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Chapter 39: Problem 14
Is it possible for a charged particle to be its own antiparticle?
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Some grand unification theories suggest that the decay \(p \rightarrow \pi^{0}+e^{+}\) may be possible, in which case all matter may eventually become radiation. Are (a) baryon number and (b) electric charge conserved in this hypothetical proton decay?
The radiation that we observe as the cosmic microwave background started out largely as infrared. Why is it now the microwave background?
Your roommate is writing a science-fiction novel set very far in the future, 60 Gy after the Big Bang. One of the characters is a cosmologist, and your roommate wants to know what the cosmologist will measure for the Hubble constant. What's your answer, assuming a steady expansion rate?
(a) By what factor must the magnetic field in a proton synchrotron be increased as the proton energy increases by a factor of \(10 ?\) Assume the protons are highly relativistic, so \(\gamma \gg 1\). (b) By what factor must the diameter of the accelerator be increased to raise the energy by a factor of 10 without changing the magnetic field?
Many particles are far too short-lived for their lifetimes to be measured directly. Instead, tables of particle properties often list "width," measured in energy units and indicating the width of the distribution of measured rest energies. For example, the \(Z^{0}\) has mass \(91.18 \mathrm{GeV}\) and width 2.5 GeV. Use the energy-time uncertainty relation to estimate its corresponding lifetime.
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