An element $\mathrm{X}$ (atomic weight $=24 \mathrm{g}/\mathrm{mol}$) forms a face centred cubic lattice. If the edge length of the lattice is $4\times {10}^{-8} \mathrm{cm}$, and the observed density is $2.40\times {10}^3$$\mathrm{kg}/{\mathrm{m}}^3,$ then the percentage occupancy of the lattice points by element $\left.\mathrm{X}: ({\mathrm{N}}_{\mathrm{A}}=6\times {10}^{23}\right)$, is-

Ferrous oxide has a cubic structure and the edge length of the unit cell is $5.0 \mathrm{\AA }$. Assuming the density of ferrous oxide is $3.84 \mathrm{g}/{\mathrm{cm}}^3,$ the number of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{O}}^{2-}$ ions present in each unit cell will be-

(Use ${\mathrm{N}}_{\mathrm{A}}=6\times {10}^{23}$)

$\mathrm{TlAl}{\left({\mathrm{SO}}_4\right)}_2·{\mathrm{xH}}_2\mathrm{O}$ is BCC with $\text{'}\mathrm{a}\text{'}=1.22 \mathrm{nm}.$ If the density of the solid is $2.32 \mathrm{g} {\mathrm{cc}}^{-1}$, then the value of $\mathrm{x}$ is:

$\left(\text{Given}: {\mathrm{N}}_{\mathrm{A}}=6\times {10}^{23}; \text{atomic weights}:\mathrm{Tl}=204, \mathrm{Al}=27, \mathrm{S}=32.\right)$

Sodium ($\mathrm{Na} =23$) crystallizes in BCC arrangement with the interfacial separation between the atoms at the edge as, $53.6 \mathrm{pm}$. The density of sodium crystal is

The density of solid argon $(\mathrm{Ar}=40 \mathrm{g} {\mathrm{mol}}^{-1})$ is $1.68 \mathrm{g} {\mathrm{mL}}^{-1}$ at $40 \mathrm{K}$. If the argon atom is assumed to be a sphere of radius $1.50\times {10}^{-8} \mathrm{cm}$, what $\%$ of solid $\mathrm{Ar}$ is apparently empty space?

$(\mathrm{Use}:\left.{\mathrm{N}}_{\mathrm{A}}=6\times {10}^{23}\right)$