Calculate the molar mass of an element having a density of $8.6 \ g \ cm^{-3}$ if it forms a $bcc$ structure $[a^3 \times N_{A} = 22.0 \ cm^3 \ mol^{-1}]$.

Sodium metal crystallizes in a $bcc$ lattice with a unit cell edge length of $a = 4.29 \ \mathring{A}$. What is the radius of the sodium atom in $\mathring{A}$?

How many atoms of niobium are present in $2.43 \ g$ if it forms $bcc$ structure with density $9 \ g \ cm^{-3}$ and volume of unit cell $2.7 \times 10^{-23} \ cm^3$?

Gold crystallises in $fcc$ lattice. The edge length of the unit cell is $4 \ \mathring{A}$. The closest distance between gold atoms is '$x$' $\mathring{A}$ and density of gold is '$y$' $g \ cm^{-3}$. What are $x$ and $y$ respectively?
$($ Molar mass of gold $= 197 \ g \ mol^{-1} ; N_A = 6 \times 10^{23} \ mol^{-1} )$

$NH_4Cl$ crystallizes in a $bcc$ lattice. If the edge length of the unit cell is $387 \, pm$, the distance between oppositely charged ions is ........ $pm$.

$NaCl$ has $4$ formula units per unit cell. If the edge length of the unit cell is $0.564 \, nm$,then the density of the crystal is ............ $\text{g/cm}^3$. $(NaCl = 58.5 \, \text{g/mol})$