Gold crystallizes in a face-centered cubic lattice. How many unit cells are there in a gold sample whose mass is 1.50 grams? The atomic weight of gold is 196.97 g mol^-1.Hint: Use dimensional analysis and the number of atoms per unit cell.

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The correct answer is A.Explanation:The number of unit cells in a sample can be calculated using the following formula:Number of unit cells = (Mass of sample / Molar mass of gold) * (Number of atoms per unit cell / Volume of unit cell)The molar mass of gold is 196.97 g mol-1, and the number of atoms per unit cell in a face-centered cubic lattice is 4. The volume of a unit cell can be calculated using the following formula:Volume of unit cell = (a^3) / 4where a is the length of the side of the unit cell.The length of the side of the unit cell can be calculated using the following formula:a = 2rwhere r is the radius of the gold atom.The radius of the gold atom is 0.144 nm.Substituting these values into the formula for the number of unit cells, we get:Number of unit cells = (1.50 g / 196.97 g mol-1) * (4 / (2 * 0.144 nm)^3) = 1.15 × 10^21 unit cellsTherefore, the correct answer is A.

Gold Crystallizes in a Face-Centered Cubic Lattice