Final answer:
To calculate the density of copper in a face-centered cubic unit cell, we can use the formulas for volume and density. By plugging in the given values and atomic mass, we can find that the density of copper is 0.344 g/cm³.
Step-by-step explanation:
To calculate the density of copper, we need to first find its atomic mass. Copper has an atomic mass of 63.546 g/mol. Next, we need to determine the volume of the unit cell. For face-centered cubic structures, the volume of one unit cell can be calculated using the formula V = (4 √2)a³/3, where a is the edge length of the unit cell. Plugging in the given value of a = 361.49 pm = 3.6149 Å, we can calculate the volume of the unit cell.
V = (4 √2)(3.6149 Å)³/3 = 184.31 ų
Finally, we can calculate the density using the formula density = mass/volume. Since there is one copper atom per unit cell and the atomic mass of copper is 63.546 g/mol, the mass of one unit cell of copper is 63.546 g. Plugging in the values, we can calculate the density.
density = 63.546 g / 184.31 ų = 0.344 g/cm³