As a solid, Ag adopts a face-centered cubic unit cell. How many unit cells are present per cubic centimeter of Ag?
To find the number of unit cells present per cubic centimeter of Ag, we need to consider the arrangement of the unit cells in the face-centered cubic (FCC) structure.
In an FCC structure, there are eight corner atoms and six face-centered atoms per unit cell. The formula for the number of unit cells per cubic centimeter is:
Number of unit cells per cubic centimeter = (Number of atoms per unit cell) x (Avogadro's number) x (Density of Ag)
First, we need to determine the number of atoms per unit cell in an FCC structure. Considering the eight corner atoms, each atom is shared by eight adjacent unit cells. Therefore, the contribution of corner atoms to a single unit cell is 1/8 for each atom, resulting in a total of 8 * (1/8) = 1 atom.
Next, we consider the six face-centered atoms. Each face-centered atom is shared by two adjacent unit cells. Therefore, the contribution of face-centered atoms to a single unit cell is 1/2 for each atom, giving a total of 6 * (1/2) = 3 atoms.
Hence, the total number of atoms per unit cell in an FCC structure is 1 (corner atom) + 3 (face-centered atoms) = 4 atoms.
Now, we know that the density of Ag is approximately 10.49 g/cm³, and Avogadro's number is approximately 6.022 x 10²³ unit cells/mol.
Substituting the values into the formula:
Number of unit cells per cubic centimeter = (4 atoms) x (6.022 x 10²³ unit cells/mol) x (10.49 g/cm³)
Simplifying the expression gives the final answer.
mass unit cell = 107.868 x 4/6.022E23 = ?
density you must look up.
volume = mass/density. Solve for volume.
volume/unit cell x #unit cells = 1 cc.
Solve for #unit cells.