Question

The percentages of void space for simple cubic, body centred cubic and hexagonal close packed arranged respectively are:
A. 48, 32, 26
B. 48, 26, 32
C. 26, 48, 32
D. 32, 48, 26

Answer 1

this question is asked from the chapter of solid states. Void space is the space which is left empty in a crystal while the packing fraction is how much the space of the crystals are occupied. By knowing these two concepts, we can solve this problem.

Complete step by step answer:
The crystal lattices are made up of a very large number of unit cells where constituent particles are occupied in every lattice point. The percentage of spaces occupied by the particles in the unit cell is known as the packing fraction of the unit cell. So, the empty spaces in a unit cell is known as the void space. We can find out the void space easily by subtracting the packing fraction from 100.
We know that packing fractions of a simple cubic unit cell is 52%. So, the void space is equal to (100-52) = 48%.
The packing fraction of body centred cubic unit cells is 68%. So, the void space in the body centred cubic unit cell will be (100-68) = 32%.
The packing fraction of hexagonal close packing is 74%. So, the void space in hexagonal close packing will be (100-74) = 26%.
Therefore, the percentage of void spaces for simple cubic, body centred and hexagonal close packing are 48%, 32% and 26% respectively.

So, the correct option will be A.

Note:
The packing fraction of a unit cell is determined by the ratio of volume occupied by constituent particles in the unit cell to the total volume of the unit cell.