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 volume of the unit cell of an element having a molar mass of $27 \ g \ mol^{-1}$ that forms an $fcc$ unit cell. Given: $\rho \cdot N_{A} = 16.0 \times 10^{23} \ g \ cm^{-3} \ mol^{-1}$.

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.52 \ \mathring{A}$. Its atomic weight is $39$. Its density (in $kg \ m^{-3}$) will be:

$A$ diatomic molecule $X_2$ has a body-centred cubic (bcc) structure with a cell edge of $300 \ pm$. The density of the molecule is $6.17 \ g \ cm^{-3}$. The number of molecules present in $200 \ g$ of $X_2$ is (Avogadro constant $N_A = 6 \times 10^{23} \ mol^{-1}$) (in $N_A$)

Fill in the blanks:
$1.$ Density of unit cell $(d) = ........$
$2.$ Mass of atoms present in unit cell $(m) = ........$

An element has a density of $6.8 \ g \ cm^{-3}$ and crystallizes in a $bcc$ structure with a unit cell edge length of $290 \ pm$. The number of atoms in $200 \ g$ of the element is: