Chapter 39: Problem 2
Which of the following is a composite particle? (select all that apply) a) electron b) neutrino c) proton d) muon
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The fundamental observation underlying the Big Bang theory of cosmology is Edwin Hubble's 1929 discovery that the arrangement of galaxies throughout space is expanding. Like the photons of the cosmic microwave background, the light from distant galaxies is stretched to longer wavelengths by the expansion of the universe. This is not a Doppler shift: Except for their local motions around each other, the galaxies are essentially at rest in space; it is the space itself that expands. The ratio of the wavelength of light \(\lambda_{\text {rec }}\) Earth receives from a galaxy to its wavelength \(\lambda_{\text {emit }}\) at emission is equal to the ratio of the scale factor (e.g., radius of curvature) \(a\) of the universe at reception to its value at emission. The redshift \(z\) of the light-which is what Hubble could measure - is defined by \(1+z=\lambda_{\text {rec }} / \lambda_{\text {emit }}=a_{\text {rec }} / a_{\text {emit }}\). a) Hubble's Law states that the redshift \(z\) of light from a galaxy is proportional to the galaxy's distance from us (for reasonably nearby galaxies): \(z \cong c^{-1} H \Delta s\), where \(c\) is the vacuum speed of light, \(H\) is the Hubble constant, and \(\Delta s\) is the distance of the galaxy. Derive this law from the first relationships stated in the problem, and determine the Hubble constant in terms of the scale-factor function \(a(t)\). b) If the present Hubble constant has the value \(H_{0}=72(\mathrm{~km} / \mathrm{s}) / \mathrm{Mpc},\) how far away is a galaxy, the light from which has redshift \(z=0.10\) ? (The megaparsec \((\mathrm{Mpc})\) is a unit of length equal to \(3.26 \cdot 10^{6}\) light-years. For comparison, the Great Nebula in Andromeda is approximately 0.60 Mpc from us.)
At about \(10^{-6}\) s after the Big Bang, the universe had cooled to a temperature of approximately \(10^{13} \mathrm{~K}\). a) Calculate the thermal energy. b) Explain what would happen to most of the hadronsprotons and neutrons. c) Explain also about the electrons and positrons in terms of temperature and time.
Draw possible Feynman diagrams for the following phenomena: a) protons scattering off each other b) neutron beta decays to a proton: \(n \rightarrow p+e^{-}+\bar{\nu}_{e}\).
Within three years after it begins operation, the proton beam at the Large Hadron Collider at CERN is expected to reach a luminosity of \(10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}\) (this means that in a \(1-\mathrm{cm}^{2}\) area, \(10^{34}\) protons encounter each other every second). The cross section for collisions, which could lead to direct evidence of the Higgs boson, is approximately \(1 \mathrm{pb}\) (picobarn). [These numbers were obtained from "Introduction to LHC physics," by G. Polesello, Journal of Physics: Conference Series \(53(2006), 107-116 .]\) If the accelerator runs without interruption, approximately how many of these Higgs events can one expect in one year at the LHC?
a) Calculate the kinetic energy of a neutron that has a de Broglie's wavelength of \(0.15 \mathrm{nm}\). Compare this with the energy of an X-ray photon that has the same wavelength. b) Comment on how this would be relevant for investigating biological samples with neutrons vs. X-rays.
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