The minimum wavelength of the $X$-rays produced by electrons accelerated through a potential difference of $V$ volts is directly proportional to

The figure represents the observed intensity of $X-$ rays emitted by an $X-$ ray tube as a function of wavelength. The sharp peaks $A$ and $B$ denote

What does the $K\alpha$ characteristic $X$-ray represent?

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.

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.

The wavelength of the most energetic $X$-rays emitted when a metal target is bombarded by $40 \ keV$ electrons is approximately .............. $\mathring{A}$.