Chapter 39: Problem 4
?An exchange particle for the weak force is the a) photon. b) meson. c) \(W\) boson. d) graviton. e) gluon.
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Protons with a kinetic energy of \(2.00 \mathrm{MeV}\) scatter off gold nuclei in a foil target. Each gold nucleus contains 79 protons. If both the incoming protons and the gold nuclei can be treated as point objects, what is the differential cross section that will cause the protons to scatter off the gold nuclei at an angle of \(30.0^{\circ}\) from their initial trajectory?
Figure 39.34 shows a Feynman diagram for the fundamental process involved in the decay of a free neutron: One of the neutron's down quarks converts to an up quark, emitting a virtual \(W^{-}\) boson, which decays into an electron and an anti-electron-neutrino (the only decay energetically possible). Sketch the basic Feynman diagram for the fundamental process involved in each of the following decays: a) \(\mu^{-} \rightarrow e^{-}+\nu_{\mu}+\bar{\nu}_{e}\) b) \(\tau^{-} \rightarrow \pi^{-}+\nu_{\tau}\) c) \(\Delta^{++} \rightarrow p+\pi^{+}\) d) \(K^{+} \rightarrow \mu^{+}+\nu_{\mu}\) e) \(\Lambda^{0} \rightarrow p+\pi\)
Which of the following formed latest in the universe? a) quarks b) protons and neutrons c) hydrogen atoms d) helium nuclei e) gluons
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 space itself that expands. The ratio of the wavelength of light received at Earth from a galaxy, \(\lambda_{\text {rec }}\), to its wavelength at emission, \(\lambda_{\text {emit }}\), is equal to the ratio of the scale factor (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 Earth (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 from Earth. Derive this law from the relationships described in the problem statement, and determine the Hubble constant in terms of the scale- factor function \(a(t)\). b) If the Hubble constant currently has the value \(H_{0}=72(\mathrm{~km} / \mathrm{s}) / \mathrm{Mpc},\) how far away is a galaxy whose light has the 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 Earth.)
A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of \(I\left(94.9^{\circ}\right)=853\) counts/s at a scattering angle of \(94.9^{\circ} \pm 0.7^{\circ} .\) What is the intensity (in counts/s) at a scattering angle of \(60.5^{\circ} \pm 0.7^{\circ}\) if the scattering obeys the Rutherford formula?
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