Silicon crystallises in fcc lattice, a single crystal of high purity like diamond. Gram atomic weight of silicon is 28 g `mol^(-1)`. Edge length of unit cell is 0.543nm. Calculate the number of silicon atoms per unit cell and density of unit cell.

Explanation

To solve the problem of calculating the number of silicon atoms per unit cell and the density of the unit cell for silicon crystallizing in a face-centered cubic (FCC) lattice, we will follow these steps:

### Step 1: Determine the number of atoms per unit cell in FCC
In a face-centered cubic (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.

The total number of atoms \( z \) in the unit cell can be calculated as follows:
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