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

Find the radius of an atom in $fcc$ unit cell having edge length $405 \ pm$. (in $pm$)

Gold (atomic radius $= 0.144 \, nm$) crystallises in a face-centred unit cell. What is the length of a side of the cell?

$CsCl$ crystallises in a cubic structure that has $Cl^{-}$ at each corner and $Cs^{+}$ at the centre of the unit cell. If $r_{Cs^{+}} = 1.69 \ \mathring{A}$ and $r_{Cl^{-}} = 1.81 \ \mathring{A}$,what is the value of the edge length of the cube in $\mathring{A}$?

$A$ metal (atomic mass $= 50$) has a body-centered cubic $(bcc)$ crystal structure. If the density of the metal is $5.96 \, g \, cm^{-3}$,then the volume of the unit cell is ............ $\times 10^{-24} \, cm^3$.

Calculate the volume of the unit cell of an element having a molar mass of $63.5 \ g \ mol^{-1}$ that forms an $fcc$ structure $\left[\varrho \times N_{A} = 5.5 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$.