Calculate the packing fraction and density of diamond if a=3.57 Å. Diamond crystallizes in fcc lattice with some more carbon atoms in alternate tetrahedral voids.

Explanation

To calculate the packing fraction and density of diamond, we will follow these steps:

### Step 1: Determine the number of carbon atoms in the unit cell
Diamond crystallizes in a face-centered cubic (FCC) lattice. In an FCC lattice, there are 4 carbon atoms per unit cell. Additionally, diamond has carbon atoms occupying alternate tetrahedral voids, which adds another 4 carbon atoms.

**Total number of carbon atoms in the unit cell:**
\[
\text{Total atoms} = 4 \text{ (from FCC)} + 4 \text{ (from tetrahedral voids)} = 8 \text{ atoms}
...