For the study of bone fractures,the minimum wavelength of $X$-rays should be $10^{-11} \ m$. The accelerating voltage for electrons in the $X$-ray machine will be .......

Calculate the wavelength of the $K_{\alpha}$ line for $Z=31$, when $a=5 \times 10^7 \, Hz^{1/2}$ for a characteristic $X$-ray spectrum.

Absorption of $X$-rays is maximum in which of the following different sheets?

$\Delta \lambda$ is the difference between the wavelength of the $K_\alpha$ line and the minimum wavelength of the continuous $X$-ray spectrum when the $X$-ray tube is operated at a voltage $V$. If the operating voltage is changed to $V / 3$,then the above difference is $\Delta \lambda^{\prime}$. Then:

When a beam of accelerated electrons hits a target,a continuous $X$-ray spectrum is emitted from the target. Which of the following wavelengths is absent in the $X$-ray spectrum,if the $X$-ray tube is operating at $40,000 \ V$?

How does the wavelength $\lambda$ of the $K_\alpha$ line in the $X$-ray spectrum depend on the atomic number $Z$?