Particles accelerators such as the Large Hadron Collider (LHC) can accelerate particles up to tremendous energies. Suppose the LHC accelerates alpha particles (a.k.a. helium nuclei with a charge of +2e and a mass of 6.645 x 10^-27 kg) with a kinetic energy of 7.5 TeV*, what would the speed of one particle be if relativistic effects** are ignored?Give your answer in units of Gm/s.*T as in Tera, for 10^12. “eV” stands for “electron volt,” which is a non-SI unit of energy equal to what one electron would gain after travelling through 1V. 1eV = 1.602 x 10^-19 J.**Special relativity is necessary to correctly account for the limiting speed of light, which is about 3 x 10^8 m/s. Note that in ignoring this effect and applying Newtonian mechanics (what you learned in Phys1210 or equivalent), you’ll be getting a speed way above 0.3 Gm/s. That’s just how insanely energetic the LHC is.

Mass of alpha particles (m) = 6.645×10-27 kg Kinetic energy (E) = 7.5 TeV

Answered: Particles accelerators such as the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Derive an expression for E using the attached equation (Lorentz Force Law), and calculate a predicted value for E in N/C if a particle had v = 40 m/s, q = -0.001 C, m = 0.3 ⨉ 10 -3 kg, and B = 0.6 T.
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measured by this observer to be 10 times longer than its lifetime when at rest relative to the observer? 3. The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.9 x 108m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? 4. A computer in a laboratory requires 2.50 us to make a certain calcu- lation, as measured by a scientist in the lab. To someone moving past the lab at a relative speed of 0.995c, how long will the same cal- culation take? 5. The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as V1-v²/c² times the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 95 percent the speed of light? 6. If an electron is speeding down the two-mile-long Stanford Linear Accelerator at 99.98 percent the speed of light,…
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1. A cosmic ray particle enters the Earth's atmosphere at 97% of the speed of light (0.970c). The proper time of travel to the ground is 2.749 x 10 sec. What is the relativistic, 'dilated' time? 2. The Starship Enterprise, according some Trekkie analysts, is 300 meters long. If it is traveling at 0.952c, what would its length, L, be as seen from Earth? [Ch 28] 3. A given photon has a frequency of 6.5 x 10" sec". What is this photon's energy? CHAPTER 29-30 The electron in a hydrogen atom undergoes a transition from the 2nd excited state (n-3) to the ground state (n-1).* How much energy, in eV, will be given off by the electron? Use three significant figures. Note that, for hydrogen, E, =-13.6 eV. *This is a transition in the Lyman series, which involves transitions between n= 1 and higher states. The wavelengths are in the ultraviolet. The Balmer series, which involves transitions between n 2 and higher states, yields light in the visible.

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