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Chapter 30: Problem 5

Which fundamental force is responsible for each of the decays shown here? [Hint: In each case, one of the decay products reveals the interaction force.] (a) \(\pi^{+} \rightarrow\) \(\mu^{+}+v_{\mu},\) (b) $\pi^{0} \rightarrow \gamma+\gamma(\mathrm{c}) \mathrm{n} \rightarrow \mathrm{p}^{+}+\mathrm{e}^{-}+\bar{v}_{\mathrm{e}}$

Short Answer

Expert verified
Answer: (a) Weak force, (b) Electromagnetic force, (c) Weak force.

Step by step solution

01

Identify the decay of a positive pion

The decay of a positive pion is represented as: \(\pi^{+} \rightarrow \mu^{+} + v_{\mu}\) Since one of the decay products is a muon (a charged lepton) the interaction force involved is the weak force, also called the weak nuclear force, which is responsible for decays involving charged leptons and neutrinos.
02

Identify the decay of neutral pion

The decay of a neutral pion is represented as: \(\pi^{0} \rightarrow \gamma + \gamma\) The decay products consist solely of photons, which indicate that the electromagnetic force is involved in this decay process. The electromagnetic force mediates interactions between charged particles, and photons are the quanta that carry this force.
03

Identify the decay of a neutron

The decay of a neutron is represented as: \(n \rightarrow p^{+} + e^{-} + \bar{v}_{e}\) Since one of the decay products is an electron (a charged lepton) and an anti-electron neutrino, the interaction force involved is again the weak force. The weak nuclear force is responsible for decays involving charged leptons and neutrinos. In conclusion, the responsible fundamental forces for the decay processes are: (a) Weak force (b) Electromagnetic force (c) Weak force

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Most popular questions from this chapter

The \(K^{0}\) meson can decay to two pions: \(K^{0} \rightarrow \pi^{+}+\pi^{-}\) The rest energies of the particles are: \(K^{0}=497.7 \mathrm{MeV}\) \(\pi^{+}=\pi^{-}=139.6 \mathrm{MeV} .\) If the \(K^{0}\) is at rest before it decays, what are the kinetic energies of the \(\pi^{+}\) and the \(\pi^{-}\) after the decay?
When a proton and an antiproton annihilate, the annihilation products are usually pions. (a) Suppose three pions are produced. What combination(s) of \(\pi^{+}, \pi^{-},\) and \(\pi^{0}\) are possible? (b) Suppose five pions are produced. What combination(s) of \(\pi^{+}, \pi^{-},\) and \(\pi^{0}\) are possible? (c) What is the maximum number of pions that could be produced if the kinetic energies of the proton and antiproton are negligibly small? The mass of a charged pion is \(0.140 \mathrm{GeV} / c^{2}\) and the mass of a neutral pion is \(0.135 \mathrm{GeV} / c^{2}.\)
At the Stanford Linear Accelerator, electrons and positrons collide together at very high energies to create other elementary particles. Suppose an electron and a positron, each with rest energies of \(0.511 \mathrm{MeV},\) collide to create a proton (rest energy \(938 \mathrm{MeV}\) ), an electrically neutral kaon \((498 \mathrm{MeV}),\) and a negatively charged sigma baryon \((1197 \mathrm{MeV}) .\) The reaction can be written as: $$\mathrm{e}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{p}^{+}+\mathrm{K}^{0}+\Sigma^{-}$$ (a) What is the minimum kinetic energy the electron and positron must have to make this reaction go? Assume they each have the same energy. (b) The sigma can decay in the reaction \(\Sigma^{-} \rightarrow \mathrm{n}+\pi^{-}\) with rest energies of \(940 \mathrm{MeV}\) (neutron) and \(140 \mathrm{MeV}\) (pion). What is the kinetic energy of each decay particle if the sigma decays at rest?
Two factors that can determine the distance over which a force can act are the mass of the exchange particle that carries the force and the Heisenberg uncertainty principle \([\mathrm{Eq} .(28-3)] .\) Assume that the uncertainty in the energy of an exchange particle is given by its rest energy and that the particle travels at nearly the speed of light. What is the range of the weak force carried by the \(\mathbf{Z}\) particle that has a mass of $92 \mathrm{GeV} / \mathrm{c}^{2} ?$ Compare this with the range of the weak force given in Table 30.3
In the Cornell Electron Storage Ring, electrons and positrons circulate in opposite directions with kinetic energies of 6.0 GeV each. When an electron collides with a positron and the two annihilate, one possible (though unlikely) outcome is the production of one or more proton-antiproton pairs. What is the maximum possible number of proton-antiproton pairs that could be formed?
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