The edge length of the unit cell of a crystal is $288 \ pm$. If its density is $7.2 \ g \ cm^{-3}$ and the molar mass is $52 \ g \ mol^{-1}$, determine the type of unit cell.

Find the radius of an atom in $fcc$ unit cell having edge length $405 \ pm$. (in $pm$)

An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length of $405 \ pm$. If its density is $2.7 \times 10^3 \ kg \ m^{-3}$, the nature of the cubic unit cell is: $(N_{A} = 6.02 \times 10^{23} \ mol^{-1})$

Niobium crystallizes in a $bcc$ structure. If its density is $8.55 \, g/cm^3$, calculate the atomic radius of niobium. [Atomic mass of $Nb = 93 \, u$] (in $pm$)

Calculate the density of a metal having a molar mass of $210 \ g \ mol^{-1}$ that forms a simple cubic unit cell. $(a^3 \cdot N_{A} = 21.5 \ cm^3 \ mol^{-1})$ (in $g \ cm^{-3}$)

What is the molar mass of a metal with a $BCC$ structure having a density of $10 \ g \ cm^{-3}$ and an edge length of $200 \ pm$?