Question

Review. Around the core of a nuclear reactor shielded by a large pool of water, Cerenkov radiation appears as a blue glow. (See Fig. P 17.38 on page 507.) Cerenkov radiation occurs when a particle travels faster through a medium than the speed of light in that medium. It is the electromagnetic equivalent of a bow wave or a sonic boom. An electron is traveling through water at a speed 10.0 % faster than the speed of light in water. Determine the electron's(d) Find the angle between the shock wave and the electron's direction of motion.

Answer 1

The angle between the shock wave and the electron's direction of motion in Cerenkov radiation can be found using the formula θ = cos^{-1}(1/β), where β is the ratio of the particle's speed to the speed of light in water.

Step-by-step explanation:

Cerenkov radiation is a phenomenon where charged particles emit a characteristic blue glow when they travel through a medium at speeds greater than the speed of light in that medium. To find the angle between the shock wave and the electron's direction of motion, we can use the formula for Cerenkov radiation, which is given by θ = β{-1}, where β is the ratio of the particle's speed to the speed of light in the medium. Since the electron is moving at a speed 10% faster than the speed of light in water (β = 1.10), we use the inverse cosine function to determine the angle, θ = cos{-1}(1/β) = cos{-1}(1/1.10).

Answer 2

The angle between the Cerenkov radiation shock wave and the electron's direction of motion, when the electron travels through water at a speed 10% faster than the speed of light in that medium, is approximately 24.6°.

Step-by-step explanation:

The student is asking about Cerenkov radiation and the angle formed between the shock wave (or light cone) and the direction of an electron's motion as it passes through water at a speed greater than the speed of light in that medium. To find this angle, we can use the Cerenkov radiation condition which states that the radiation occurs when a charged particle (like an electron) moves through a dielectric medium at a speed greater than the phase velocity of light in that medium. Since the speed of light in water is approximately 0.75c, and the electron is moving at 1.10c (10% faster), we can use the equation derived from the Cerenkov effect: cos(θ) = β∑1, where θ is the angle between the shock wave and the electron's direction of motion and β is the velocity of the particle divided by the speed of light in the same medium.

The angle θ can be calculated using the expression 1/β, which equals the ratio of the speed of light in water to the electron's speed. Since β is 1.10 (the speed of the electron is 1.10 times the speed of light in water), the calculation becomes cos(θ) = 1/1.10, which simplifies to cos(θ) = 0.909. Using the inverse cosine function, we find that θ is approximately 24.6°. Therefore, the angle between the shock wave and the electron's direction of motion is approximately 24.6°.