When high-energy charged particles move through a transparent medium with a spee

Question

When high-energy charged particles move through a transparent medium with a speed greater than the speed of light in that medium, a shock wave, or bow wave, of light is produced. This phenomenon is called the Cerenkov effect. When a nuclear reactor is shielded by a large pool of water, Cerenkov radiation can be seen as a blue glow in the vicinity of the reactor core due to high-speed electrons moving through the water. In a particular case, the Cerenkov radiation produces a wave front with an apex half-angle of 53.5degree. Calculate the speed of the electrons in the water. The speed of light in water is 2.25 x 108 m/s.

Explanation / Answer

Let the velocity of electrons be v.

For Cherenkov effect, if apex half angle = theta,

cos (theta) = velocity of light in the medium / velocity of electrons in the medium

So,

cos (53.5) = 2.25 * 108 / v

v = 2.25 * 108 / 0.5948

v = 3.782 * 108 m/s

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