Question

An element crystallizes bothe in fcc and bcc lattices. If the density of the element in the two forms is the same, the ratio of unit cell volume of fcc to that of bcc lattice is:

Answer 1

We know,
$Density,d=\frac{z\times M}{V\times N_A}$
For fcc, $z_{eff}=4$
For bcc, $z_{eff}=2$
$d_{fcc}=\frac{4\times M}{V_{fcc}\times N_A}\left(i\right)$
$d_{bcc}=\frac{2\times M}{V_{bcc}\times N_A}$(ii)
On dividing (i) by (ii)
$\Rightarrow \frac{d_{fcc}}{d_{bcc}}=\frac{\frac{4\times M}{V_{fcc}\times N_A}}{\frac{2\times M}{V_{bcc}\times N_A}}$
$\Rightarrow 1=\frac{4\times V_{bcc}}{2\times V_{fcc}}$
$\Rightarrow V_{fcc}=2\times V_{bcc}$
$\Rightarrow \frac{V_{fcc}}{V_{bcc}}=2$