Q.Silver forms ccp lattice and X-ray studies of its crystals show that the edge length of its unit cell is 408.6 pm. Calculate the density of silver (Atomic mass = 107.9 u).

The body-centred cubic (bcc) unit cell has atoms at all 8 corners plus 1 at the body centre, giving an effective $z = 2$ atoms per cell ($8 \times \tfrac18 + 1 = 2$).

Density is found from the general relation:

where $M$ is molar mass, $a$ the edge length, and $N_A$ Avogadro's number. For bcc the atoms touch along the body diagonal, so

$\sqrt{3}\,a = 4r \quad\Rightarrow\quad r = \frac{\sqrt{3}}{4}a.$ …