1. Light = energy, shorter wavelengths= higher energy. Blue light has a shorter wavelength than red light. UV has even more energy. X-Rays have a lot more energy. For reference in the visible spectrum were talking about maybe 1-4 eV (this may be wrong, I'm too drunk to look it up rn).

2. If we want to produce light, the aim is to find an energy gap that has the exact energy gap that corresponds to the wavelength we're interested in. Typically this corresponds to an electronic transition, i.e. an electron "jumps" into a higher orbital, on its way down it will emit the energy difference as light.

2.1 X-Rays rn are produced by accelerating electrons onto a metal plate with high voltage. The impact of the electron "rips" out an electron in the close vicinity of the nucleus. Another electron will take the place of that electron, the energy gap associated with that process is large, which is why it produces X-Rays.

3. If we want to produce LEDs that emit in the far UV range we have to find large energy gaps in materials which is difficult. We still have to have a way to get the electron across the energy gap using electricity.

4. X-Ray LEDs are probably not realistic, as the energy of x-rays is so large that we have to rip out electrons from the close vicinity of the nucleus... which is already what we're doing with X-ray tubes.