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:

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 $Z=31$, given $a=5 \times 10^7 \text{ Hz}^{1/2}$ for a characteristic $X$-ray spectrum.

The structure of solids is investigated by using

Which of the following is related to the characteristic emission of $X$-rays?

The energy of $X$-rays with a wavelength of $1.65 \, \mathring{A}$ is ............. $keV$ (Given: $h = 6.6 \times 10^{-34} \, J \cdot s$,$c = 3 \times 10^{8} \, m/s$,$1 \, eV = 1.6 \times 10^{-19} \, J$). (in $.5$)