Calculate the density of an element having molar mass $63 \ g \ mol^{-1}$ that forms $FCC$ structure $\left[a^3 \times N_{A} = 28 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

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 $Z$? $(Fe = 56 \ g \ mol^{-1}; N_{A} = 6.022 \times 10^{23} \ mol^{-1})$

Identify the instrument used to determine the crystal structure from the following:

Find the molar mass of an element that crystallizes forming a unit cell structure having an edge length of $4 \times 10^{-8} \ cm$ and containing $4$ particles. (Density $\rho = 19.7 \ g \ cm^{-3}$)

Derive the expression to calculate the density of a unit cell.

Calculate the number of unit cells in $1 \ cm^3$ volume of metal if the unit cell edge length is $1.25 \times 10^{-8} \ cm$.