Calculate the number of unit cells in $1 \ cm^3$ volume of an element if unit cell edge length is $4.0 \times 10^{-8} \ cm$.

An element has a $bcc$ structure. If its edge length is $250 \, pm$ and its density is $8 \, g/cm^3$,calculate its molar mass and the radius of the atom.

Calculate the molar mass of a metal having a density of $7.8 \ g \ cm^{-3}$ that crystallizes in a $bcc$ structure with an edge length of $288 \ pm$.

What is the relation between edge length $a$ and the total volume occupied by atoms in a $BCC$ unit cell?

If the density of a gold $(Au)$ crystal crystallizing in a $ccp$ structure is $19.3 \, g/cm^3$,what will be the radius of the atom? (Given: $Au = 197 \, amu$)

$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is
$(N_{A} = 6 \times 10^{23} \ mol^{-1})$