Calculate the edge length of $fcc$ unit cell if the radius of the metal atom is $139 \ pm$.

An element has a density of $6.8 \ g \ cm^{-3}$ and crystallizes in a $bcc$ structure with a unit cell edge length of $290 \ pm$. The number of atoms in $200 \ g$ of the element is:

Calculate the number of unit cells in $1 \ cm^3$ volume of an element if unit cell edge length is $4.0 \times 10^{-8} \ cm$.

An element has a body-centered cubic structure with a unit cell edge length of $400 \ pm$. The atomic mass of the element is $24 \ g \ mol^{-1}$. What is the density of the element (in $g \ cm^{-3}$)? $(N_{A} = 6 \times 10^{23} \ mol^{-1})$

Each edge of a cubic unit cell is $400 \ pm$ long. If the atomic weight of the element is $120$ and its density is $6.25 \ g/cm^3$, identify the crystal lattice $(N_A = 6 \times 10^{23} \ mol^{-1})$.

$KCl$ has the same structure as $NaCl$. If ${r_{Na^+}}/{r_{Cl^-}} = 0.5$ and ${r_{Na^+}}/{r_{K^+}} = 0.7$,then the ratio of the densities of $NaCl$ and $KCl$ will be .... (Molar mass $NaCl = 58.5 \, amu$,$KCl = 74.5 \, amu$)