Final answer:
To calculate the number of atoms in a cubic crystal's unit cell, you must use the unit cell's density, atomic weight, and volume combined with Avogadro's number to determine whether it's a body-centered or face-centered cubic lattice, leading to 2 or 4 atoms respectively.
Step-by-step explanation:
To calculate the number of atoms in a unit cell of a cubic crystal with an edge length of 3.65 Å, we must first identify the type of cubic unit cell. The density of the material is given as 7.87 g/cm³, and the atomic weight is 55.85 g/mol. Given this information, we will use these values along with Avogadro's number (6.022×10³³ atoms/mol) to find the number of atoms per unit cell.
To perform this calculation, we can use the formula:
Density = (Mass of atoms in a unit cell / Volume of the unit cell)
Since the volume of the unit cell is the cube of its edge length, the volume of the unit cell is (3.65×10⁻¸ cm)³. We can convert the volume to cubic centimeters by multiplying by (1×10²¸³) to get the volume in cm³. Next, we calculate the mass of atoms in the unit cell by multiplying the density by the volume of the unit cell.
Finally, we divide the mass of atoms per unit cell by the atomic weight and then by Avogadro's number to get the number of atoms per unit cell. For cubic crystals such as body-centered cubic (BCC) and face-centered cubic (FCC), there are respectively 2 and 4 atoms per unit cell.