Calculate the volume of the unit cell of an element having a molar mass of $63.5 \ g \ mol^{-1}$ that forms an $fcc$ structure $\left[\varrho \times N_{A} = 5.5 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$.

An element crystallising in $fcc$ lattice has a density of $8.92 \ g \ cm^{-3}$ and edge length of $3.61 \times 10^{-8} \ cm$. What is the atomic weight of the element (in $u$)? $(N_A = 6.022 \times 10^{23} \ mol^{-1})$

$Cu$ metal crystallizes in an $fcc$ or $ccp$ lattice. If the edge length of its unit cell is $361 \ pm$, what is the radius of the $Cu$ atom (in $pm$)?

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 volume of a $bcc$ unit cell if the radius of an atom present in it is $1.86 \times 10^{-8} \ cm$.

$KBr$ has $NaCl$ structure. Its density is $2.75 \ g \ cm^{-3}$. The edge length of the unit cell will be (molar mass of $KBr$ is $119 \ g \ mol^{-1}$):