How many unit cells are present in $39 \ g$ of potassium that crystallizes in a body-centred cubic structure? $[At. \ wt. \ of \ K = 39]$

Element $X$ crystallizes in a $12$ coordination face-centered cubic $(fcc)$ lattice. On applying high temperature,it changes to an $8$ coordination body-centered cubic $(bcc)$ lattice. Find the ratio of the density of the crystal lattice before and after applying high temperature. The atomic radius of $X$ is the same in both crystals.

An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length of $405 \ pm$. If its density is $2.7 \times 10^3 \ kg \ m^{-3}$, the nature of the cubic unit cell is: $(N_{A} = 6.02 \times 10^{23} \ mol^{-1})$

Niobium crystallizes in a $bcc$ structure. If its density is $8.55 \, g/cm^3$, calculate the atomic radius of niobium. [Atomic mass of $Nb = 93 \, u$] (in $pm$)

Niobium crystallises in a body-centred cubic $(bcc)$ structure. If the density is $8.55 \, g \, cm^{-3}$,calculate the atomic radius of niobium using its atomic mass $93 \, u$.

$X$-rays of wavelength $1 \ \mathring{A}$ are diffracted by the planes of particles in a metal. The second-order diffraction occurs at an angle of $60^{\circ}$. Calculate the distance between two parallel planes in $\mathring{A}$.