Voids in Close Packed Structures — Prelims Questions

An element crystallizes in a face-centered cubic (FCC) lattice. If the edge length of the unit cell is $a$, what is the distance between the center of an octahedral void and the center of a tetrahedral void in this unit cell?

A compound is formed by elements A and B. Element B forms a cubic close-packed (CCP) structure, and atoms of A occupy 2/3rd of the tetrahedral voids. What is the formula of the compound?

In a solid, oxide ions (O$^{2-}$) are arranged in a hexagonal close-packed (HCP) array. Aluminum ions (Al$^{3+}$) occupy 2/3rd of the octahedral voids. What is the formula of the compound?

If the radius of a cation ($r_+$) is $0.8,\text{Å}$ and the radius of an anion ($r_-$) is $1.6,\text{Å}$, what type of void would the cation most likely occupy in a close-packed structure formed by the anions?

Which of the following statements about voids in close-packed structures is INCORRECT?

A compound has a structure where anion Y forms a hexagonal close-packed (HCP) lattice, and cation X occupies 1/3rd of the tetrahedral voids. What is the formula of the compound?