An element $X$ (At. wt. $= 80 \ g/mol$) has an $fcc$ structure. Calculate the number of unit cells in $8 \ g$ of $X$.

An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length $405 \ pm$. If its density is $2.7 \times 10^{3} \ kg \ m^{-3},$ the radius of the element is approximately......... $\times 10^{-12} \ m$ (to the nearest integer).

$A$ metal has a $fcc$ lattice. The edge length of the unit cell is $404 \, pm$. The density of the metal is $2.72 \, g \, cm^{-3}$. The molar mass of the metal is :- ............ $g \, mol^{-1}$ ( $N_A$ Avogadro constant $= 6.02 \times 10^{23} \, mol^{-1}$ )

An element with $BCC$ structure has an edge length of $500 \ pm$. If its density is $4 \ g \ cm^{-3}$, find the atomic mass of the element.

Aluminium crystallises in a cubic close-packed structure. Its metallic radius is $125 \ pm$.
$(i)$ What is the length of the side of the unit cell?
$(ii)$ How many unit cells are there in $1.00 \ cm^3$ of aluminium?

Gold has a cubic close-packed structure which can be viewed as spheres occupying $74\%$ of the total volume. What is the edge length of the unit cell if the density of gold is $19.3 \ g/cm^3$? $(Au = 197 \ amu)$