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

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.$]$

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

When an electron in an excited atom jumps from the $L$ shell to the $K$ shell,$X$-rays are emitted. These $X$-rays undergo first-order diffraction at an angle of $7.75^{\circ}$ by a crystal with an interplanar spacing of $2.64 \ \mathring{A}$. Calculate the energy difference between the $K$ shell and the $L$ shell. $(\sin \ 7.75^{\circ} = 0.1349)$

Iron oxide $FeO$ crystallises in a cubic lattice with a unit cell edge length of $5.0 \ \mathring{A}$. If the density of the $FeO$ in the crystal is $4.0 \ g \ cm^{-3}$,then the number of $FeO$ units present per unit cell is $...........$ (Nearest integer).
Given: Molar mass of $Fe$ and $O$ is $56$ and $16 \ g \ mol^{-1}$ respectively.
$N_{A} = 6.0 \times 10^{23} \ mol^{-1}$

Polonium (atomic mass = $209$) crystallises in a simple cubic structure with a density of $9.32 \ g \ cm^{-3}$. Its lattice parameter (in $pm$) is closest to: