Potassium has a $bcc$ structure with a nearest neighbour distance of $4.52 \ \mathring{A}$. Its atomic weight is $39$. Its density (in $kg \ m^{-3}$) will be:

$X$-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 radius of a metal atom in a $bcc$ unit cell having an edge length of $287 \ pm$. (in $pm$)

To obtain a diffraction peak for a crystalline solid with interplane distance equal to the wavelength of incident $X$-ray radiation,the angle of incidence should be $....\,^{\circ}$

Gold crystallises in $fcc$ lattice. The edge length of the unit cell is $4 \ \mathring{A}$. The closest distance between gold atoms is '$x$' $\mathring{A}$ and density of gold is '$y$' $g \ cm^{-3}$. What are $x$ and $y$ respectively?
$($ Molar mass of gold $= 197 \ g \ mol^{-1} ; N_A = 6 \times 10^{23} \ mol^{-1} )$

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