons outside the nucleus, while gamma rays are emitted by the nucleus.

## Linear Attenuation Coefficient – X-rays

The attenuation of X-rays can be then described by the following equation.

I=I0.e-μx

, where I is intensity after attenuation,  Io is incident intensity,  μ is the linear attenuation coefficient (cm-1), and physical thickness of absorber (cm).

The materials listed in the table are air, water and a different elements from carbon (Z=6) through to lead (Z=82) and their linear attenuation coefficients are given for two X-ray energies. There are two main features of the linear attenuation coefficient:

• The linear attenuation coefficient increases as the atomic number of the absorber increases.
• The linear attenuation coefficient for all materials decreases with the energy of the X-rays.

## Mass Attenuation Coefficient

When characterizing an absorbing material, we can use sometimes the mass attenuation coefficient.  The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). The attenuation of X-rays can be then described by the following equation:

I=I0.e-(μ/ρ).ρl

, where ρ is the material density, (μ/ρ) is the mass attenuation coefficient and ρ.l is the mass thickness. The measurement unit used for the mass attenuation coefficient cm2g-1. For intermediate energies the Compton scattering dominates and different absorbers have approximately equal mass attenuation coefficients. This is due to the fact that cross section of Compton scattering is proportional to the Z (atomic number) and therefore the coefficient is proportional to the material density ρ. At small values of X-ray energy, where the coefficient is proportional to higher powers of the atomic number Z (for photoelectric effect σf ~ Z3), the attenuation coefficient μ is not a constant.

See also XCOM – photon cross-section DB: XCOM: Photon Cross Sections Database

## Example:

How much water schielding do you require, if you want to reduce the intensity of a 100 keV monoenergetic X-ray beam (narrow beam) to 1% of its incident intensity? The half value layer for 100 keV X-rays in water is 4.15 cm and the linear attenuation coefficient for 100 keV X-rays in water is 0.167 cm-1. The problem is quite simple and can be described by following equation:

If the half value layer for water is 4.15 cm, the linear attenuation coefficient is:Now we can use the exponential attenuation equation:

So the required thickness of water is about 27.58 cm.  This is relatively large thickness and it is caused by small atomic numbers of hydrogen and oxygen. If we calculate the same problem for lead (Pb), we obtain the thickness x=0.077 cm.

Linear Attenuation Coefficients

Table of Linear Attenuation Coefficients (in cm-1) for a different materials at photon energies of 100, 200 and 500 keV.

 Absorber 100 keV 200 keV 500 keV Air 0.000195/cm 0.000159/cm 0.000112/cm Water 0.167/cm 0.136/cm 0.097/cm Carbon 0.335/cm 0.274/cm 0.196/cm Aluminium 0.435/cm 0.324/cm 0.227/cm Iron 2.72/cm 1.09/cm 0.655/cm Copper 3.8/cm 1.309/cm 0.73/cm Lead 59.7/cm 10.15/cm 1.64/cm
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