Radius of cation and anion are $2.5 \ \mathring{A}$ and $2.6 \ \mathring{A}$ respectively. If a cubic crystal system is prepared by combination of above cation and anion then edge length of unit cell is ................ $\mathring{A}$ (Take $\sqrt{3} = 1.7$)

The edge length of a $bcc$ unit cell is $4 \times 10^{-10} \ m$. What is the radius of the atom occupying the body center of the cubic unit cell?

Calculate the number of unit cells present in $1 \text{ g}$ of a metal if the product of the density of the metal and the volume of the unit cell is $2.5 \times 10^{-22} \text{ g}$.

An element with molar mass $2.7 \times 10^{-2} \,kg \,mol^{-1}$ forms a cubic unit cell with edge length $405 \,pm$. If its density is $2.7 \times 10^{3} \,kg \,m^{-3}$, what is the nature of the cubic unit cell?

Gold crystallises in $fcc$ lattice. The edge length of the unit cell is $4 \ \mathring{A}$. The closest distance between gold atoms is '$x$' $\mathring{A}$ and density of gold is '$y$' $g \ cm^{-3}$. What are $x$ and $y$ respectively?
$($ Molar mass of gold $= 197 \ g \ mol^{-1} ; N_A = 6 \times 10^{23} \ mol^{-1} )$

The correct relationship between unit cell edge length '$a$' and radius of sphere '$r$' for face-centred and body-centred cubic structures respectively are: