Calculate the number of atoms present in $1 \ g$ of an element if it forms an $fcc$ unit cell structure. [ $\varrho \times a^3 = 6.8 \times 10^{-22} \ g$ ]

In a cubic unit cell of an ionic compound, the eight corners are occupied by anions and cations are at the center of the cube. Calculate the volume of the unit cell if the density of the unit cell is $4 \text{ g cm}^{-3}$. [Molar mass of compound $= 168.6 \text{ g mol}^{-1}$ and $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$]

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 volume of a $bcc$ unit cell if the radius of an atom present in it is $1.86 \times 10^{-8} \ cm$.

$A$ metallic element crystallises in a simple cubic lattice. If the edge length of the unit cell is $3 \mathring{A}$ and the density is $8 \ g/cm^{3}$,what is the number of unit cells in $100 \ g$ of the metal? (Molar mass of metal $= 108 \ g/mol$)

Calculate the edge length of a unit cell for a metal with an atomic radius of $128 \ pm$ that forms an $fcc$ unit cell structure.