(Solution) - Approximately 15 of the particles in a shipment of silver bearing -(2025 Original AI-Free Solution)

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Approximately 15% of the particles in a shipment of silver-bearing ore are judged to be argentite, Ag2S (d = 7.3 g cm-3, 87% Ag); the remainder are siliceous (d = 2.6 g cm-3) and contain essentially no silver.
(a) Calculate the number of particles that should be taken for the gross sample if the relative standard deviation due to sampling is to be 2% or less.
(b) Estimate the mass of the gross sample, assuming that the particles are spherical and have an average diameter of 3.5 mm.
(c) The sample taken for analysis is to weigh 0.500 g and contain the same number of particles as the gross sample. To what diameter must the particles be ground to satisfy these criteria?