In an $A_{x} B_{y}$ crystal structure,$A$ atoms occupy all octahedral as well as all tetrahedral voids,and $B$ atoms are at the $FCC$ lattice points. What is the formula of the compound $A_{x} B_{y}$?

When sodium is heated above $1000 \ K$,its crystal structure changes from $bcc$ to $fcc$. Assuming the metallic radius of the atom remains unchanged,the ratio of the fraction of volume occupied by atoms in $bcc$ and $fcc$ structures will be .......

$A$ compound formed by $Mg$,$Al$,and $O$ is found to have a cubic close-packed $(CCP)$ array of oxide ions,in which $Mg^{2+}$ ions occupy $\frac{1}{8}^{th}$ of the tetrahedral voids and $Al^{3+}$ ions occupy $\frac{1}{2}$ of the octahedral voids. The formula for the compound is:

In a face-centred cubic lattice,atom $A$ occupies the corner positions and atom $B$ occupies the face-centred positions. If one atom of $B$ is missing from one of the face-centred points,the formula of the compound is

In a solid $AB_2$,the coordination number of $A$ is $8$. It has a cubic close-packed $(ccp)$ lattice. Half of the $B$ atoms are,however,ejected from the solid. Now,the number of tetrahedral holes (voids) that remain filled is:

Atom $(A)$ is present in $ccp$ form,atom $(B)$ is present in all the octahedral voids,and atom $(C)$ is present in all the tetrahedral voids. If all particles touching one of the body diagonal axes are removed,find the empirical formula of the solid.