The range of wavelength for $X$-rays is from . . . . . . .

$X$-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 ......... $pm$.

If the energy of an electron in the $K$-shell is $40000 \,eV$ and an accelerating potential of $60000 \,eV$ is applied across a Coolidge tube,which of the following $X$-rays will be obtained?

In a Coolidge tube,the potential difference between the cathode and the anode is $120 \, kV$. What will be the maximum energy of the emitted $X$-rays?

If the series limit of the Balmer series for hydrogen is $3646 \ \mathring{A}$,calculate the atomic number $(Z)$ of the element which gives an $X$-ray wavelength of the $K_{\alpha}$ line as $1.0 \ \mathring{A}$.

The wavelength of an $X$-ray beam is $10 \, \mathring{A}$. The mass of a fictitious particle having the same energy as that of the $X$-ray photons is $\frac{x}{3} h \, \text{kg}$. The value of $x$ is ....... . ($h =$ Planck's constant)