Question

An element crystallises separately both in hcp and ccp structures. Will the two structures have the same density? If yes, why?

Answer 1

Yes, the two structures will have the same density.

Reason:

1. The percentage of the occupied volume in the two types of structures is the same (i.e., 74%), and both structures have the same coordination number of 12.
2. Both hcp (hexagonal close packing) and ccp (cubic close packing) have the same packing efficiency, which is 74%.
3. This means that in both structures, 74% of the available volume is occupied by the atoms and 26% is empty space.
4. The number of atoms per unit cell is also the same (6 atoms per unit cell in hcp and 4 atoms per unit cell in ccp), but the unit cell volumes are different, maintaining the same overall packing efficiency.
5. Since density depends on packing efficiency and atomic mass, which are the same in both cases, the densities will be identical.