Question

Element ‘X’ crystallizes in a 12 coordination FCC lattice, on applying high temperature, it changes to 8 coordination bcc lattice. The ratio of the density of the crystal lattice before and after applying high temperature will be :

• A. $2(\sqrt{2}{)}^3:(\sqrt{3}{)}^3$
• B. $\sqrt{2}:\sqrt{3}$
• C. 3 : 2
• D. 1 : 1

Answer 1

The correct option is A

$2(\sqrt{2}{)}^3:(\sqrt{3}{)}^3$

For fcc $a=2\sqrt{2}r;z=4$ and $d=\frac{ZM}{a^3{N}_0}$

For bcc $a^{\prime }=\frac{4}{\sqrt{3}}t;z^{\prime }=2$ and $d=\frac{Z^{\prime }\times M}{a^{\prime 3}{N}_0}$

$\frac{d}{d^{\prime }}=\frac{z}{z^{\prime }}\times \frac{(a^{\prime }{)}^3}{a^3}=\frac{4}{2}\times \frac{{\left(\frac{4r}{\sqrt{3}}\right)}^3}{{\left(2\sqrt{2}r\right)}^3}$

$\Rightarrow 2(\sqrt{2}{)}^3:(\sqrt{3}{)}^3$