Answer:
Based on the given question, the dimensions of the plate is 15 cm in length, 12.5 cm in width, and 3.50 mm in thickness (0.350 cm). Now the volume of the plate will be,
V = 15 cm × 12.5 cm × 0.350 cm = 65.62 cm³
A hole of diameter 2.50 cm is drilled through the center of the plate, at the height of 3.50 mm or 0.350 cm. Now the volume of the hole is π(r)²h,
= 22/7 × (1.25 cm)² × 0.350 cm = 1.72 cm³
Thus, the volume of the plate will be determined by subtracting the volume of plate with the volume of hole, which will be,
65.62 cm³ - 1.72 cm³ = 63.9 cm³
The density of the alloy is 8.80 g/cm³, therefore, the mass of the alloy can be determined by using the formula, mass = density * volume
mass = 8.80 g/cm³ × 63.9 cm³ = 562.32 grams
Of the total alloy, 0.090 percent is Si, that is,
(0.090/100) × 562.32 g = 0.506 grams of Si
The natural abundance of the element is not determined by mass but by the number of atoms it possess. For this Avogadro's number and atomic mass of Si is used. Now the number of atoms of Si present is,
(0.506 g) (1 mol/28.0855 g) (6.023 × 10²³ atoms /mol) = 1.08 × 10²² Si atoms
Of these Si atoms, 3.10 percent are Si-30 so,
= (3.10 / 100) × (1.08 × 10²² atoms) / 1000 = 3.34 × 10²⁰ atoms of Si-30. or 3.4 × 10²⁰ atoms
