Chapter 39: Problem 3
Which of the following formed latest in the universe? a) quarks b) protons and neutrons c) hydrogen atoms d) helium nuclei e) gluons
Chapter 39: Problem 3
Which of the following formed latest in the universe? a) quarks b) protons and neutrons c) hydrogen atoms d) helium nuclei e) gluons
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Get started for freeA Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of \(I\left(95.1^{\circ}\right)=1129\) counts/s at a scattering angle of \(95.1^{\circ} \pm 0.4^{\circ} .\) At a second scattering angle, the intensity is measured to be 4840 counts/s. Assuming that the scattering obeys the Rutherford formula, what is that second angle (in degrees, to the same uncertainty)?
Some particle detectors measure the total number of particles integrated over part of a sphere of radius \(R,\) where the target is at the center of the sphere. Assuming symmetry about the axis of the incoming particle beam, use the Rutherford scattering formula to obtain the total number of particles detected in an an interval of width \(d \theta\) as a function of the scattering angle, \(\theta .\)
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 \(k_{\mathrm{B}} T\) of the universe at that temperature. b) Explain what happened to most of the hadrons-protons and neutrons-at that time. c) Explain what happened to electrons and positrons in terms of temperature and time.
A proton and a neutron interact via the strong nuclear force. Their interaction is mediated by a meson, much like the interaction between charged particles is mediated by photons-the particles of the electromagnetic field. a) Perform a rough estimate of the mass of the meson from the uncertainty principle and the known dimensions of a nucleus \(\left(\sim 10^{-15} \mathrm{~m}\right)\). Assume that the meson travels at relativistic speed. b) Use a line of reasoning similar to that in part (a) to prove that the theoretically expected rest mass of the photon is zero.
An electron-positron pair, traveling toward each other with a speed of \(0.99 c\) with respect to their center of mass, collide and annihilate according to \(e^{-}+e^{+} \rightarrow \gamma+\gamma\). Assuming that the observer is at rest with respect to the center of mass of the electron-positron pair, what is the wavelength of the emitted photons?
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