$A$ metal crystallizes in a lattice having $AB AB AB$ sequence of layers. This arrangement of spheres corresponds to which type of packing,and what is the percentage of empty space (void volume) in this lattice?

In a crystal,atoms of $A$ form an $FCC$ lattice,atoms of $B$ occupy all octahedral voids,and atoms of $C$ occupy $25\%$ of the tetrahedral voids. The possible molecular formula of the compound is:

In an ionic oxide,the oxide anions form an $hcp$ arrangement,while the metal cations occupy $\frac{2}{3}$ of the octahedral voids. Determine the formula of this oxide.

In a $ccp$ structure of a mixed oxide,$1/8$ of the tetrahedral voids are occupied by divalent $X^{+2}$ ions and $50\%$ of the octahedral voids are occupied by trivalent $Y^{+3}$ ions. The formula of the oxide is:

Consider the $bcc$ unit cells of the solid $1$ and $2$ with the position of atoms as shown below. The radius of atom $B$ is twice that of atom $A$. The unit cell edge length is $50\%$ more in solid $2$ than in $1$. What is the approximate packing efficiency in solid $2$? $........... \%$

In a close-packed structure of mixed oxides,the lattice is composed of oxide ions. One-eighth of the tetrahedral voids are occupied by divalent cations $(A^{2+})$,while one-half of the octahedral voids are occupied by trivalent cations $(B^{3+})$. The formula of the mixed oxide is: