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

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.

The frequencies of $K_{\alpha}$,$K_{\beta}$,and $L_{\alpha}$ $X$-rays of a material are $\nu_1$,$\nu_2$,and $\nu_3$ respectively. Which of the following relations holds good?

The $X$-ray wavelength of the $L_{\alpha}$ line of platinum $(Z=78)$ is $1.30 \ \mathring{A}$. The $X$-ray wavelength of the $L_{\alpha}$ line of Molybdenum $(Z=42)$ is ............. $\mathring{A}$.

The emission of continuous $X$-rays is due to:

The binding energy of the innermost electron in tungsten is $40 \, keV$. The energy of the characteristic $X$-rays emitted is: