Ch 44: Particle Physics and Cosmology

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 44: Particle Physics and Cosmology

Problem 18

Chapter 44, Problem 18

How much energy is released when a $µ^{-}$ muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.

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Identify the particles involved in the decay: a muon (µ⁻) at rest decays into an electron (e⁻) and two neutrinos. Since the neutrinos have negligible mass, their rest mass energy can be ignored.

Recall that the energy released in the decay comes from the difference in rest mass energies between the initial particle and the final particles. The muon has a rest mass energy of $m_\mu c^2$, and the electron has a rest mass energy of $m_e c^2$.

Write the expression for the energy released (Q-value) as the difference between the initial and final rest mass energies: $Q = (m_\mu - m_e) c^2$

Look up or recall the rest masses of the muon and electron (in kilograms or atomic mass units) and the speed of light $c$ (approximately $3 \times 10^8$ m/s) to use in the calculation.

Substitute the values into the equation and calculate the energy released, remembering to keep the units consistent (e.g., joules or electronvolts).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Muon Decay and Particle Rest Mass

Muon decay is a weak interaction process where a muon at rest transforms into an electron and two neutrinos. The muon’s rest mass energy is converted into the kinetic energy of the decay products. Understanding the rest mass energies of the particles involved is essential to calculate the energy released.

Conservation of Energy in Particle Decay

In particle decay, the total energy before and after the decay must be conserved. The initial rest mass energy of the muon equals the sum of the kinetic energies and rest mass energies of the decay products. Neglecting neutrino masses simplifies the calculation by focusing on the electron’s rest mass and kinetic energy.

Mass-Energy Equivalence (E=mc²)

Mass-energy equivalence states that mass can be converted into energy and vice versa, as described by Einstein’s equation E=mc². The difference in rest mass between the initial muon and the final electron corresponds to the energy released during decay, primarily carried away as kinetic energy of the decay products.

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Related Practice

Textbook Question

In Example $44.3$ , it was shown that a proton beam with an $800$ -GeV beam energy gives an available energy of $38.7$ GeV for collisions with a stationary proton target. In a colliding-beam experiment, what total energy of each beam is needed to give an available energy of $2 open paren 38.7$ GeV $close paren equals 77.4$ GeV?

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Textbook Question

You work for a start-up company that is planning to use antiproton annihilation to produce radioactive isotopes for medical applications. One way to produce antiprotons is by the reaction $p + p \to p + p + p + \overset{ˉ}{p}$ in proton-proton collisions. You first consider a colliding-beam experiment in which the two proton beams have equal kinetic energies. To produce an antiproton via this reaction, what is the required minimum kinetic energy of the protons in each beam?

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Textbook Question

A $K^{+}$ meson at rest decays into two $p$ mesons. What are the allowed combinations of $pi to the 0 power$ , $π^{+}$ , and $π^{-}$ as decay products?

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Textbook Question

Table $44.3$ shows that a $Σ^0$ decays into a $Lamda to the 0 power$ and a photon. What is the magnitude of the momentum of the photon? Is it reasonable to ignore the final momentum and kinetic energy of the $Lamda to the 0 power$ ? Explain.

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Textbook Question

If a $Σ^{+}$ at rest decays into a proton and a $pi to the 0 power$ , what is the total kinetic energy of the decay products?

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Textbook Question

Table $44.3$ shows that a $Sigma to the 0 power$ decays into a $Lamda to the 0 power$ and a photon. Calculate the energy of the photon emitted in this decay, if the $Lamda to the 0 power$ is at rest.

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How much energy is released when a µ−µ^- muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.

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Key Concepts

Muon Decay and Particle Rest Mass

Conservation of Energy in Particle Decay

Mass-Energy Equivalence (E=mc²)

How much energy is released when a $µ^{-}$ muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.