Final answer:
In a face-centered cubic (FCC) lattice with a cell edge of 200 pm and a density of 5 g/cm³, 200 g of the element contains 2 × 10²´ atoms.
Step-by-step explanation:
To determine how many atoms are contained in 200 g of an element that crystallizes into an fcc lattice with a cell edge of 200 pm and a density of 5 g/cm³, we use the properties of a face-centered cubic (FCC) unit cell.
In an FCC lattice, each unit cell contains 4 atoms. We can find the volume of the unit cell by cubing the edge length (in centimeters). So, the volume is (200 × 10⁻¹² cm)³ = 8 × 10⁻²³ cm³/unit cell. Then, we calculate the mass of one unit cell by multiplying this volume by the density: mass = volume × density = 8 × 10⁻²³ cm³/unit cell × 5 g/cm³ = 4 × 10⁻²± g/unit cell.
The number of unit cells in 200 g of the element is total mass / mass of one unit cell = 200 g / (4 × 10⁻²± g/unit cell), which gives 5 × 10²² unit cells. Finally, to find the total number of atoms, we multiply the number of unit cells by the number of atoms per unit cell: 5 × 10²² unit cells × 4 atoms/unit cell = 2 × 10²´ atoms.