The coordination number of an atom in a body-centered cubic structure is _______.
[Assume that the lattice is made up of atoms.]

Solution

Chemistry ma’am · 4 steps

Look at the atom in the body centre: it touches all 8 corner atoms and nothing closer.

1. Pick an atom. Coordination number is the number of nearest neighbours touching an atom. Take the atom at the body centre of the cube, because its neighbours are easy to count.
2. Count neighbours. In bcc, atoms touch along the body diagonal, not along the edge. So the body-centre atom touches all 8 corner atoms, each at a distance √3/2a.
3. Check the next shell. The next-closest atoms are the body centres of the 6 neighbouring cubes, at distance a. Since a > √3/2a ≈ 0.866a, they do not touch and are not counted.
4. So. Every atom in bcc is equivalent, so each has a coordination number of 8.

The common slip: 14. Counting the next-nearest atoms as well, 8 at √3/2a plus 6 at a, gives 14, not 8. Only the atoms that actually touch count.

The idea to keep. Remember the set: simple cubic 6, bcc 8, fcc 12. In bcc, atoms touch along the body diagonal, so the body-centre atom touches the 8 corners.

Answer from the NTA final answer key. Solution by PrepWiser.