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Chapter 11: Problem 50

At full energy, protons in the 2.00 -km-diameter Fermilab synchrotron travel at nearly the speed of light, since their energy is about 1000 times their rest mass energy. (a) How long does it take for a proton to complete one trip around? (b) How many times per second will it pass through the target area?

Short Answer

Expert verified
(a) The time it takes for a proton to complete one trip around the Fermilab synchrotron is approximately \(2.0944 \times 10^{-5}\) seconds. (b) The proton will pass through the target area about 47765.71 times per second.

Step by step solution

01

Calculate the circumference of the synchrotron

Given the diameter of the synchrotron is 2.00 km, we can find its circumference using the formula: Circumference (C) = π × diameter Since the diameter is given in km, let's first convert it to meters (1 km = 1000 m): Diameter = 2.00 km × 1000 m/km = 2000 m Now, we can calculate the circumference: C = π × 2000 m ≈ 6283.185 m
02

Calculate the time taken for one trip around

We know that the protons travel at nearly the speed of light, which is approximately 3.00 × 10^8 m/s. We can use the formula for speed to find out how long it takes for the proton to complete one trip: Time (t) = Distance (C) / Speed (v) t = 6283.185 m / (3.00 × 10^8 m/s) ≈ 2.0944 × 10^{-5} s
03

Calculate the number of times the proton passes through the target area per second

To find out how many times the proton passes through the target area per second, we need to calculate the reciprocal of the time taken for one trip around: Frequency (f) = 1 / Time (t) f = 1 / (2.0944 × 10^{-5} s) ≈ 47765.71 times/s Therefore, (a) the time it takes for a proton to complete one trip around the Fermilab synchrotron is approximately 2.0944 × 10^{-5} seconds, and (b) the proton will pass through the target area about 47765.71 times per second.

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Most popular questions from this chapter

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Which of the following reactions cannot because the law of conservation of strangeness is violated? (a) \(\mathrm{p}+\mathrm{n} \rightarrow \mathrm{p}+\mathrm{p}+\pi^{-}\) (b) \(\mathrm{p}+\mathrm{n} \rightarrow \mathrm{p}+\mathrm{p}+\mathrm{K}^{-}\) (c) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \mathrm{K}^{-}+\sum^{+}\) (d) \(\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{+}+\sum^{-}\) (e) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \Xi^{0}+\mathrm{K}^{+}+\pi^{-}\) (f) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \Xi^{0}+\pi^{-}+\pi^{-}\) (g) \(\pi^{+}+\mathrm{p} \rightarrow \Sigma^{+}+\mathrm{K}^{+}\) (h) \(\pi^{-}+\mathrm{n} \rightarrow \mathrm{K}^{-}+\Lambda^{0}\)

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