The seller of a mining claim took a random ore sample that weighed approximately 5 lb and had an average particle diameter of 5.0 mm. Inspection revealed that about 1% of the sample was argentite (see Problem), and the remainder had a density of about 2.6 g/cm3 and contained no silver. The prospective buyer insisted on knowing the silver content of the claim with a relative error no greater than 5%. Determine whether the seller provided a sufficiently large sample to permit such an evaluation. Give the details of your analysis.
Problem 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?
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