Question: What is the number of atoms in an end centered unit cell? a.) 2 b.) 4 c.) 1 d.) 6...

Question

What is the number of atoms in an end centered unit cell?
a.) 2
b.) 4
c.) 1
d.) 6

Answer 1

Solution

Hint: End centered unit cell is present in the crystal lattice. We can analyse the number of atoms by the position of constituent particles. In the end centered, look into the 8 corners and 2 opposite faces of a cube.

Complete step by step answer:
Firstly, let us know about the unit cell. We know crystal lattice is made up of numerous unit cells.
Now, the number of atoms, ions, or molecules in a unit cell can be easily known by the nature and position of constituent particles.
We can see that there are various types of unit cell i.e. primitive cubic, body-centred cubic, face-centred cubic, and end-centred cubic unit cell.
Talking about the end-centred cubic unit cell, 8 atoms are placed on the 8 corners of the cube and 1 atom each is placed on two opposite faces of the cube.
Thus, we can say that, if 8 atoms are present on 8 corners, then each atom will contribute $\dfrac{1}{8}$ $^{th}$ portion.
So, 8 $\times$ $\dfrac{1}{8}$ =1 atom
Now, if 2 atoms located at the opposite faces, each contributes $\dfrac{1}{2}$ $^{th}$ portion
So, 2 $\times$ $\dfrac{1}{2}$ =1 atom.
Therefore, the total number of atoms is 2. The correct option is A.

Note: Don’t get confused between the types of unit cells. In the end-centred unit cell just relate the term to the corners and opposite faces of the cube, or we can say the atoms present at the centre in the cell.