The following table shows the recommended thickness of lead shielding in function of X-ray energy, from the Recommendations by the Second International Congress of Radiology
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Lead is the most common shield against X-rays because of its high density (11340 kg/m3), stopping power, ease of installation and low cost. The maximum range of a high-energy photon such as an X-ray in matter is infinite; at every point in the matter traversed by the photon, there is a probability of interaction. Thus there is a very small probability of no interaction over very large distances. The shielding of photon beam is therefore exponential (with an attenuation length being close to the radiation length of the material); doubling the thickness of shielding will square the shielding effect.
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