Find the molar mass of an element that crystallizes forming a unit cell structure having an edge length of $4 \times 10^{-8} \ cm$ and containing $4$ particles. (Density $\rho = 19.7 \ g \ cm^{-3}$)

$A$ compound has $fcc$ structure. If the density of the unit cell is $3.4 \text{ g cm}^{-3}$,what is the edge length of the unit cell? (Molar mass $= 98.99 \text{ g mol}^{-1}$)

When silver crystallizes, it forms face-centered cubic $(FCC)$ unit cells. If the volume of the unit cell is $6.84 \times 10^{-23} \text{ cm}^3$, calculate the density of silver. (Molar mass of silver is $108 \text{ g/mol}$, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$) (in $\text{ g cm}^{-3}$)

Calculate the volume of a $bcc$ unit cell if the radius of an atom present in it is $1.86 \times 10^{-8} \ cm$.

$Cu$ 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 $pm$)?

An element $M$ crystallises in a body-centred cubic unit cell with a cell edge of $300 \, pm$. The density of the element is $6.0 \, g \, cm^{-3}$. The number of atoms present in $180 \, g$ of the element is $............ \times 10^{23}$ (Nearest integer).