How fast does an electron have to move to emit Cherenkov Radiation?

I have a friend whom I'm haveing an argument with and he doesn't think that there is anything that can move faster than light in real life. that it's all just theoretical. So my questions are: What is the speed that an Electron begins to emit Cherenkov radiation? and what is the fastest an Electron can theoreticly travel?How fast does an electron have to move to emit Cherenkov Radiation?
From the Wikipedia article:



膶erenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle (such as a proton) passes through an insulator at a speed greater than the speed of light in that medium.



Hence, a general answer is: faster than the speed of light.



As to your second question, I couldn't find a clear statement; however, I did turn this up, which is interesting:



"Electrometers measure electric charge, but there must be a fundamental speed limit to measuring one electric charge. Since there are no dimensional inputs to this question, the answer must be expressible in terms of the fundamental physical constants of Nature, e,h,m,c. In general the question should be posed without reference to any specific technology, but for definiteness, we analyze the field effect transistor, which is essentially an electrometer. In spite of selecting a specific technology, we find that the speed limit is related to a fundamental constant, the Rydberg frequency, or as appropriate, the semiconductor Rydberg frequency including the electron effective mass, and the relative dielectric constant. We do not know whether the Rydberg frequency represents the upper speed limit, but on dimensional grounds we claim that the final limit can only differ by some power of the fine-structure-constant."How fast does an electron have to move to emit Cherenkov Radiation?
Cherenkov radiation is emitted when an electron creates a "light shockwave" basically this means that it is moving faster then the speed of light in the given medium. This is impossible in a vacuum, and very difficult in air where the speed of light is very nearly the same as in a vacuum because the maximum speed an electron can achieve is 3E8 m/s however in water it is only 2.2556E8 m/s.How fast does an electron have to move to emit Cherenkov Radiation?
this type of radiations are emitted when a charge particle moves with or more than speed of light,i-e;3*10exp8m/sec.
it has to move faster than the speed of light in the media it is in.



For example, it would have to move faster than ~3x10^8 m/s in a vacuum.



The best example is in water, where a substance undergoing Beta decay emits electrons at a faster speed than the speed of light in the water, hence why radioactive things "glow" underwater.



NOTE: Radioactive things don't usually glow in air, only in high-density fluids.