$A$ compound is formed by two elements $X$ and $Y$. Atoms of the element $Y$ (anions) form an $hcp$ structure and atoms of the element $X$ (cations) occupy all the tetrahedral voids. Determine the formula of the compound.

The molecular formula of a crystalline solid is $X_3Y_2$. Atoms of $Y$ form $ccp$ lattice,and atoms of $X$ occupy $50\%$ octahedral voids and $x\%$ of tetrahedral voids. What is the percentage of unoccupied tetrahedral voids?

How many total voids are present in $1 \ mol$ of a compound that forms an $hcp$ structure?

If the unit cell of a mineral has cubic close packed $(ccp)$ array of oxygen atoms with $m$ fraction of octahedral holes occupied by aluminium ions and $n$ fraction of tetrahedral holes occupied by magnesium ions,$m$ and $n$,respectively,are

$A$ metal crystallizes in a simple cubic unit cell. Calculate the void volume of the unit cell. $[a = 3.36 \times 10^{-8} \text{ cm}]$

$A$ two-dimensional solid is made by alternating circles with radius $a$ and $b$ such that the sides of the circles touch. The packing fraction is defined as the ratio of the area under the circles to the area under the rectangle with sides of length $x$ and $y$. The ratio $r=b/a$ for which the packing fraction is minimised is closest to $.....$