The rate of energy loss of protons traveling a material of density ρ typically follows a power law
dxdE=−ρK(E0E)−p
where the constants K and p are characteristic of the material and E0 is a reference calibration energy that we can take to be 1 MeV.
(a) Find an expression for the thickness of material that will reduce the energy of a proton by half the value it has upon entering the material.
(b) For Carbon, K=212 g-MeV/cm2, and p=0.757; for Lead, K=89.5 g-MeV/cm2, and p=0.694. How much thicker must a slab of Carbon be than a slab of Lead in order to reduce a proton of incident energy 150 MeV by half?