Question

The number of constituent particles in a bcc lattice is:
A. 9
B. 8
C. 12
D. 16

Answer 1

Hint: From bcc i.e. body centred cubic (bcc) it means that there is one atom is at the centre of lattice and rest are at the corners.

Complete step-by-step answer:
A crystal lattice is made of a very large number of unit cells and lattice points are the representation of constituent particles. In primitive unit cells, atoms are present at corners only. In a crystal lattice every corner is shared by eight adjacent unit cells. Therefore only 1/8 of an atom, or other constituent particles, belongs to a particular unit cell. There are 8 atoms present in a primitive cubic unit cell on every corner, therefore the total number of atoms in the unit cubic cell = \[8\times \dfrac{1}{8}\] = 1. Now, in bcc (body centred cubic) one atom is present at the centre of the cell and eight atoms are present at each corner.
So, total atoms in a bcc unit cell = 8 corners x \[\dfrac{1}{8}\]atoms per corner + 1centre x 1 atom per unit cell
                    = \[8\times \dfrac{1}{8}\] + 1
                    = 2 atoms
But in bcc lattice for constituent particles we count 1 particle at each corner not the 1/8th part.
So, number of constituent particles = 8 at corners + 1 at body centre
       = 8+1 = 9 particles
So, the correct answer is “A”.

Note: We should be careful that in this problem we have to calculate the number of constituent particles for the bcc lattice not for the bcc unit cell. If we get confused in both these things then the answer will change.