Question

The Russian physicist P. A.Čerenkov discovered that a charged particle traveling in a solid with a speed exceeding the speed of light in that material radiates electromagnetic radiation. (This phenomenon is analogous to the sonic boom produced by an aircraft moving faster than the speed of sound in air.) Čerenkov shared the 1958 Nobel Prize for this discovery.

What is the minimum kinetic energy (in electronvolts) that an electron must have while traveling inside a slab of crown glass n = 1.48 in order to create Čerenkov radiation?

Answer 1

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>1 for v>c.

For n=1.48, 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