Calculate the volume of the unit cell of an element with a density of $7.2 \ g \ cm^{-3}$ that forms a $bcc$ structure. ($288 \ g$ of this element contains $3.35 \times 10^{24}$ atoms).

Calculate the number of atoms present in $1.58 \ g$ of a metal that forms a $bcc$ structure,given that $\varrho \times a^3 = 1.58 \times 10^{-22} \ g$.

The cubic unit cell structure of a compound containing cation $M$ and anion $X$ is shown below. When compared to the anion,the cation has a smaller ionic radius. Choose the correct statement$(s)$:
$(A)$ The empirical formula of the compound is $MX$.
$(B)$ The cation $M$ and anion $X$ have different coordination geometries.
$(C)$ The ratio of $M-X$ bond length to the cubic unit cell edge length is $0.866$.
$(D)$ The ratio of the ionic radii of cation $M$ to anion $X$ is $0.414$.

Silver (atomic weight $= 108 \ g \ mol^{-1}$) has a density of $10.5 \ g \ cm^{-3}$. The number of silver atoms on a surface of area $10^{-12} \ m^2$ can be expressed in scientific notation as $y \times 10^x$. The value of $x$ is

Silver has an atomic radius of $144 \ pm$ and the density of silver is $10.6 \ g \ cm^{-3}$. Based on this information, identify the correct statement.

Give the correct order of initials $T$ (true) or $F$ (false) for the following statements:
$I.$ In an anti-fluorite structure,anions form $FCC$ lattice and cations occupy all tetrahedral voids.
$II.$ If the radius of cations and anions are $0.2 \ \mathring{A}$ and $0.95 \ \mathring{A}$,then the coordination number of the cation in the crystal is $4$.
$III.$ An atom/ion is transferred from a lattice site to an interstitial position in a Frenkel defect.
$IV.$ The density of a crystal always increases due to a substitutional impurity defect.