The edge length of an $FCC$ unit cell is given by:

Derive the expression to calculate the density of a unit cell.

How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.

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

$A$ metal has a $fcc$ structure. If the edge length of the unit cell is $200 \text{ pm}$, calculate the volume occupied by the particles in a unit cell.

What is the density of an element (At. mass $100 \ g \ mol^{-1}$) having $BCC$ structure with edge length $400 \ pm$ (in $g \ cm^{-3}$)?