If the edge length of the unit cell of an element crystallizing in a $bcc$ structure is $400 \, pm$, then the density of the crystal will be ............ $\text{g/cm}^3$. (Atomic weight $= 100 \, \text{g/mol}$)

If the atomic radius of an element is $75 \, pm$ and it crystallizes in a body-centered cubic $(BCC)$ lattice,what is the edge length of the unit cell in $pm$?

$A$ copper complex crystallising in a $CCP$ lattice with a cell edge of $0.4518 \ nm$ has been revealed by employing $X$-ray diffraction studies. The density of the copper complex is found to be $7.62 \ g \ cm^{-3}$. The molar mass of the copper complex is $..... \ g \ mol^{-1}$. (Nearest integer)
[Given : $N_{A} = 6.022 \times 10^{23} \ mol^{-1}$]

An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length of $405 \ pm$. If its density is $2.7 \times 10^3 \ kg \ m^{-3}$, the number of atoms present in one unit cell of it is (Given : $N_{A}=6.023 \times 10^{23} \ mol^{-1}$)

Calculate the edge length of the unit cell of a metal which crystallises in a $bcc$ structure. (Radius of metal atom $= 173 \ pm$)

Calculate the volume of the unit cell for an element having a molar mass of $92 \ g \ mol^{-1}$ that forms a $bcc$ structure,given $\left[\varrho \times N_{A} = 5.0 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$.