$Au$ crystallizes in an $fcc$ lattice. If the edge length of the unit cell is $4.07 \ \mathring{A}$,then the distance between two nearest $Au$ atoms is ............... $\mathring{A}$.

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

If the radius of an atom of an element which forms a body centered cubic unit cell is $173.2 \ pm$, the volume of the unit cell in $cm^3$ is:

What is the molar mass of a metal with a $BCC$ structure having a density of $10 \ g \ cm^{-3}$ and an edge length of $200 \ pm$?

Aluminium metal has a density of $2.72 \ g \ cm^{-3}$ and crystallizes in a cubic lattice with an edge length of $404 \ pm$. Which of the following is correct?

Elements $A$ and $B$ have $fcc$ and $bcc$ structures respectively with a unit cell edge length of $3 \mathring{A}$ for both elements. The number of atoms in $210 \ g$ of $A$ is equal to the number of atoms in $594 \ g$ of $B$. If the density of $A$ is $7 \ g \ cm^{-3}$,what is the density of $B$ (in $g \ cm^{-3}$)?