For a narrow beam of mono-energetic photons, the change in x-ray beam intensity at some distance in a material can be expressed in the form of an equation as:

Where:	dI	=	the change in intensity
	I	=	the initial intensity
	n	=	the number of atoms/cm3
	s	=	a proportionality constant that reflects the total probability of a photon being scattered or absorbed
	dx	=	the incremental thickness of material traversed

When this equation is integrated, it becomes:

The number of atoms/cm³ (n) and the proportionality constant (s) are usually combined to yield the linear attenuation coefficient (m). Therefore the equation becomes:

The Linear Attenuation Coefficient (m)
The linear attenuation coefficient (m) describes the fraction of a beam of x-rays or gamma rays that is absorbed or scattered per unit thickness of the absorber. This value basically accounts for the number of atoms in a cubic cm volume of material and the probability of a photon being scattered or absorbed from the nucleus or an electron of one of these atoms. The linear attenuation coefficients for a variety of materials and x-ray energies are available in various reference books.

Using the transmitted intensity equation above, linear attenuation coefficients can be used to make a number of calculations. These include:

• the intensity of the energy transmitted through a material when the incident x-ray intensity, the material and the material thickness are known.
• the intensity of the incident x-ray energy when the transmitted x-ray intensity, material, and material thickness are known.
• the thickness of the material when the incident and transmitted intensity, and the material are known.
• the material can be determined from the value of m when the incident and transmitted intensity, and the material thickness are known.