Question

The number of atoms per unit cell of a bcc lattice is :
(A) 4
(B) 2
(C) 1
(D) 8

Answer 1

Hint: A bcc unit cell is one which has atoms present at the corners and at the body centre. The total number of atoms per unit cell of bcc lattice is double of that present in the simple cubic lattice and it is half of that present in face-centred lattice.

Complete step by step answer:
First, let us understand what a bcc lattice is.
The bcc stands for the body-centred cubic lattice. It is the cubic lattice in which all the corners of the cube are covered with atoms and one atom is present at the centre of the cube.
We have to calculate the number of atoms per unit cell of bcc lattice.
We know that a cube has eight corners.
One atom at the corner is shared with eight other cubes. So, each atom is shared with eight other cubes.
Thus, the contribution of one corner atom to the one unit cell is = $\dfrac{1}{8}$
As there are eight corners.
So, all the eight atoms at the corners will contribute = $\dfrac{1}{8} \times 8$
The contribution from corner atoms = 1
Further, one atom is present in the body centre. This atom is not shared by any other unit cell. So, its contribution will be 100 % in the unit cell.
So, the contribution by centre atom = 1
So, the total number of atoms in bcc unit cell = contribution of all the atoms of corners + contribution of body centre atom
total number of atoms in bcc unit cell = 1 + 1
total number of atoms in bcc unit cell = 2

Thus, option (B) is the correct answer.

Note: It must be noted that a bcc unit cell has only one atom at the centre of the cube in addition to atoms at the corners. No atom at the face centre or at any diagonal is present. There are tetrahedral and octahedral holes present in the unit cell which are called tetrahedral voids and octahedral voids.