An element crystallises in fcc lattice with cell edge of 400 pm. Calculate its density if 250 g of this element contain `2.5 xx 10^(24)` atoms.

Explanation

To calculate the density of an element that crystallizes in a face-centered cubic (FCC) lattice, we will follow these steps:

### Step 1: Determine the number of atoms per unit cell
In a face-centered cubic (FCC) lattice, there are 4 atoms per unit cell. This can be calculated as follows:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell: \( 8 \times \frac{1}{8} = 1 \) atom.
- There are 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom to the unit cell: \( 6 \times \frac{1}{2} = 3 \) atoms.
- Total atoms per unit cell = \( 1 + 3 = 4 \) atoms.

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