Chapter 33: Q22CQ (page 1211)
Suppose leptons are created in a reaction. Does this imply the weak force is acting? (for example, consider \(\beta \)decay.)
Yes, creation of leptons in a reaction signifies action of weak force.
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The 3.20 - km - longSLAC produces a beam of 50 GeV electrons. If there are 15,000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?
(a) Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible?
(b) This number is less than the number of known baryons. Explain why.
The decay mode of the positive tau is\({{\bf{\tau }}^ + } \to {\rm{ }}{{\bf{\mu }}^ + }{\rm{ }} + {\rm{ }}{{\bf{\nu }}_{\bf{\mu }}}{\rm{ }} + {\rm{ }}{{\bf{\bar \nu }}_{\bf{\tau }}}\).
(a) What energy is released?
(b) Verify that charge and lepton family numbers are conserved.
(c) The \({\tau ^ + }\)is the antiparticle of the \({\tau ^ - }\). Verify that all the decay products of the \({\tau ^ + }\)are the antiparticles of those in the decay of the \({\tau ^ - }\) given in the text.
The principal decay mode of the sigma zero is \[{{\rm{\Sigma }}^{\rm{0}}}{\rm{ }} \to {\rm{ }}{{\rm{\Lambda }}^{\rm{0}}}{\rm{ + \gamma }}\]. (a) What energy is released? (b) Considering the quark structure of the two baryons, does it appear that the \[{{\rm{\Sigma }}^{\rm{0}}}\]is an excited state of the \[{{\rm{\Lambda }}^{\rm{0}}}\]? (c) Verify that strangeness, charge, and baryon number are conserved in the decay. (d) Considering the preceding and the short lifetime, can the weak force be responsible? State why or why not.
In supernovas, neutrinos are produced in huge amounts. They were detected from the \({\rm{1987 A}}\) supernova in the Magellanic Cloud, which is about \({\rm{120,000}}\) light years away from the Earth (relatively close to our Milky Way galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, they can get close.
(a) Suppose a neutrino with a \({\rm{7 - eV/}}{{\rm{c}}^{\rm{2}}}\) mass has a kinetic energy of \({\rm{700 KeV}}\). Find the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/ {\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) for it.
(b) If the neutrino leaves the \({\rm{1987 A}}\) supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find \({\rm{v}}\) for the neutrino, since it \(\gamma \) is so large.)
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