Chemistry - Solid State Question with Solution | TestHub

Co. number is 12 means it is fcc lattice

Co. number is 8 means it is bcc lattice

fcc bcc

${\mathrm{\rho }}_1=\frac{4\times \mathrm{a}\mathrm{t}.\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}{{\mathrm{N}}_{\mathrm{a}}\times {\mathrm{a}}_1^3}$${\mathrm{\rho }}_2=\frac{2\times \mathrm{a}\mathrm{t}.\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}{{\mathrm{N}}_{\mathrm{a}}\times {\mathrm{a}}_2^3}$

$\frac{{\text{ρ}}_1}{{\text{ρ}}_2}=\frac{4}{2}\times \frac{{\text{a}}_2^3}{{\text{a}}_1^3}=\frac{2\times {\left(\frac{4\text{r}}{\sqrt{3}}\right)}^3}{{(2\sqrt{2\text{r}})}^3}$

$=\frac{2\times 4\times 4\times 4}{2\times 2\times 2\times 2\times \sqrt{2}\left(3\sqrt{3}\right)}$

$=\frac{4\sqrt{2}}{3\sqrt{3}}=\frac{2(\sqrt{2}{)}^3}{(\sqrt{3}{)}^3}$