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 $\text{g cm}^{-3}$.

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

Calculate the density of an element having molar mass $225 \text{ g mol}^{-1}$ forming a $bcc$ structure. Given: $[a^3 \times N_A = 75 \text{ cm}^3 \text{ mol}^{-1}]$ (in $\text{ g cm}^{-3}$)

Lithium has a body-centered cubic $(BCC)$ structure. If the edge length of its unit cell is $351 \ pm$, what is the atomic radius of lithium in $pm$?

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?

The second order Bragg's diffraction of $X$-rays with $\lambda = 1 \ \mathring{A}$ from a set of parallel planes in a metal occurs at an angle of $60^\circ$. The distance between the scattering planes in the crystal is ................ $\mathring{A}$.