$20 \ kV$ electrons can produce $X$-rays with a minimum wavelength of

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 $.5$)

Find the $(a)$ maximum frequency,and $(b)$ minimum wavelength of $X$-rays produced by $30 \; kV$ electrons.

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:

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.

If the minimum wavelength obtained in an $X-ray$ tube is $2.5 \times 10^{-10} \ m$,the operating potential of the tube will be.....$kV$.