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

Explanation

To solve the problem of calculating the packing fraction and density of diamond, we will follow these steps:

### Step 1: Determine the effective number of atoms in the unit cell (Z)
Diamond crystallizes in a face-centered cubic (FCC) lattice. In an FCC lattice:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell.
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom to the unit cell.

Calculating the total contribution:
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