An element with $BCC$ structure has an edge length of $500 \ pm$. If its density is $4 \ g \ cm^{-3}$, find the atomic mass of the element.

The density of $Na$ is $0.613 \ g \ cm^{-3}$. If the edge length of the unit cell of $Na$ is $5 \ \mathring{A}$,the effective number of atoms of $Na$ per unit cell is (Atomic weight of $Na = 23 \ u$)

The crystal of $CsBr$ has an edge length of $437 \ pm$. If the density of the crystal is $4.24 \ g \ cm^{-3}$, determine the type of crystal structure of $CsBr$ (Atomic mass of $Cs = 133, Br = 80$).

Fill in the blanks:
$1.$ Density of unit cell $(d) = ........$
$2.$ Mass of atoms present in unit cell $(m) = ........$

What is the volume of one particle in $BCC$ structure if '$a$' is edge length?

Iron exhibits $bcc$ structure at room temperature. Above $500^{\circ} C$,it transforms to $fcc$ structure. Find the ratio of the density of iron at room temperature to that at $500^{\circ} C$. (Assume the atomic radii and the molar mass of iron remain constant even with variation in temperature)