What is the edge length of a simple cubic unit cell if the radius of the atom is $174 \ pm$ (in $pm$)?

Derive the expression for the density $(d)$ of a unit cell: $d = \frac{zM}{a^3 N_A}$.

$A$ metal crystallizes in a $BCC$ structure. The edge length of its unit cell is $3.04 \ \mathring{A}$. What is the volume of its unit cell in $cm^3$?

Calculate the volume of $fcc$ unit cell if the radius of a particle in it is $106.05 \ pm$.

Copper crystallises in $fcc$ unit cell with cell edge length of $3.608 \times 10^{-8} \, cm$. The density of copper is $8.92 \, g \, cm^{-3}$. Calculate the atomic mass of copper. (In $u$)

Calculate the number of unit cells in $1 \text{ cm}^3$ of metal if it forms a simple cubic structure with a unit cell edge length of $500 \text{ pm}$.