Under one experimental condition, an element crystallises in face-centred cubic structure with a unit-cell edge length of `a_(1)`, while under another experimental condition, it crystallises in body-centred cubic structure with a unit-cell edge length of `a_(2)`. Find the ratio of the densities of these structures.

Explanation

If the density of an element forming cubical crystal is `rho`, then, `rho=(ZxxM)/(Nxxa^(3))`, where Z = number of particles per cubic unit cell, M = atomic weight of the element, N = Avogadro's number, a = edge length of the cubic unit cell.
In case of face-centred cubic (fcc) unit cell, Z = 4 and for a body-centred cubic (bcc) unit cell, Z = 2.
If the densities of fcc and bcc unit cells are `rho_(1)andrho_(2)` respectively, then `rho_(1)=(4xxM)/(Nxxa_(1)^(3))andrho_(2)=(2xxM)/(Nxxa_(2)^(3))`
Thus, `rho_(1)/rho_(2)=(4xxa_(2)^(3))/(2xxa_(1)^(3))=2(a_(2)/a_(1))^(3)`