Diamond has a face-centered cubic (FCC) lattice arrangement of carbon atoms, with additional carbon atoms occupying half of the tetrahedral voids. The number of carbon atoms from the FCC lattice points (corners and face centers) is $8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4$. There are 8 tetrahedral voids in an FCC unit cell, and since half of them are occupied by carbon atoms, there are $8 \times \frac{1}{2} = 4$ carbon atoms in the voids. Therefore, the total number of carbon atoms per unit cell of diamond is $4 + 4 = 8$.