Calculate the radius of an atom of metal if it forms a simple cubic unit cell with an edge length of $380 \ pm$. (in $pm$)

The density of $\beta-Fe$ is $7.6 \ g \ cm^{-3}$. It crystallizes in a cubic lattice with $a = 290 \ pm$. What is the value of $Z$? $(Fe = 56 \ g \ mol^{-1}; N_{A} = 6.022 \times 10^{23} \ mol^{-1})$

An element has a $bcc$ structure with an atomic mass of $50$. If the edge length of the unit cell is $290 \ pm$, calculate the density of the unit cell in $\text{g/cm}^{-3}$.

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?

Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

Calculate the molar mass of a metal with density $1 \ g \ cm^{-3}$ forming a $bcc$ structure with an edge length of $420 \ pm$.