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 $[a^3 \times N_{A} = 21.5 \ cm^3 \ mol^{-1}]$.

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

In the Bragg's equation for diffraction of $X$-rays, $n$ represents:

Nickel crystallises in a $fcc$ type of unit cell,with edge length $0.3524 \ nm$. Calculate the radius of nickel atom. (in $nm$)

An element has a crystalline structure where the unit cell is a cube with one atom at each corner and two atoms on its body diagonal. If the volume of this unit cell is $24 \times 10^{-24} \, cm^3$ and the density of the element is $7.2 \, g \, cm^{-3}$,then the number of atoms present in $200 \, g$ of the element is:

$A$ 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 $= 108 \ g/mol$)