Explanation Refractive index of the crown glass is 1.52 . Write the expression for velocity of light in a medium v = c n (I) Here, v is the velocity of light in the medium, c is the speed of light in vacuum and n is the refractive index of the medium. To create Cerenkov radiation, the velocity of the particle in the medium should be greater than the velocity of light in that medium. Thus, minimum velocity of the particle to create Cerenkov radiation is v . Write the expression for relativistic kinetic energy. K = E 0 ( 1 1 − ( u / c ) 2 − 1 ) (II) Here, K is the kinetic energy of the electron, u is the speed of the electron and E 0 is the rest mass energy. The expression for rest mass energy is. E 0 = m c 2 (III) Here, m is the mass of the electron. Conclusion: Substitute 1.52 for n in (I) to find v in terms of c v = c 1.52 = 0.658 c Substitute 9.11 × 10 − 31 kg for m and 3.00 × 10 8 ms − 1 for c in (III) to find E 0

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Chapter 27, Problem 51GP

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Find the minimum kinetic energy of an electron to create Cerenkov radiation in a crown glass.

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Chapter 27, Problem 50GP

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