Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics

Question

Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics industry. A particular alloy with a density of 8.80 g/cm3 and containing 0.082% Si by mass is used to make a rectangular plate that is 15.0 cm long, 12.5 cm wide, and 3.50mm thick and has a 2.50-cm-diameter hole drilled through its center such that the height of the hole is 3.50mm .

The silicon in the plate is a mixture of naturally occurring isotopes. One of the those isotopes is silicon-30, which has an atomic mass of 29.97376 amu and a percent natural abundance of 3.10%.

What is the Volume of the Plate?

Explanation / Answer

density = mass / volume

volume = (15.0 cm) * (12.5 cm) * (0.45 cm) = 84.375 cm^3

8.80 grams/cm^3 = mass / 84.375 cm^3
mass = 742.5 grams alloy

mass of Si in alloy = (742.5 grams alloy) * (0.00041) = 0.304 grams Si

mass of Si-30 = (0.304 grams Si in metal) * (0.0310) = 0.009424 grams Si-30

atoms Si-30 = (0.009424 grams Si-30) * (1 mol Si-30 / 29.97376 grams Si-30) * (6.02*10^23 atoms Si-30 / 1 mol Si-30) = 1.893*10^20 atoms Si-30 is the answer

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