The $K_{\alpha}$ characteristic $X$-ray refers to the transition:

An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce $X$-rays. It produces continuous as well as characteristic $X$-rays. If $\lambda_{\min}$ is the smallest possible wavelength of $X$-ray in the spectrum,the variation of $\log \lambda_{\min}$ with $\log V$ is correctly represented in:

The minimum wavelength of $X$-rays produced in a Coolidge tube operating at $40 \ kV$ is ..... $\mathring A$.

In an $X$-ray tube, electrons emitted from a filament (cathode) carrying current $I$ hit a target (anode) at a distance $d$ from the cathode. The target is kept at a potential $V$ higher than the cathode, resulting in the emission of continuous and characteristic $X$-rays. If the filament current $I$ is decreased to $I/2$, the potential difference $V$ is increased to $2V$, and the separation distance $d$ is reduced to $d/2$, then:
$(A)$ The cut-off wavelength will reduce to half, and the wavelengths of the characteristic $X$-rays will remain the same.
$(B)$ The cut-off wavelength as well as the wavelengths of the characteristic $X$-rays will remain the same.
$(C)$ The cut-off wavelength will reduce to half, and the intensities of all the $X$-rays will decrease.
$(D)$ The cut-off wavelength will become two times larger, and the intensity of all the $X$-rays will decrease.

When the accelerating voltage applied to the electrons is increased beyond a critical value in an $X$-ray tube,what happens to the $X$-ray spectrum?

$X$-rays are produced when ...