Calculate the number of atoms present per unit cell if the product of density and volume of the unit cell is $1.8 \times 10^{-22} \ g$. [Mass of an atom $= 4.5 \times 10^{-23} \ g$]

An element has a body-centered cubic structure with a unit cell edge length of $400 \ pm$. The atomic mass of the element is $24 \ g \ mol^{-1}$. What is the density of the element (in $g \ cm^{-3}$)? $(N_{A} = 6 \times 10^{23} \ mol^{-1})$

Copper crystallises into a $fcc$ lattice with edge length $3.61 \times 10^{-8} \, cm$. Show that the calculated density is in agreement with its measured value of $8.92 \, g \, cm^{-3}$.

Calculate the number of atoms present in a unit cell of an element having molar mass $190 \ g \ mol^{-1}$ and density $20 \ g \ cm^{-3}$. Given that $[a^3 \cdot N_A = 38 \ cm^3 \ mol^{-1}]$.

An element is found to crystallize with $BCC$ structure having density $8.55 \ g \ cm^{-3}$. What is the edge length of the unit cell? (Atomic mass of element $= 93$)

$Xe$ crystallizes in an $FCC$ structure. The edge length of its unit cell is $620 \, pm$. The radius of $Xe$ is $=$ ...... $pm$.