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Half-Value Layer Calculation

The thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL).  The HVL is inversely proportional to the attenuation coefficient (m) and the two values are related by the following equation.  Since m is normally given in units of cm-1, the HVL is commonly expressed in units of cm. 

This relationship comes from the intensity attenuation equation. 

It can be seen that if an incident energy of 1 and a transmitted energy is 0.5 (1/2 the incident energy) is plugged into the equation, the thickness (x) multiplied by m must equal 0.693 (since the number 0.693 is the exponent value that give a value of 0.5). X in this case is the half-value layer.

Example Calculation
What is the HVL for a material with a attenuation coefficient of 0.4/cm?