In an ionic solid compound,$A$ ions are at the corners of the cube and $B$ ions are at the center of each face. The molecular formula of the compound will be ..............

In hexagonal systems of crystals,a frequently encountered arrangement of atoms is described as a hexagonal prism. Here,the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. $A$ space-filling model of this structure,called hexagonal close-packed $(HCP)$,is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally,the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be $r$.
$1.$ The number of atoms on this $HCP$ unit cell is
$(A)$ $4$ $(B)$ $6$ $(C)$ $12$ $(D)$ $17$
$2.$ The volume of this $HCP$ unit cell is
$(A)$ $24 \sqrt{2} r^3$ $(B)$ $16 \sqrt{2} r^3$
$(C)$ $12 \sqrt{2} r^3$ $(D)$ $\frac{64 r^3}{3 \sqrt{3}}$
$3.$ The empty space in this $HCP$ unit cell is
$(A)$ $74 \%$ $(B)$ $47.6 \%$ $(C)$ $32 \%$ $(D)$ $26 \%$
Give the answer for questions $1, 2$ and $3.$

Calculate the volume occupied by a particle in $bcc$ unit cell if the volume of unit cell is $8.2 \times 10^{-23} \ cm^3$.

Calculate the packing efficiency in a metal crystal for a face-centred cubic $(FCC)$ unit cell (assuming that atoms are touching each other).

In a face-centered cubic $(FCC)$ close-packed structure,the third layer covers the ..... voids created between the first and second layers.

Ferric oxide crystallises in a hexagonal close-packed array of oxide ions with two out of every three octahedral holes occupied by ferric ions. Derive the formula of the ferric oxide.