Calculate the volume of $fcc$ unit cell if the radius of a particle in it is $106.05 \ pm$.

$X$-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.

Lithium forms a body-centred cubic $(BCC)$ structure. The length of the side of its unit cell is $351 \ pm$. The atomic radius of lithium will be: ............. $pm$

If the angle of incidence of $X$-ray of wavelength $3 \mathring{A}$ which produces a second order diffracted beam from the $(100)$ planes in a simple cubic lattice with interlayer spacing $a = 6 \mathring{A}$ is $30^{\circ}$,the angle of incidence that produces a first order diffracted beam from the $(200)$ planes is $.... \, ^{\circ}$

Gold (edge length $0.144 \ nm$) crystallizes in a face-centered cubic unit cell. What is the radius $(r)$ of the gold atom in $pm$?

Aluminium crystallises in a cubic close-packed structure. Its metallic radius is $125 \ pm$.
$(i)$ What is the length of the side of the unit cell?
$(ii)$ How many unit cells are there in $1.00 \ cm^3$ of aluminium?