What is the minimum kinetic energy on an electron traveling in crown glass to create Cerenkov Radiation?

What is the minimum kinetic energy (in keV) an electron must have while traveling inside a slab of crown glass (n = 1.52) in order to create Cerenkov Radiation?What is the minimum kinetic energy on an electron traveling in crown glass to create Cerenkov Radiation?
When a charged particle travels faster than the speed of light in a certain medium, then there is a release of energy in the form of "shock waves". For light, these shock waves are the Cerenkov radiation of which you ask. Perhaps it goes without saying that in a vacuum, no such radiation is possible, because n%26gt;1 for v%26gt;c.



For n=1.52, the speed of light is c (vacuum)/n (index of refraction).



V (light) in crown glass is = 1.97 E 8 m/s = .658c



We need our electron to have this velocity, and need to account for the relativistic mass...



m=m(rest)/SQRT((1-(v^2/c^2)) =

1.33m(rest) = 1.21E-30 kg



K.E. = 1/2 mv^2 = 2.36 E-14 J = 147keV (to three sig. figs.)



-Fred