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

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 $= 107.9 \,u$ ).

The face diagonal of a cubic close-packed unit cell is $4 \ \mathring{A}$. What will be the edge length?

$A$ metallic element crystallises in a simple cubic lattice. If the edge length of the unit cell is $3 \mathring{A}$ and the density is $8 \ g/cm^{3}$,what is the number of unit cells in $100 \ g$ of the metal? (Molar mass of metal $= 108 \ g/mol$)

Niobium crystallises in a body-centred cubic $(bcc)$ structure. If the density is $8.55 \, g \, cm^{-3}$,calculate the atomic radius of niobium using its atomic mass $93 \, u$.

Calculate the number of unit cells in $0.5 \text{ g}$ of a metal if the product of the volume and density of the unit cell is $6.65 \times 10^{-23} \text{ g}$.