$X$-rays can be used to study crystal structure if the wavelength lies in the range:

$\Delta \lambda$ 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:

In an $X$-ray tube,electrons bombarding the target produce $X$-rays of minimum wavelength $1\; \mathring{A}$. What must be the energy of the bombarding electrons in $eV$?

For continuous $X-$rays,the minimum wavelength produced is:

The electron transition required for the emission of characteristic $K_\beta$ $X$-rays is:

What is the difference between soft and hard $X-$rays?