What $kV$ potential is to be applied on an $X$-ray tube so that the minimum wavelength of emitted $X$-rays may be $1 \text{ Å}$? $(h = 6.625 \times 10^{-34} \text{ J-s})$

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.

When $X$-rays from a Coolidge tube pass through an aluminum foil of thickness $0.3 \, mm$,$50\%$ of the $X$-rays are transmitted. If the potential difference between the target and the cathode is increased,the fraction of $X$-rays transmitted through the same foil will be .......

The ratio of the energy of an $X$-ray photon of wavelength $1 \mathring{A}$ to that of visible light of wavelength $5000 \mathring{A}$ is:

The order of voltage applied across the ends of an $X$-ray tube is ...... $V$.