The volume of a simple cubic unit cell is $x \times 10^{-23} \ cm^3$. Calculate the value of $x$ if the volume occupied by a particle in it is $2.1 \times 10^{-23} \ cm^3$.

If the edge length of a $bcc$ unit cell is $386 \ pm$, then the atomic radius will be ........... $pm$.

Calculate the volume of a simple cubic unit cell if the radius of the particle in it is $400 \ pm$.

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

An element with atomic mass $100$ has a $bcc$ structure and edge length $400 \, pm$. The density of the element is .............. $g \, cm^{-3}$.

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