Question

A metal crystallises into two cubic phases, face-centred cubic (fcc) and body-centred cubic (bcc) whose unit lengths are 3.5 and 3.0 $\mathring{A}$ respectively. Calculate the ratio of densities of fcc and bcc.

Answer 1

Density of fcc $=\frac{Z_1\times At.mass}{Av.no.\times V_1}$

and density in bcc $=\frac{Z_2\times At.mass}{Av.no.\times V_2}$

$\frac{d_{fcc}}{d_{bcc}}=\frac{Z_1}{Z_2}\times \frac{V_2}{V_1}$

For fcc $Z_1=4;V_1=a^3=(3.5\times {10}^{-8}{)}^3$

For bcc $Z_2=2;V_2=a^3=(3.0\times {10}^{-8}{)}^3$

$\frac{d_{fcc}}{d_{bcc}}=\frac{4\times (3.0\times {10}^{-8}{)}^3}{2\times (3.5\times {10}^{-8}{)}^3}=1.259$