Calculate the molar mass of an element with density $2.7 \ g \ cm^{-3}$ that forms $fcc$ structure. $\left[a^3 \cdot N_{A}=40 \ cm^3 \ mol^{-1}\right]$

How many unit cells are present in a cube-shaped ideal crystal of $NaCl$ of mass $1.00 \ g$? [Atomic masses: $Na = 23, Cl = 35.5$]

An element crystallizes in a $bcc$ lattice. The atomic radius of the element is $2.598 \ \mathring{A}$. What is the volume (in $cm^3$) of one unit cell?

$Xe$ crystallizes in an $FCC$ structure. The edge length of its unit cell is $620 \, pm$. The radius of $Xe$ is $=$ ...... $pm$.

$CsBr$ crystallises in a body-centred cubic lattice. The unit cell length is $436.6 \, pm$. Given that the atomic mass of $Cs = 133$ and that of $Br = 80 \, amu$ and Avogadro number being $6.02 \times 10^{23} \, mol^{-1}$,the density of $CsBr$ is .............. $g/cm^{3}$.

For a crystal,the diffraction angle for the second-order diffraction is $2\theta = 90^{\circ}$. If the distance between two parallel planes is $2.28 \ \mathring{A}$,then the wavelength of the $X$-rays used for Bragg diffraction (in $\mathring{A}$) will be .........