33.6 GUTs: The Unification of Forces

What is the wavelength of a 50-GeV electron, which is produced at SLAC? This provides an idea of the limit to the detail it can probe.

The primary decay mode for the negative pion is $\pi^{- } \rightarrow \mu^{- } + \left(\overset{-}{\nu}\right)_{\mu}$. (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the $\pi^{- }$ is at rest when it decays? You may assume the muon antineutrino is massless and has momentum $p = E / c$, just like a photon.

Suppose you are designing a proton decay experiment and you can detect 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 $\text{10}^{\text{31}} \text{y}$? (b) How many cubic meters of water is this? (c) If the actual lifetime is $\text{10}^{\text{33}} \text{y}$, how long would you have to wait on an average to see a single proton decay?

(a) How much mass is converted to energy when a proton and antiproton annihilate each other? (b) How much energy is produced in the conversion above? (c) If energy were to produce a proton-antiproton pair, how much energy would this take? (d) What characteristic other than one being antimatter is different for a proton and an antiproton?