Calculate the molar mass of an element if it forms $fcc$ unit cell structure. [Mass of unit cell $= 1.8 \times 10^{-22} \ g$,$N_A = 6.022 \times 10^{23} \ mol^{-1}$]

Element $X$ crystallizes in a $12$ coordination face-centered cubic $(fcc)$ lattice. On applying high temperature,it changes to an $8$ coordination body-centered cubic $(bcc)$ lattice. Find the ratio of the density of the crystal lattice before and after applying high temperature. The atomic radius of $X$ is the same in both crystals.

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

$Na$ metal crystallizes in a $BCC$ structure. If the edge length of the unit cell is $4.29 \ \overset{o}{A}$,then the radius of the $Na$ atom is = ...... $cm$.

In a $NaCl$ crystal,the distance between $Na^+$ and $Cl^-$ ions is $2.814 \ \overset{\circ}{A}$ and the density of the crystal is $2.167 \ g/cm^3$. Calculate the value of Avogadro's number $(N_A)$.

An element has an $fcc$ structure. If its edge length is $200 \, pm$, calculate the density of this element having a mass of $200 \, g$. $[200 \, g$ of the element contains $24 \times 10^{23}$ atoms.$]$