Question

The empty space in hcp and ccp is about:
A.$26\% $
B.$30\% $
C.$35\% $
D.$40\% $

Answer 1

Hint: Unit of crystal: It is defined as the repeating unit in the crystal. They are of three types: (I) primitive cubic unit cell, (II) Body-centered cubic unit cell (III) Face-centered cubic unit cell.

Complete step by step answer:
Primitive cubic unit cell: In this unit cell, atoms are present only at the corners of the cube. We know that there are eight corners in a cube. So one atom is shared by right corners. So the contribution of an atom in one corner is $\dfrac{1}{8}$. The number of atoms present in a primitive cubic unit cell is one.
Body-centered cubic unit cell: In this unit cell, atoms are present at the centre and corners of the cube. We know that there is only one centre in a cube. So one atom is completely present there. And one atom is contributing to the eight corners. So the total number of atoms present in a Body-centered cubic unit cell is $2$.
Face-centered cubic unit cell: In this unit cell, atoms are present at corners and at the face centres of the cube. There are a total six faces in a cube. So one atom contributes to two face centres i.e. one atom is half. And one atom contributing to all eight corners of the cube. So there are four atoms present in the face-centered cubic unit cell.
HCP unit cells have eight atoms per unit cell and in a CCP unit cell there are four atoms per unit cell.
In hexagonal closed packed molecules (HCP) packing efficiency is $74\% $ so its empty space is $26\% $. And in the CCP also packing efficiency is $74\% $ so its empty space is $26\% $.

So option A is correct.

Note:
Packing efficiency: It is defined as the percentage of space occupied by constituent particles packed in the lattice. Empty space is defined as the empty space between the particles in the lattice and empty space is equal to $100 - $ packing efficiency.