Calculate the density of a metal having a unit cell volume of $64 \times 10^{-24} \ cm^3$ and a molar mass of $192 \ g \ mol^{-1}$,containing $4$ particles per unit cell. (in $g \ cm^{-3}$)

An element crystallises in a $bcc$ type of unit cell. The density and edge length of the unit cell are $4 \ g \ cm^{-3}$ and $500 \ pm$ respectively. What is the atomic mass of the element?

Calculate the density of an element having molar mass $27 \ g \ mol^{-1}$ that forms $fcc$ unit cell. $[a^3 \cdot N_A = 38.5 \ cm^3 \ mol^{-1}]$ (in $g \ cm^{-3}$)

Gold crystallizes in an $fcc$ unit cell with an edge length of $408 \text{ pm}$. What is the radius of the gold atom (in $\text{ pm}$)?

The edge length of a $bcc$ unit cell is $4 \times 10^{-10} \ m$. What is the radius of the atom occupying the body center of the cubic unit cell?

Calculate the number of atoms per unit cell of an element having a molar mass of $92.0 \ g \ mol^{-1}$ and a density of $8.6 \ g \ cm^{-3}$ forming a cubic unit cell structure. Given $[a^3 \times N_{A} = 21.5 \ cm^3 \ mol^{-1}]$.