An element with a simple cubic structure has an edge length of unit cell $3.86 \ \mathring{A}$. What is the radius of the atom?

An element crystallizes in an $fcc$ structure with an edge length of $200 \, pm$. If $200 \, g$ of this element contains $24 \times 10^{23}$ atoms,calculate its density in $g \, cm^{-3}$.

Salt $AB$ has a zinc blende structure. The radii of $A^{2+}$ and $B^{2-}$ ions are $0.7 \ \mathring{A}$ and $1.8 \ \mathring{A}$ respectively. The edge length of the $AB$ unit cell is ........... $\mathring{A}$.

Aluminium metal has a density of $2.72 \ g \ cm^{-3}$ and crystallizes in a cubic lattice with an edge length of $404 \ pm$. Which of the following is correct?

Sodium crystallises in $bcc$ structure with radius $1.86 \times 10^{-8} \ cm$. Calculate the edge length of the unit cell.

Iron exhibits $bcc$ structure at room temperature. Above $500^{\circ} C$,it transforms to $fcc$ structure. Find the ratio of the density of iron at room temperature to that at $500^{\circ} C$. (Assume the atomic radii and the molar mass of iron remain constant even with variation in temperature)