$A$ 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 $.... . \times 10^7$.

Calculate the density of a metal having molar mass $197 \ g \ mol^{-1}$ if it forms $fcc$ structure. $\left[a^3 \times N_{A}=40 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

$Cu$ metal crystallizes in an $fcc$ or $ccp$ lattice. If the edge length of its unit cell is $361 \ pm$, what is the radius of the $Cu$ atom (in $pm$)?

Calculate the volume of the unit cell for an element having a molar mass of $56 \ g \ mol^{-1}$ that forms $bcc$ unit cells. $\left[\rho \cdot N_{A} = 4.8 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$

Calculate the volume of a simple cubic unit cell if the radius of the particle in it is $400 \ pm$.

Calculate the radius of an atom of metal if it forms a simple cubic unit cell with an edge length of $380 \ pm$. (in $pm$)