3) Consider the following materials and their Half Value Layer (HVL): Material HVL (cm) at 10 keV HVL (cm) at 100 keV Al 9.79 x 10-3 1.51 Cu 3.58 x 10-4 0.169 (a) For each material, find the linear attenuation coefficient at each energy level. (2 marks) (b) What thickness of each material can be used to filter a 100 keV monoenergetic photon beam such that 5% of the photons are absorbed by the filter? What percentage of the photons in a 10 keV monoenergetic beam are absorbed by the filter for the calculated thicknesses? Assume a narrow beam geometry. (4 marks) (c) Copper has a K-edge at 9 keV. Discuss the complications of using Cu as a filter for polyenergetic beams and propose a solution. (2 marks) (d) Most materials have larger attenuation coefficients at lower X-ray energies. What phenomenon, concerning polyenergetic beams, occurs due to this property? Describe this phenomenon. (2 marks)