A metal crystallises in two phases, one as fcc and other as bcc with unit cell edge lengths of $3.5 Å$ and…
A metal crystallises in two phases, one as fcc and other as bcc with unit cell edge lengths of $3.5 Å$ and $3.0 Å$ respectively. The ratio of density of fcc and bcc phases approximately is
1.5 : 1.0
1.0 : 1.5
1.26 : 1
1 : 1.26
Solution
Density
(d) of fcc $=\frac{Z_1 \times \text { atomic mass }}{\left(N_0\right) \times V_1}$
and density (d) in bcc $=\frac{Z_2 \times \text { Atomic mass }}{N_0 \times V_2}$
where, $N_0=$ Avogadro number and $Z_1$ and $Z_2$ are the number of atoms per cent cell in fcc and bcc respectively.
$
\frac{d_{\mathrm{fcc}}}{d_{\mathrm{bcc}}}=\frac{Z_1}{Z_2} \times \frac{V_2}{V_1}
$
For fcc $Z_1=4, V_1=a^3=\left(3.5 \times 10^{-8}\right)^3$
$
\frac{d_{\mathrm{fcc}}}{d_{\mathrm{bcc}}}=\frac{4 \times\left(3.0 \times 10^{-8}\right)^3}{2 \times\left(3.5 \times 10^{-8}\right)^3}=1.259
$