007 (part 1 of 3) 10.0 points Cherenkov radiation takes place when an electron t
ID: 1507732 • Letter: 0
Question
007 (part 1 of 3) 10.0 points Cherenkov radiation takes place when an electron travels faster than the speed of light in a medium. This is a relativistic analogy of a sonic boom. Consider an electron traveling 11.2 percent faster than the speed of light in water. What is the total energy? The speed of light is 3 × 108 m/s and the index of refraction in water is 1.33. Answer in units of MeV. 008 (part 2 of 3) 10.0 points What is its kinetic energy? Answer in units of MeV. 009 (part 3 of 3) 10.0 points What is its momentum? Answer in units of MeV/c
Explanation / Answer
In relativistic mechanics,
total energy = gamma mc^2
rest energy = mc^2
kinetic energy = (gamma - 1)mc^2
So calculate gamma for v = 1.112 * c / nwater = 0.836 c
gamma = 1 / sqrt ( 1- 0.836^2) = 1.8224
mc^2 for an electron is 0.511 MeV.
momentum = gamma× mv
= 1.8224 × m×0.836c = 1.5235 mc
= 1.5235 * 0.511 MeV/c
=0.78 MeV/c
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