What is the relationship between the edge length $(a)$ and the radius of the atom $(r)$ in a simple cubic unit cell?

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

The density of a body-centered cubic $(BCC)$ crystal of Molybdenum is $10.3 \ g \ cm^{-3}$. Calculate the edge length of the unit cell in $pm$. (Atomic mass of $Mo = 95.94 \ g \ mol^{-1}$) (in $.9$)

What is the number of atoms present per unit cell of aluminium having edge length $4 \ \mathring{A}$? (Given: density of $Al = 2.7 \ g \ cm^{-3}$,atomic mass of $Al = 27 \ g \ mol^{-1}$)

An element has $2.03 \times 10^{24}$ atoms in $135 \ g$. If the element crystallizes in a face-centered cubic $(FCC)$ lattice structure with an edge length of $150 \ pm$, then the density of the element is ............... $g \ cm^{-3}$.

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centred cubic,and face-centred cubic,then the ratio of radii of the spheres in these systems will be respectively: