A carload of Hg-ore containing grains of cinnabar (86%Hg by mass; density = 8.19 g/cm3) and grains of basalt (containing no Hg; density=2.84 g/cm3) is to be sampled and analyzed for mercury. The average density of the bulk material is found to be 3.04g/cm3. To keep the relative sampling error below 0.5% it is determined that 1.44 106 particles are needed in the gross sample. Supposing the grains in the sample had an approximate spherical radius of 3.0 mm, then the gross sample should weigh about 4.95 105 g (roughly half a ton). This is an impracticably large amount for lab analysis. Therefore, the carload of ore is repeatedly crushed or ground, mixed and divided until the grains are of a sufficiently smaller radius such that only a 120-gram gross sample will be required in the lab to obtain the same level of sampling uncertainty. a) In the final ground and mixed sample, what should be the average particle mass? b) In the final ground and mixed sample, what should be the approximate particle radius