In an orthorhombic crystal system,the values of $a$,$b$,and $c$ are $4.2 \, \mathring{A}$,$8.6 \, \mathring{A}$,and $8.3 \, \mathring{A}$ respectively. Given the molar mass of the solute is $155 \, g \, mol^{-1}$ and the density is $3.3 \, g \, cm^{-3}$,calculate the number of formula units $(Z)$ per unit cell.

What is the atomic mass of an element with $BCC$ structure and density $10 \ g \ cm^{-3}$ having an edge length of $300 \ pm$?

The crystal of $CsBr$ has an edge length of $437 \ pm$. If the density of the crystal is $4.24 \ g \ cm^{-3}$, determine the type of crystal structure of $CsBr$ (Atomic mass of $Cs = 133, Br = 80$).

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

Calculate the molar mass of an element if it forms $fcc$ unit cell structure. [Mass of unit cell $= 1.8 \times 10^{-22} \ g$,$N_A = 6.022 \times 10^{23} \ mol^{-1}$]

An $X^{+}Y^{-}$ ionic compound has a $bcc$ structure. The distance between two nearest ions is $1.73 \ \mathring{A}$. What is the edge length of the unit cell?