Silver has a face-centered cubic (FCC) unit cell structure, which is essential for understanding its atomic arrangement. In an FCC unit cell, there are a total of 4 atoms per unit cell, derived from the contributions of atoms located at the corners and the faces of the cube.
To calculate the number of atoms, consider the 8 corners of the cube. Each corner atom is shared among 8 adjacent unit cells, contributing only \(\frac{1}{8}\) of an atom to the unit cell. Therefore, the total contribution from the corners is:
\[\text{Corner contribution} = 8 \times \frac{1}{8} = 1 \text{ atom}\]
Next, examine the 6 faces of the cube. Each face contains half of an atom, as it is shared with an adjacent unit cell. Thus, the total contribution from the faces is:
\[\text{Face contribution} = 6 \times \frac{1}{2} = 3 \text{ atoms}\]
By adding the contributions from both the corners and the faces, we find the total number of atoms in the FCC unit cell:
\[\text{Total atoms per unit cell} = 1 + 3 = 4 \text{ atoms}\]
This calculation illustrates that the ratio of atoms to unit cell in a face-centered cubic structure is 4 to 1, highlighting the efficient packing and arrangement of atoms in silver's crystalline structure.