Ionic radii of cation $A^{+}$ and anion $B^{-}$ are $102 \ pm$ and $181 \ pm$ respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for $B^{-}$ and $A^{+}$ is present in all octahedral voids. The edge length of the unit cell of the crystal $AB$ is $pm$.
- A$566$
- B$555$
- C$544$
- D$533$
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$(i)$ What is the length of the side of the unit cell?
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$(ii)$ How many unit cells are there in $1.00 \ cm^3$ of aluminium?
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