An element crystallizes in an $fcc$ unit cell structure with an edge length of $200 \, pm$. If $200 \, g$ of the element contains $24 \times 10^{23}$ atoms, what is its density in $g/cm^3$?

$A$ metal crystallizes in a simple cubic lattice. The radius of the metal atom is $x \ pm$. What is the volume of the unit cell in $pm^3$?

Ferrous oxide has a cubic structure and each edge of the unit cell is $5.0 \ \mathring{A}$. Assuming the density of the oxide is $4.0 \ g \ cm^{-3}$,calculate the number of $Fe^{2+}$ and $O^{2-}$ ions present in each unit cell ($M_w$ of $FeO = 72 \ g/mol$).

In $CsCl$ type structure, if the radius of the cation and anion are $80 \ pm$ and $100 \ pm$ respectively, then the closest distance between two cations is:

$Cu$ metal crystallizes in an $fcc$ or $ccp$ lattice. If the edge length of its unit cell is $361 \ pm$, what is the radius of the $Cu$ atom (in $pm$)?

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 $.... \, ^{\circ}$