Question -
Answer -
(i) simple cubic
(ii) body-centred cubic
(iii) face-centred cubic (with the assumptions that atoms aretouching each other).
Answer
(i) Simple cubic
In a simple cubic lattice, the particles arelocated only at the corners of the cube and touch each other along the edge.
Let the edge length of the cube be ‘a’and the radius of each particle be r.
So, we can write:
a = 2r
Now, volume of the cubic unit cell = a3
= (2r)3
= 8r3
Therefore, volume of the occupied unit cell 
Hence, packing efficiency 
(ii) Body-centredcubic
It can be observed from the above figurethat the atom at the centre is in contact with the other two atoms diagonallyarranged.
From ΔFED, we have:
Again, from ΔAFD, we have:
Let the radius of theatom be r.
Length of the bodydiagonal, c = 4π
or
Volume of the cube, 
A body-centred cubiclattice contains 2 atoms.
So, volume of the occupied cubic lattice 
(iii) Face-centredcubic
Let the edge length ofthe unit cell be ‘a’ and the length of the face diagonal AC be b.
From ΔABC, we have:
Let r bethe radius of the atom.
Now, from the figure, itcan be observed that:
Now, volume of the cube, 
We know that the numberof atoms per unit cell is 4.
So, volume of the occupied unit cell 
