Question

What is the number of atoms in an end centered unit cell?
A. $2$
B. $4$
C. $1$
D. $6$

Answer 1

In End centered cubic unit cells, atoms are present at $8$ corner cube with atoms present at two opposite faces of the cube. Each corner atom contributes its $\dfrac{1}{8}th$ part to the unit cell and each atom present at face contributes $\dfrac{1}{2}th$ part of it to the unit cell.

Complete step-by-step answer:
The unit cell is defined as the smallest unit of the crystal structure which has been repeated again and again. Types of unit cells depend on the position of atoms present in crystal structure. In the end centered cubic unit cell, atoms are present or can say they are located at the corners of the cube and also at the two opposite faces. The each atom at corner contribute $\dfrac{1}{8}th$ part of atom in the cube and the each atom of the opposite face contribute $\dfrac{1}{2}th$ part of it in the cube. As shown in given figure:
Self-made figure
Number of atoms present at corner= $8$
Each atom contribute $\dfrac{1}{8}th$ part so,
$8$ atom will contribute= $\dfrac{1}{8} \times 8$ atom
= $1$ atom
Number of atom present in the faces= $2$
Each atom contribute $\dfrac{1}{2}th$ part so,
2 atom will contribute= $\dfrac{1}{2} \times 2$ atom
$1$ atom
Total number of atoms= $1 + 1$ atoms
= $2$ atoms
Hence, in the end centered cubic unit cell there are total $2$ atoms.

So, option A is correct.

Note: There are a few crystal structures, called the perovskite structure, they show ferroelectric behavior. This is similar to ferromagnetism, in that, in the absence of an electric field during production, the ferroelectric crystal does not show polarization. On the application of an electric field of sufficient magnitude, the crystal will get changed into permanently polarized. By a sufficiently large counter-charge the polarization can be reversed, in the same way a ferromagnet can be reversed. They are called ferroelectrics, the effect is due to the crystal structure.