For a crystal, the angle of diffraction $(2 \theta)$ is $90^{\circ}$ and the second order line has a $d$ value of $2.28 \ \text{Å}$. The wavelength (in $\text{Å}$) of $X$-rays used for Bragg's diffraction is

Calculate the number of unit cells in $1 \, g$ of $NaCl$ crystal,which crystallizes in an $fcc$ structure. (Molar mass of $NaCl = 58.5 \, g/mol$)

Calculate the number of unit cells in $0.5 \text{ g}$ of a metal if the product of the volume and density of the unit cell is $6.65 \times 10^{-23} \text{ g}$.

The crystal structure of an element has an $fcc$ lattice. If the edge length of the crystal is $4 \ \mathring{A}$,what is the atomic weight (in $g \ mol^{-1}$) of the element,if the density of the crystal is $11.21 \ g \ cm^{-3}$ $(N_{A} = 6.023 \times 10^{23} \ mol^{-1})$?

Calculate the molar mass of an element having density $21 \ g \ cm^{-3}$ that forms $fcc$ unit cell $[a^3 \cdot N_{A} = 36 \ cm^3 \ mol^{-1}]$

$KCl$ has the same structure as $NaCl$. If ${r_{Na^+}}/{r_{Cl^-}} = 0.5$ and ${r_{Na^+}}/{r_{K^+}} = 0.7$,then the ratio of the densities of $NaCl$ and $KCl$ will be .... (Molar mass $NaCl = 58.5 \, amu$,$KCl = 74.5 \, amu$)