The second order Bragg's diffraction of $X$-rays with $\lambda = 1 \ \mathring{A}$ from a set of parallel planes in a metal occurs at an angle of $60^\circ$. The distance between the scattering planes in the crystal is ................ $\mathring{A}$.

Iron oxide $FeO$ crystallises in a cubic lattice with a unit cell edge length of $5.0 \ \mathring{A}$. If the density of the $FeO$ in the crystal is $4.0 \ g \ cm^{-3}$,then the number of $FeO$ units present per unit cell is $...........$ (Nearest integer).
Given: Molar mass of $Fe$ and $O$ is $56$ and $16 \ g \ mol^{-1}$ respectively.
$N_{A} = 6.0 \times 10^{23} \ mol^{-1}$

The edge length of a face centered cubic cell of an ionic substance is $508 \, pm.$ If the radius of the cation is $110 \, pm,$ the radius of the anion is ........... $pm$.

When an electron in an excited atom jumps from the $L$ shell to the $K$ shell,$X$-rays are emitted. These $X$-rays undergo first-order diffraction at an angle of $7.75^{\circ}$ by a crystal with an interplanar spacing of $2.64 \ \mathring{A}$. Calculate the energy difference between the $K$ shell and the $L$ shell. $(\sin \ 7.75^{\circ} = 0.1349)$

$A$ copper complex crystallising in a $CCP$ lattice with a cell edge of $0.4518 \ nm$ has been revealed by employing $X$-ray diffraction studies. The density of the copper complex is found to be $7.62 \ g \ cm^{-3}$. The molar mass of the copper complex is $..... \ g \ mol^{-1}$. (Nearest integer)
[Given : $N_{A} = 6.022 \times 10^{23} \ mol^{-1}$]

Calculate the molar mass of a metal with density $1 \ g \ cm^{-3}$ forming a $bcc$ structure with an edge length of $420 \ pm$.