You are required to determine the decay curves for radioactive decay of a set of heavy isotopes. The isotope, 234U decays into 230Th with a half-life of 246000 years. The isotope, 230Th decays into 226Rn with a half-life of 75380 years. The isotope, 226Rn decays with a half-life of 1600 years. You should construct a set of coupled linear differential equations that describes the time evolution of the system. Then use Laplace transformations to determine the functions that describe the time evolution of 234U, 230Th, and 226Rn. for some radioactive material that initially contains 2.0 mols of 234U and 0.010 mols of 230Th.
Use the method of Laplace transforms to determine the subsidiary equation for y```+y``-y`-y = 0 y(0) = 1 y`(0) = ?1 y??(0) = 1 You do not have to determine y(t), you only have to determine the subsidiary equation.