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

The percentage of vacant space for $bcc$ unit cell is ............. $\%$

Calculate the volume of $fcc$ unit cell in $cm^3$ if void volume of it is $4.16 \times 10^{-24} \ cm^3$.

In a compound $XY$,the atoms of element $Y$ form an $fcc$ structure,while the atoms of element $X$ occupy $25\%$ of the tetrahedral voids. The molecular formula of the compound will be .......

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.

In a compound made of atoms $A$ and $B$,atoms $A$ form an $fcc$ lattice,while atoms $B$ occupy $25\%$ of the tetrahedral voids and $50\%$ of the octahedral voids. If the crystal is cut such that all face-centered atoms along one axis are removed,the molecular formula of the resulting solid will be ...........