Chapter 33: Q11CQ (page 1210)
Why does the \({\eta ^0}\) meson have such a short lifetime compared to most other mesons?
As, the \({\eta ^0}\) meson consists of quark-antiquark pairs of the same flavour, its lifetime is short.
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Suppose you are designing a proton decay experiment and you can detect \({\rm{50}}\) percent of the proton decays in a tank of water.
(a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of \({\rm{1}}{{\rm{0}}^{{\rm{31}}}}{\rm{ y}}\)?
(b) How many cubic meters of water is this?
(c) If the actual lifetime is \({\rm{1}}{{\rm{0}}^{{\rm{33}}}}{\rm{ y}}\), how long would you have to wait on an average to see a single proton decay?
Consider a detector needed to observe the proposed, but extremely rare, decay of an electron. Construct a problem in which you calculate the amount of matter needed in the detector to be able to observe the decay, assuming that it has a signature that is clearly identifiable. Among the things to consider are the estimated half-life (long for rare events), and the number of decays per unit time that you wish to observe, as well as the number of electrons in the detector substance.
Suppose a \[{{\rm{W}}^{\rm{ - }}}\]created in a bubble chamber lives for \[{\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 25}}}}{\rm{\;s}}\]. What distance does it move in this time if it is traveling at \[{\rm{0}}{\rm{.900c}}\]? Since this distance is too short to make a track, the presence of the \[{{\rm{W}}^{\rm{ - }}}\]must be inferred from its decay products. Note that the time is longer than the given \[{{\rm{W}}^{\rm{ - }}}\]lifetime, which can be due to the statistical nature of decay or time dilation.
Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00 TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?
What lifetime do you expect for an antineutron isolated from normal matter?
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