Re: x-ray absorbtion equations for wavelength vs. material density

Theoretically, it is not possible to stop X or gamma rays completely by 
any thickness. Photons in X ray or Gamma rays region have infinite range. 
The interaction processes are always stochastic and hence, they can travel 
without interaction deep into the materials even with heavy density and 
thicknesses. The intensity of radiation reduces exponentionally as 
Intensity passed=(original intensity)*exp(-ux)
Here, u is stopping power and x is thickness of the material. u depends on 
many factors, prominently on density and atomic number of the elements in 
the material

However, the penetration capability increases with increase in energy or 
in other words, with increase in frequency or with decrease in wave 
length. The thickness required to stop X rays is always mentioned in half 
value or tenth value layers (HVL and TVL). Suppose, the material is two 
half value layers, the X ray intensity is reduced by a factor of four and 
if it is three layers, the intensity is reduced by a factor of eight 
(i.e., in the order of 2^n). The values of HVL and TVL for different 
materials and X ray energies can be obtained from ICRU publications.

As you rightly mentioned, a single photon can escape any limit of 
thickness. Theoretically, it requires infinite thickness to surely stop a 
X ray photon.