Co-ordination Number in Different Unit Cells

Co-ordination number is the number of nearest neighbours of an atom in a crystal lattice. The co-ordination number depends on the type of unit cell in the crystal lattice.

The co-ordination number in different unit cells is given below:

- Simple Cubic (SC) Unit Cell: In an SC unit cell, each atom is in contact with 6 nearest neighbours arranged at the corners of a cube. Therefore, the co-ordination number of an SC unit cell is 6.
- Body-Centred Cubic (BCC) Unit Cell: In a BCC unit cell, each atom is in contact with 8 nearest neighbours. Six of these neighbours are arranged at the corners of the cubic unit cell, and the other two are located at the body-centre of the unit cell. Therefore, the co-ordination number of a BCC unit cell is 8.
- Face-Centred Cubic (FCC) Unit Cell: In an FCC unit cell, each atom is in contact with 12 nearest neighbours. Eight of these neighbours are located at the corners of the cubic unit cell, and the other four are located at the centre of the faces of the unit cell. Therefore, the co-ordination number of an FCC unit cell is 12.
- Hexagonal Close Packed (HCP) Unit Cell: In an HCP unit cell, each atom is in contact with 12 nearest neighbours. Six of these neighbours are located in the same plane as the atom, and the other six are located in the adjacent plane. Therefore, the co-ordination number of an HCP unit cell is 12.

Correct Order of Co-ordination Number

The correct order of co-ordination number in SC, BCC, FCC, and HCP unit cells is:

- SC unit cell: 6
- BCC unit cell: 8
- FCC unit cell: 12
- HCP unit cell: 12

Therefore, the correct answer is option B (6, 8, 12, 12).