Two radioactive materials X1 and X2 have decay constants 8λ and λ respectively. If initially they have the same number of nuclei, when will the ratio of the number of nuclei of X1 to that of X2 will be e-3.

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.