Calculate the edge length of a $bcc$ unit cell if the radius of the metal atom is $227 \ pm$.

$A$ metal with an atomic radius of $141.4 \, pm$ crystallises in the face-centred cubic structure. The volume of the unit cell in $pm^3$ is $.... . \times 10^7$.

An element crystallises in a $fcc$ lattice with cell edge $250 \ pm$. Calculate the density of the element (atomic mass $= 90.3 \ g \ mol^{-1}$) (in $g \ cm^{-3}$)

$A$ solid having density of $9 \times 10^3 \ kg \ m^{-3}$ forms face-centred cubic crystals of edge length $200 \sqrt{2} \ pm$. What is the molar mass of the solid? [Avogadro constant $\cong 6 \times 10^{23} \ mol^{-1}$,$\pi \cong 3$]

If the density of a gold $(Au)$ crystal crystallizing in a $ccp$ structure is $19.3 \, g/cm^3$,what will be the radius of the atom? (Given: $Au = 197 \, amu$)

An element crystallising in $fcc$ lattice has a density of $8.92 \ g \ cm^{-3}$ and edge length of $3.61 \times 10^{-8} \ cm$. What is the atomic weight of the element (in $u$)? $(N_A = 6.022 \times 10^{23} \ mol^{-1})$