Calculate the molar mass of a metal with density $1 \ g \ cm^{-3}$ forming a $bcc$ structure with an edge length of $420 \ pm$.

Calculate the number of atoms present in $90 \text{ g}$ of a metal that forms a $bcc$ structure. Given: $[\rho \times a^3 = 1.8 \times 10^{-22} \text{ g}]$, where $\rho$ is density and $a$ is the edge length of the unit cell.

Calculate the volume of a unit cell having four particles in it with a density of $19.0 \ g \ cm^{-3}$ [molar mass of element $= 190 \ g \ mol^{-1}$].

An element having an atomic radius of $0.14 \ nm$ crystallizes in an $fcc$ unit cell. What is the length of a side of the cell in $nm$?

For a crystal, the angle of diffraction $(2 \theta)$ is $90^{\circ}$ and the second order line has a $d$ value of $2.28 \ \text{Å}$. The wavelength (in $\text{Å}$) of $X$-rays used for Bragg's diffraction is

Derive the expression to calculate the density of a unit cell.