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Chapter 11: Problem 6

In general, how do we determine if a particle reaction or decay occurs?

Short Answer

Expert verified
To determine if a particle reaction or decay occurs, we must analyze the conservation laws of energy, momentum, angular momentum, and charge, as well as the conservation of specific quantum numbers like lepton number, baryon number, strangeness, and charm. By verifying that all conservation laws and quantum numbers are conserved in the initial and final states, we can decide whether a given reaction or decay is allowed or forbidden.

Step by step solution

01

Identify the Initial and Final States

Determine the particles involved in the initial state (before the reaction or decay) and the final state (after the reaction or decay). Write down the respective particle symbols and their associated quantum numbers, including charge, baryon number, lepton number, and any other relevant quantum numbers.
02

Check Conservation Laws

Verify that the conservation laws are satisfied. This includes: - Conservation of energy: The total energy of the initial state should equal the total energy of the final state. - Conservation of momentum: The total momentum of the particles in the initial state should equal the total momentum of the particles in the final state. - Conservation of angular momentum: The total angular momentum of the initial state should equal the total angular momentum of the final state. - Conservation of charge: The total charge of the particles in the initial state should equal the total charge of the particles in the final state.
03

Check Quantum Number Conservation

Verify that the quantum numbers are conserved during the reaction or decay. This includes: - Lepton number conservation: The total lepton number (electron, muon, and tau) of the initial state should equal the total lepton number of the final state. - Baryon number conservation: The total baryon number of the initial state should equal the total baryon number of the final state. - Strangeness, charm, and other relevant quantum numbers: For specific particle reactions or decays, check the conservation of other relevant quantum numbers, such as the strangeness, charm, etc.
04

Analyze the Reaction or Decay

If all conservation laws and quantum numbers are conserved during the particle reaction or decay, then the process is allowed to occur. If one or more conservation laws or quantum numbers are not conserved, the process is forbidden and will not occur.

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Most popular questions from this chapter

Which of the following decays cannot occur because the law of conservation of lepton number is violated? (a) \(\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}\) (b) \(\mu^{+} \rightarrow \mathrm{e}^{+}+v_{\mathrm{e}}\) (c) \(\pi^{+} \rightarrow \mathrm{e}^{+}+v_{\mathrm{e}}+\bar{v}_{\mu}\) (d) \(\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^{+}+v_{\mathrm{e}}\) (e) \(\pi^{-} \rightarrow \mathrm{e}^{-}+\bar{v}_{\mathrm{e}}\) (f) \(\mu^{-} \rightarrow \mathrm{e}^{-}+\bar{v}_{\mathrm{e}}+v_{\mu}\) (g) \(\Lambda^{0} \rightarrow \pi^{-}+\mathrm{p}\) (h) \(\mathbf{K}^{+} \rightarrow \mu^{+}+v_{\mu}\)

Mesons are formed from the following combinations of quarks (subscripts indicate color and \(A R=\text { antired }):\) \(\left(d_{\mathrm{R}}, \bar{d}_{\mathrm{AR}}\right),\left(s_{\mathrm{G}}, \bar{u}_{\mathrm{AG}}\right),\) and \(\left(s_{\mathrm{R}}, \bar{s}_{\mathrm{AR}}\right)\). (a) Determine the charge and strangeness of each combination. (b) Identify one or more mesons formed by each quark-antiquark combination.

The peak intensity of the CMBR occurs at a wavelength of \(1.1 \mathrm{mm}\). (a) What is the energy in eV of a 1.1-mm photon? (b) There are approximately \(10^{9}\) photons for each massive particle in deep space. Calculate the energy of \(10^{9}\) such photons. (c) If the average massive particle in space has a mass half that of a proton, what energy would be created by converting its mass to energy? (d) Does this imply that space is "matter dominated"? Explain briefly.

Assuming a circular orbit for the Sun about the center of the Milky Way Galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass \(1.5 \times 10^{11}\) times that of the Sun (or \(3 \times 10^{41}\) kg ), located 30,000 ly away.

Distinguish between elementary particles and antiparticles. Describe their interactions.
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