Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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The range of the nuclear strong force is believed to be about 1.2 x 10-15 m. An early theory of nuclear physics proposed that the particle that “mediates” the strong force (similar to the photon mediating the electromagnetic force) is the pion. Assume that the pion moves at the speed of light in the nucleus, and calculate the time ∆t it takes to travel between nucleons. Assume that the distance between nucleons is also about 1.2 x 10-15 m. Use this time ∆t to calculate the energy ∆E for which energy conservation is violated during the time ∆t. This ∆E has been used to estimate the mass of the pion. What value do you determine for the mass? Compare this value with the measured value of 135 MeV/c2 for the neutral pion.
What is the uncertainty in the energy released in the decay of a π0 due to its short lifetime?
The f meson has mass 1019.4 MeV/c2 and a measured energy width of 4.4 MeV/c2 . Using the uncertainty principle, estimate the lifetime of the f meson.
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- If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV, what is the difference in their mass in kilograms?arrow_forwardThe Σ* particle has a rest energy of 1385 MeV and a lifetime of 2.0 × 10-23 s. What would be a typical range of outcomes of measurements of the Σ* rest energy?arrow_forward34. (a) A charged pi meson has a rest energy of 140 MeV and a lifetime of 26 ns. Find the energy uncertainty of the pi meson, expressed in MeV and also as a fraction of its rest energy. (b) Repeat for the uncharged pi meson with a rest energy of 135 MeV and a lifetime of 8.3 x 10" s. (c) Repeat for the rho meson with a rest energy of 765 MeV and a lifetime of 4.4 x 10 s.arrow_forward
- Mu mesons are subatomic particles which are created when cosmic rays strike the top of the atmosphere. The travel downward at 99.5% of the speed of light. Mu meson counters were placed at the top and bottom of Mt. Washington, which is 6265 feet (1909.6 m) tall. Mu mesons are unstable particles with a half-life of 1.53 x 106 s. 3. a. How long does it take the mu mesons to go from the top to the bottom of the mountain? How many half-lives is this? 6.40x10 s, 4.18 half-lives If the counter at the top of the mountain detects 560 mu mesons per second, how many should be detected after 4 half-lives? b. ou naz 35 per second MacBook Pro escarrow_forwardAnother component of the strong nuclear force is transmitted by the exchange of virtual K-mesons. Taking Kmesons to have an average mass of 495 MeV/c2 , what is the approximate range of this component of the strong force?arrow_forwardA linear accelerator designed to produce a beam of 800-MeV protons has 2000 accelerating tubes. What average voltage must be applied between tubes (such as in the gaps shown) to achieve the desired energy?arrow_forward
- The Σ− b (5816 MeV) resonance has a lifetime of 1.3 × 10^−22 s. What is its decay width? Help please, I know the answer is 2.5 MeV just not sure how to get there.arrow_forwardThe primary decay mode for the negative pion is π− → μ− + ν-μ . (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the π− is at rest when it decays? You may assume the muon antineutrino is massless and has momentum p = E / c , justlike a photon.arrow_forwardA Λ0 particle at rest decays into a proton and a π- meson. (a) Use the data as shown to find the Q value for this decay in MeV. (b) What is the total kinetic energy shared by the proton and the π- meson after the decay? (c) What is the total momentum shared by the proton and the π- meson? (d) The proton and the π- meson have momenta with the same magnitude after the decay. Do they have equal kinetic energies? Explain.arrow_forward
- (a) The most common decay mode of the Ξ− particle is Ξ− → Λ0 + π− . Using the quantum numbers in the table given above, show that strangeness changes by 1, baryon number and charge are conserved, and lepton family numbers are unaffected. (b) Is the decay K+ → μ+ + νμ allowed, given the quantum numbers in the table given above?arrow_forwardThere is a spread of about 100 MeV in the decay energy of the ∆+ , interpreted as uncertainty due to its short lifetime. What is its approximate lifetime?arrow_forwardThe highest energy beams at LEP achieved had E=104.5 GeV. As2...(a) Calculate how much larger was the synchrotron energy loss at this energy, relative to the synchrotron energy loss at E=45.1 GeV. (b) If protons had been used instead of electrons, how much smaller would the energy loss have been, for a beam energy of E=104.5 GeV?arrow_forward
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