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.

Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

$A$ metal crystallizes in a simple cubic lattice. The radius of the metal atom is $x \ pm$. What is the volume of the unit cell in $pm^3$?

An atomic substance $A$ of molar mass $12 \ g \ mol^{-1}$ has a cubic crystal structure with an edge length of $300 \ pm$. The number of atoms present in one unit cell of $A$ is $.....$ (Nearest integer). Given the density of $A$ is $3.0 \ g \ cm^{-3}$ and $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$.

The distance between two parallel $(111)$ planes in a crystal with an edge length of $300 \, pm$ is ................ $pm$.

Silver forms $ccp$ lattice and $X$-ray studies of its crystals show that the edge length of its unit cell is $408.6 \,pm$. Calculate the density of silver ( Atomic mass $= 107.9 \,u$ ).