Calculate the number of atoms in $1 \ g$ of a metal if it forms an $fcc$ crystal structure,given that $\varrho \times a^3 = 1.728 \times 10^{-22} \ g$.

The density of $KBr$ is $2.75 \, g \, cm^{-3}$ and the unit cell edge length is $654 \, pm$. Given the atomic masses $K = 39$ and $Br = 80$, what is the crystal structure of $KBr$?

For a simple cubic system,find the ratio of the interplanar distances between the $(100)$,$(110)$,and $(111)$ planes.

If the crystal structure of $KCl$ is the same as that of $NaCl$,and the radius ratios are $r_{Na^+}/r_{Cl^-} = 0.55$ and $r_{K^+}/r_{Cl^-} = 0.74$,calculate the ratio of the edge lengths of the unit cells of $KCl$ and $NaCl$.

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

$A$ compound has $fcc$ structure. If the density of the unit cell is $3.4 \text{ g cm}^{-3}$,what is the edge length of the unit cell? (Molar mass $= 98.99 \text{ g mol}^{-1}$)