$A$ compound is formed by two elements $M$ and $N$. Element $N$ forms a hexagonal closed pack $(HCP)$ array with $2/3$ of the octahedral holes occupied by $M$. The formula of the compound is $....$

$A$ two-dimensional solid pattern formed by two different atoms $X$ and $Y$ is shown below. The black and white squares represent atoms $X$ and $Y,$ respectively. The simplest formula for the compound based on the unit cell from the pattern is

With the help of a labelled diagram,show that there are $4$ octahedral voids per unit cell in a cubic close-packed $(CCP)$ structure.

$A$ compound is formed by atoms of $A$,$B$ and $C$. Atoms of $C$ form $hcp$ lattice. Atoms of $A$ occupy $50\%$ of octahedral voids and atoms of $B$ occupy $\frac{2}{3}$ of tetrahedral voids. What is the molecular formula of the solid?

Find the void volume of a $bcc$ unit cell in $cm^3$ if the volume of the unit cell is $1.5 \times 10^{-22} \ cm^3$.

Calculate the volume occupied by all particles in an $fcc$ unit cell if the volume of the unit cell is $1.6 \times 10^{-23} \ cm^3$.