Calculate the number of unit cells in $0.9 \ g$ of a metal if it forms a $bcc$ structure. Given: $\rho \times a^3 = 3 \times 10^{-22} \ g$.

$Au$ crystallizes in an $fcc$ lattice. If the edge length of the unit cell is $4.07 \ \mathring{A}$,then the distance between two nearest $Au$ atoms is ............... $\mathring{A}$.

The diffraction pattern of a crystalline solid gave a peak at $2 \theta = 60^{\circ}$. What is the distance (in $cm$) between the layers which gave this peak? ($\lambda$ of $X$-rays is $1.54 \mathring{A}$) ($\sin 30^{\circ} = 0.5$,$\sin 60^{\circ} = 0.866$; $n = 1$)

Find the molar mass of an element that crystallizes forming a unit cell structure having an edge length of $4 \times 10^{-8} \ cm$ and containing $4$ particles. (Density $\rho = 19.7 \ g \ cm^{-3}$)

Copper crystallises in $fcc$ structure with a unit cell length of $361 \ pm$. What is the radius of copper atom? ............ $pm$

Calculate the number of unit cells in $0.5 \text{ g}$ of a metal if the product of the volume and density of the unit cell is $6.65 \times 10^{-23} \text{ g}$.