Calculate the number of atoms per unit cell of an element having a molar mass of $92.0 \ g \ mol^{-1}$ and a density of $8.6 \ g \ cm^{-3}$ forming a cubic unit cell structure. Given $[a^3 \times N_{A} = 21.5 \ cm^3 \ mol^{-1}]$.

Calculate the density of an element having molar mass $63 \ g \ mol^{-1}$ that forms $FCC$ structure $\left[a^3 \times N_{A} = 28 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

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.

Calculate the radius of a metal atom in a $bcc$ unit cell having an edge length of $287 \ pm$. (in $pm$)

An element crystallises in an $fcc$ unit cell with a cell edge length of $3.608 \times 10^{-8} \text{ cm}$. The density of the element is $8.92 \text{ g cm}^{-3}$. Calculate the atomic mass of the element $(N_A = 6.022 \times 10^{23} \text{ mol}^{-1})$. (in $\text{ g/mol}$)

At $T \ K$, copper (atomic mass $= 63.5 \ u$) has $fcc$ structure with an edge length of $x \ \mathring{A}$. The density of copper (in $g \ cm^{-3}$) at that temperature is approximately $(N_A = 6.0 \times 10^{23} \ mol^{-1})$