What is the length of the body diagonal in a $bcc$ structure?

An element (atomic mass $= 100 \ g/mol$) having $bcc$ structure has a unit cell edge of $400 \ pm$. The density of the element is ................. $g/cm^3$.

Calculate the interplanar spacing between the $111$ planes in a $Ca$ crystal (in $nm$). Given that the edge length of the $Ca$ unit cell is $0.556 \ nm$.

Calculate the molar mass of a metal having a density of $22.24 \ g \ cm^{-3}$,which crystallizes to form a unit cell containing $4$ particles. Given $a^3 = 5.6 \times 10^{-23} \ cm^3$.

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centred cubic,and face-centred cubic,then the ratio of radii of the spheres in these systems will be respectively:

Calculate the number of unit cells in $1 \ cm^3$ volume of an element if unit cell edge length is $4.0 \times 10^{-8} \ cm$.