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 $38.6 \ g$ of noble metal having density $19.3 \ g \ cm^{-3}$ and volume of one unit cell is $6.18 \times 10^{-23} \ cm^{3}$?

An element crystallises in a $bcc$ lattice with a cell edge of $500 \ pm$. The density of the element is $7.5 \ g \ cm^{-3}$. How many atoms are present in $300 \ g$ of the metal?

Elements $A$ and $B$ have $fcc$ and $bcc$ structures respectively with a unit cell edge length of $3 \mathring{A}$ for both elements. The number of atoms in $210 \ g$ of $A$ is equal to the number of atoms in $594 \ g$ of $B$. If the density of $A$ is $7 \ g \ cm^{-3}$,what is the density of $B$ (in $g \ cm^{-3}$)?

Calculate the volume of the unit cell for an element having a molar mass of $56 \ g \ mol^{-1}$ that forms $bcc$ unit cells. $\left[\rho \cdot N_{A} = 4.8 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$

Calculate the density of an element with molar mass $27 \ g \ mol^{-1}$ having $4$ atoms in a unit cell with edge length $405 \ pm$. (in $g \ cm^{-3}$)