Calculate the number of atoms present in the unit cell of a monoatomic element of (i) simple cubic (ii) body-centered cubic and (iii) face-centered cubic lattices.

Explanation

To calculate the number of atoms present in the unit cell of a monoatomic element for different types of cubic lattices, we will analyze each structure step by step.

### (i) Simple Cubic Lattice

1. **Identify the positions of atoms**: In a simple cubic lattice, atoms are located at the corners of the cube.
2. **Count the corner atoms**: There are 8 corners in a cube.
3. **Calculate the contribution of corner atoms**: Each corner atom is shared by 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
4. **Total contribution from corner atoms**:
...