Chemistry - Solid State Question with Solution | TestHub

X is in f.c.c. lattice
Number of atoms$=\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m }\mathrm{a}\mathrm{t }\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{r}\times \frac{1}{8}+\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s }\mathrm{a}\mathrm{t }\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{s}\times \frac{1}{2}$
$\mathrm{X}=8\times \frac{1}{8}+6\times \frac{1}{2}=4$
Total tetrahedral voids$=8$
As y are at T.V.
So$\mathrm{Y}=8$
Number of Octahedra voids$=4$
$\mathrm{Z}=\frac{1}{2}\times 4=2$
So$\mathrm{X}=4,\mathrm{Y}=8,\mathrm{Z}=2$
Hence the formula of solid is${\mathrm{X}}_4{\mathrm{Y}}_8{\mathrm{Z}}_2$or${\mathrm{X}}_2{\mathrm{Y}}_4\mathrm{Z}$.