Calculate the density of an element having molar mass $225 \text{ g mol}^{-1}$ forming a $bcc$ structure. Given: $[a^3 \times N_A = 75 \text{ cm}^3 \text{ mol}^{-1}]$ (in $\text{ g cm}^{-3}$)

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

$Au$ crystallizes in an $fcc$ lattice. If the edge length of the unit cell is $4.07 \ \mathring{A}$,then the distance between two nearest $Au$ atoms is ............... $\mathring{A}$.

In a body-centered cubic $(BCC)$ unit cell of a metal,the edge length is $4 \times 10^{-10} \ m$. The diameter of the atom will be:

Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

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.