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 $(N_A = 6 \times 10^{23} \ mol^{-1})$.

Copper crystallises in $fcc$ unit cell with cell edge length of $3.608 \times 10^{-8} \, cm$. The density of copper is $8.92 \, g \, cm^{-3}$. Calculate the atomic mass of copper. (In $u$)

$KF$ has a structure similar to $NaCl$. If the density of the crystal is $2.48 \, g/cm^3$, the distance between $K^+$ and $F^-$ ions will be ............. $pm$. (Atomic masses: $K = 39 \, amu, F = 19 \, amu$)

The edge length of a unit cell of a metal having a molar mass of $75 \ g/mol$ is $5 \ \mathring{A}$. It crystallizes in a cubic lattice. If the density is $2 \ g/cm^3$, find the radius of the metal atom in $pm$. (Given: $N_A = 6 \times 10^{23}$)

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:

Calculate the number of atoms in $5.4 \ g$ of a metal forming an $fcc$ structure,given that the unit cell volume $\left(a^3\right)$ multiplied by density $\left(\varrho\right)$ is $7.2 \times 10^{-22} \ g$.