When gamma rays are incident on matter, the intensity of the gamma rays passing through the material varies with depth x as I(x) = Ioe^(-ux) , where Io is the intensity of the radiation at the surface of the material (at x = 0) and u is the linear absorption coefficient. For 0.400 MeV gamma rays in lead, the linear absorption coefficient is 1.59cm^-1 .
(a) Determine the "half-thickness" for lead, that is, the thickness of lead that would absorb half the incident gamma rays.
(b) What thickness reduces the radiation by a factor of 10^4?