An element with density $2.8 \ g \ cm^{-3}$ forms an $fcc$ unit cell having an edge length of $4 \times 10^{-8} \ cm$. Calculate the molar mass of the element.

Calculate the edge length of a simple cubic unit cell if the radius of an atom is $167.3 \ pm$. (in $pm$)

The second order Bragg's diffraction of $X$-rays with $\lambda = 1 \ \mathring{A}$ from a set of parallel planes in a metal occurs at an angle of $60^\circ$. The distance between the scattering planes in the crystal is ................ $\mathring{A}$.

Calculate the volume of the unit cell of an element having a molar mass of $27 \ g \ mol^{-1}$ that forms an $fcc$ unit cell. Given: $\rho \cdot N_{A} = 16.0 \times 10^{23} \ g \ cm^{-3} \ mol^{-1}$.

The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

$CsBr$ has $bcc$ structure with edge length $4.3 \ \mathring{A}$. The shortest interionic distance in between $Cs^{+}$ and $Br^{-}$ (in $\mathring{A}$) is :