Calculate the number of unit cells in $10.8 \ g$ of metal,given that $\rho a^3 = 7.2 \times 10^{-22} \ g$.

An element has an $fcc$ structure. If its edge length is $200 \, pm$, calculate the density of this element having a mass of $200 \, g$. $[200 \, g$ of the element contains $24 \times 10^{23}$ atoms.$]$

In a $bcc$ lattice having the edge length of $200 \ pm$, the cation has the radius of $70 \ pm$. The radius ratio of $\frac{r^{+}}{r^{-}}$ is (Given, $\sqrt{2}=1.4, \sqrt{3}=1.7$ and $\sqrt{6}=2.4$ )

$A$ 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

Sodium metal crystallizes in a body-centred cubic $(bcc)$ lattice with a unit cell edge of $4.29 \ \mathring{A}$. The radius of the sodium atom is approximately ............. $\mathring{A}$.

The edge length of a $bcc$ unit cell is $4 \times 10^{-10} \ m$. What is the radius of the atom occupying the body center of the cubic unit cell?