The density of $\beta-Fe$ is $7.6 \ g \ cm^{-3}$. It crystallizes in a cubic lattice with $a = 290 \ pm$. What is the value of $Z$? $(Fe = 56 \ g \ mol^{-1}; N_{A} = 6.022 \times 10^{23} \ mol^{-1})$

$X$-ray diffraction studies show that copper crystallises in an $fcc$ unit cell with cell edge of $3.608 \times 10^{-8} \ cm$. In a separate experiment,copper is determined to have a density of $8.92 \ g / cm^{3}$,calculate the atomic mass of copper.

Calculate the number of unit cells in $0.4 \ g$ of metal if the product of density and volume of the unit cell is $1.2 \times 10^{-22} \ g$.

$A$ certain element crystallises in a $bcc$ lattice of unit cell edge length $27 \mathring{A}$. If the same element under the same conditions crystallises in the $fcc$ lattice,the edge length of the unit cell in $\mathring{A}$ will be .........
(Round off to the Nearest Integer).
[Assume each lattice point has a single atom]
[Assume $\sqrt{3}=1.73, \sqrt{2}=1.41$]

Calculate the volume of a unit cell having four particles in it with a density of $19.0 \ g \ cm^{-3}$ [molar mass of element $= 190 \ g \ mol^{-1}$].

$CsCl$ has a $bcc$ arrangement. Its unit cell edge length is $400 \, pm$. What is its inter-ionic distance?