College Physics With an Integrated Approach to Forces and Kinematics

Alan Giambattista, Betty McCarthy Richardson , Robert C. Richardson

Chapter 30

Particle Physics - all with Video Answers

Educators

Chapter Questions

Problem 1

A pion (mass $0.140 \mathrm{GeV} / c^{2}$ ) at rest decays by the weak interaction into a muon of mass $0.106 \mathrm{GeV} / \mathrm{c}^{2}$ and a
muon antineutrino: $\pi^{-} \rightarrow \mu^{-}+\bar{v}_{\mu}$. Ignoring the rest energy of the antineutrino, what is the total kinetic energy of the muon and the antineutrino?

Ren Jie Tuieng

Ren Jie Tuieng

Numerade Educator

Problem 2

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 [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 $Z$ particle that has a mass of $92 \mathrm{GeV} / c^{2}$ ? Compare this with the range of the weak force given in Table $30.3$.

Ren Jie Tuieng

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Problem 3

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 [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 $Z$ particle that has a mass of $92 \mathrm{GeV} / c^{2}$ ? Compare this with the range of the weak force given in Table $30.3$.

Ren Jie Tuieng

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Problem 4

Show that the charge of the neutron and the charge of the proton can be derived from their constituent quark content.

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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) $\pi^{+} \rightarrow$ $\mu^{+}+v_{\mu},(\mathrm{b}) \pi^{0} \rightarrow \gamma+\gamma(\mathrm{c}) \mathrm{n} \rightarrow \mathrm{p}^{+}+\mathrm{e}^{-}+\bar{v}_{\mathrm{e}}$

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Problem 6

Three types of sigma baryons can be created in accelerator collisions. Their quark contents are given by uus, uds, and dds, respectively. What are the electric charges of each of these sigma particles, respectively?

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Problem 7

The energy at which the fundamental forces are expected to unify is about $10^{19} \mathrm{GeV}$. Find the mass (in kilograms) of a particle with rest energy $10^{19} \mathrm{GeV}$.

Narayan Hari

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Problem 8

What is the de Broglie wavelength of a proton with kinetic energy $1.0 \mathrm{TeV}$ ?

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Problem 9

What is the de Broglie wavelength of an electron with kinetic energy $7.0 \mathrm{TeV} ?$

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Problem 10

In the Cornell Electron Storage Ring, electrons and positrons circulate in opposite directions with kinetic energies of $6.0 \mathrm{GeV}$ 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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Problem 11

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?

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Problem 12

A proton in Fermilab's Tevatron is accelerated through ? potential difference of $2.5$ MV during each revolution around the ring of radius $1.0 \mathrm{~km} .$ In order to reach an energy of $1 \mathrm{TeV}$, how many revolutions must the proton make? How far has it traveled?

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Problem 13

Estimate the magnetic field strength required at the $\mathrm{LHC}$ to make $7.0$ -TeV protons travel in a circle of circumference $27 \mathrm{~km}$. Start by deriving an expression, using Newton's second law, for the field strength $B$ in terms of the particle's momentum $p$, its charge $q$, and the radius $r$. Even though derived using classical physics, the expression is relativistically correct. (The estimate will come out much lower than the actual value of $8.33 \mathrm{~T}$. In the $\mathrm{LHC}$, the protons do not travel in a constant magnetic field; they move in straight-line segments between magnets.)

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Problem 14

A muon decay is described by $\mu^{-} \rightarrow \mathrm{e}^{-}+v_{\mu}+\bar{v}_{\mathrm{e}}$. What is the maximum kinetic energy of the electron, if the muon was at rest? Assume that the electron is extremely relativistic and ignore the small masses of the neutrinos.

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Problem 15

A neutral pion (mass $0.135 \mathrm{GeV} / \mathrm{c}^{2}$ ) decays via the electromagnetic interaction into two photons: $\pi^{0} \rightarrow \gamma+\gamma$ What is the energy of each photon, assuming the pion was at rest?

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Problem 16

A proton of mass $0.938 \mathrm{GeV} / c^{2}$ and an antiproton, at rest relative to an observer, annihilate each other as described by $\mathrm{p}+\overline{\mathrm{p}} \rightarrow \pi^{-}+\pi^{+}$. What are the kinetic energies of the two pions, each of which has mass $0.14 \mathrm{GeV} / \mathrm{c}^{2}$ ?

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Problem 17

In an accelerator, two protons with equal kinetic energies collide head-on. The following reaction takes place:
$\mathrm{p}+\mathrm{p} \rightarrow \mathrm{p}+\mathrm{p}+\mathrm{p}+\overline{\mathrm{p}}$. What is the minimum possible
kinetic energy of each of the incident proton beams?

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Problem 18

Determine the quark content of these particles:
A meson with charge $+e$ composed of up and/or strange quarks and/or antiquarks.

Raj Bala

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Problem 19

Determine the quark content of these particles:
A baryon with charge 0 composed of up and/or strange quarks and/or antiquarks.

Raj Bala

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Problem 20

Determine the quark content of these particles:
An antibaryon with charge $+e$ composed of up and/or strange quarks and/or antiquarks.

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Problem 21

Determine the quark content of these particles:
A meson with charge $-e$ composed of up and/or down quarks and/or antiquarks.

Raj Bala

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Problem 22

According to Figure $30.2$, higher energies correspond with times that are closer to the origin of the universe, so particle accelerators at higher energies probe conditions that existed shortly after the Big Bang. At Fermilab's Tevatron, protons and antiprotons are accelerated to kinetic energies of approximately $1 \mathrm{TeV}$. Estimate the time after the Big Bang that corresponds to protonantiproton collisions in the Tevatron.

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Problem 23

A charged pion can decay either into a muon or an electron. The two decay modes of a $\pi^{-}$ are: $\pi^{-} \rightarrow \mu^{-}+\bar{v}_{p}$ and $\pi^{-} \rightarrow \mathrm{e}^{-}+\bar{v}_{\mathrm{e}}$. Write the two decay modes for the $\pi^{+}$. [Hint: $\pi^{+}$ is the antiparticle of $\pi^{-}$. Replace each particle in the decay reaction with its corresponding antiparticle.]

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Problem 24

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 $0.135 \mathrm{GeV} / c^{2}$

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Problem 25

In Problem 1, what is the kinetic energy of the muon? [Hint: The muon is nonrelativistic, so its kinetic energymomentum relationship is $K=p^{2} /(2 m) .$ The antineutrino is extremely relativistic.]

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Problem 26

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\textrm{MeV} ) . \text { 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 $\Sigma^{-} \rightarrow n+\pi^{-}$ 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?

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Problem 27

A sigma baryon at rest decays into a lambda baryon and a photon: $\Sigma^{0} \rightarrow \Lambda^{0}+\gamma$. The rest energies of the baryons are given by $\Sigma^{0}=1192 \mathrm{MeV}$ and $\Lambda^{0}=1116 \mathrm{MeV}$. What is the photon wavelength? [Hint: Use relativistic formulas and be sure momentum is conserved as well as
energy.]

Ren Jie Tuieng

Numerade Educator