**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 (3×10^{16} Hz to 3×10^{19} 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=I _{0}.e^{-μx}**

, where I is intensity after attenuation, I_{o} 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=I _{0}.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 cm^{2}g^{-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 σ_{f} ~ Z^{3}), the attenuation coefficient μ is not a constant.

See also calculator: Gamma activity to dose rate (with/without shield)

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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