The number of tetrahedral voids per unit $HCP$ cell is

What is the number of tetrahedral voids present in $0.5 \text{ mole}$ of a compound forming an $hcp$ structure?

The molecular formula of a crystal is $AB_2O_4$. Oxygen atoms form $ccp$ lattice. Atoms of $A$ occupy $x \%$ of tetrahedral voids and atoms of $B$ occupy $y \%$ of octahedral voids. $x$ and $y$ are respectively:

In a face-centered cubic $(FCC)$ unit cell (or cubic close packing $(CCP)$ unit cell),the edge length $a$ is equal to:

If the radius of the octahedral void is $r$ and the radius of the atoms in close packing is $R$,derive the relation between $r$ and $R$.

In a solid compound,the oxide ions are arranged in $CCP$. Cations $A$ occupy $1/6^{th}$ of the tetrahedral voids and cations $B$ occupy one third of the octahedral voids. The probable formula of the compound is