$X$-rays of wavelength $22 \, pm$ are scattered from a carbon target at an angle of $85^{\circ}$ to the incident beam. The Compton shift for $X$-rays is ......... $pm$.

The energy of the $L$ shell is $7200$ units and the energy of the $K$ shell is $1800$ units. Therefore,the energy of the $K_\alpha$ line is equal to ...... units.

The difference between $\lambda_{K_{\alpha}}$ and $\lambda_{min}$ becomes twice if the accelerating potential changes from $3100 \ V$ to $12400 \ V$. Find $\lambda_{K_{\alpha}}$ in $\mathring{A}$. (Given $hc = 12400 \ eV \mathring{A}$)

The structure of solids is investigated by using

Hard $X$-rays for the study of fractures in bones should have a minimum wavelength of $10^{-11} \, m$. The accelerating voltage for electrons in the $X$-ray machine should be:

The $K_\alpha$ $X$-ray emission line for tungsten occurs at $\lambda = 0.021 \ nm$. What is the energy difference between the $K$ and $L$ levels in this atom in $keV$?