An element crystallizes in a face-centered cubic lattice and has a density of 3.16 g/cm³. The edge of its unit cell is 7.49 x 10^-8 cm. How many atoms are in each unit cell?

• A. 4 atoms
• B. 2 atoms
• C. 1 atom
• D. 3 atoms

Answer: (A)

Verified step by step guidance

1. Understand that a face-centered cubic (FCC) lattice has atoms at each of the corners and at the center of each face of the cube.
2. In an FCC lattice, there are 8 corner atoms, each shared by 8 unit cells, and 6 face atoms, each shared by 2 unit cells.
3. Calculate the total number of atoms per unit cell: \( \text{Number of corner atoms} = \frac{8}{8} = 1 \) and \( \text{Number of face atoms} = \frac{6}{2} = 3 \).
4. Add the contributions from corner and face atoms to find the total number of atoms in the unit cell: \( 1 + 3 = 4 \) atoms.
5. Verify the calculation by considering the density and edge length, but the structure of the FCC lattice already confirms the number of atoms as 4.