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

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 $2.1 \times 10^{-23} \ cm^3$.

$A$ crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400 \ pm$. If the density of the substance in the crystal is $8 \ g \ cm^{-3}$, then the number of atoms present in $256 \ g$ of the crystal is $N \times 10^{24}$. The value of $N$ is

Calculate the volume of the unit cell for an element having a molar mass of $56 \ g \ mol^{-1}$ that forms $bcc$ unit cells. $\left[\rho \cdot N_{A} = 4.8 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$

How many atoms of niobium are present in $2.43 \ g$ if it forms $bcc$ structure with density $9 \ g \ cm^{-3}$ and volume of unit cell $2.7 \times 10^{-23} \ cm^3$?

An element crystallizes in an $fcc$ unit cell structure with an edge length of $200 \, pm$. If $200 \, g$ of the element contains $24 \times 10^{23}$ atoms, what is its density in $g/cm^3$?