Chapter Questions
Why is it easier to create proton-antiproton pairs by colliding beams of protons, rather than firing a proton beam into a stationary target?
Discuss the similarities and differences between the photon and neutrino.
For a particle that mediates a particular force, what is the relationship between the particle's mass and the range of the force?
Two protons collide, and out come three protons and an antiproton. How is this possible?
Discuss similarities and differences between the pion and muon. When the muon was first detected, physicists thought it may have been a pion. Why was there confusion?
What particle mediates the force between two positrons?
Of the 12 fundamental matter particles (six leptons and six quarks), which can only be found as constituents of composite particles?
All quarks have spin $\frac{1}{2}$. Explain why baryons have spin $\frac{1}{2}$ or $3 / 2$ but mesons all have spin 0 .
Why is it necessary to attach the property of "color" to quarks?
Why is synchrotron radiation a feature of circular particle accelerators but not linear accelerators?
Explain the origin of the cosmic microwave background.
In reactions that create new particles, a conserved quantity is(a) the number of particles;(b) kinetic energy; (c) electric charge.
In $\beta^{-}$ decay, the particles produced are an electron and (a) a neutrino; (b) an antineutrino; (c) a photon; (d) a proton.
The rest energy of the negative pion $\left(\pi^{-},\right.$ mediator of the nuclear force) is $140 \mathrm{MeV}$. Based on the pion's rest energy, the range ofthe nuclear force should be about (a) $0.35 \mathrm{fm} ;$ (b) $1.0 \mathrm{fm} ;$ (c) $1.4 \mathrm{fm}$ (d) $1.8 \mathrm{fm}$
Which one of the following reactions is allowed? (a) $p+$ $p \rightarrow p+p+n ;$ (b) $p+p \rightarrow p+\pi^{+}+\gamma ;$ (c) $p \rightarrow n+\pi^{+}$(d) $p+\bar{p} \rightarrow \Lambda+\bar{\Lambda}$
Which one of the following reactions is allowed? (a) $\mu^{-}+$ $p \rightarrow n+\bar{\nu}_{\mu} ;$ (b) $\mu^{-}+p \rightarrow n+\nu_{\mu}$ (c) $e^{-}+p \rightarrow n+\bar{\nu}_{e}$ (d) $\mu^{-} \rightarrow n+e^{-}+\bar{\nu}_{\mu}+\nu_{e}$.
Complete the following reaction: $\tau^{-}+p \rightarrow n+$ _______ . (a) $e^{-}$; (b) $e^{+} ;(\mathrm{c}) \nu_{\tau} ;(\mathrm{d}) \bar{\nu}_{\tau}$
The quark compositions of four mesons are given. Which has strangeness $-1 ?($ a $) u \bar{s}$ (b) $s \bar{s} ;(\operatorname{c}) s \bar{u} ;(\mathrm{d}) c \bar{c}$.
The quark compositions of four mesons are given. Which meson has a charm number of $-1 ?(\mathrm{a}) c \bar{d} ;(\mathrm{b}) c \bar{u} ;(\mathrm{c}) s \bar{c} ;(\mathrm{d}) c \bar{c} .$
The predominant constituent of the universe is (a) ordinary matter, (b) dark matter, (c) dark energy.
How much energy is required to produce a neutron-antineutron pair?
An electron and positron at rest annihilate and form two photons, which have the same energy and emerge in opposite directions. Find the energy and wavelength of each photon.
Repeat the preceding problem if the electron and positron were moving toward each other at $0.5 c$ in the lab frame.
If you want to produce a neutron-antineutron pair using colliding neutron beams, what should be the speed of the colliding neutrons?
Consider the beta decay ${ }^{10} \mathrm{Be} \rightarrow{ }^{10} \mathrm{~B}+\beta^{-},$ with the beryllium nucleus initially at rest. (a) How much energy is released?(b) What other particle is produced? (c) What are the possible energies of that other particle?
The starship Enter prise on the television program Star Trek was powered by a matter-antimatter reactor. Suppose you have a 25,000 -metric-ton starship and wish to accelerate it to $0.01 c$. What is the total mass of matter and antimatter required, assuming a $100 \%$ efficient engine?
The positive pion $\pi^{+}$ has rest energy $140 \mathrm{MeV}$. Use this value to estimate the range of the strong force.
Physicists have proposed a particle called the Higgs particle, which would explain why other particles have the masses they do. If the Higgs' rest energy is $150 \mathrm{GeV},$ what's the range of the force it mediates?
What mass do you expect the graviton to have, if it is detected? What difficulties might there be in detecting a particle with this mass?
Physicists believe that the omega particle $(\omega),$ with rest energy of $782 \mathrm{MeV},$ might be the mediator of a short-range repulsive force. What would be the range of that force?
The neutral pion is unstable, with lifetime around $8.4 \times 10^{-17} \mathrm{~s}$. (a) Use the uncertainty principle to estimate the interaction time when the pion mediates the nuclear force, and compare with the pion's lifetime. Repeat for the charged pions, with lifetimes of $2.6 \times 10^{-8} \mathrm{~s}.$
To use high-energy particles as probes of other subatomic particles, the probe particles' de Broglie wavelength must be comparable to the distance being probed. Suppose you want to probe an elementary particle on a distance scale of about $1.0 \times 10^{-18} \mathrm{~m} .$ Find the kinetic energy of $(\mathrm{a})$ a proton and $(\mathrm{b})$ an electron used to probe this distance scale.
Draw a Feynman diagram for the $\beta^{+}$ decay of $22 \mathrm{Na}$. (Remember that $\beta^{+}$ decay produces a positron and a neutrino.)
Fill in the following reactions with the missing particle or particles: (a) $\mu^{-} \rightarrow e^{-}+$ ______ ; (b) $\mu^{+} \rightarrow e^{+}+$ _____.
Fill in the following reactions with the missing particle or particles: (a) $\tau^{-} \rightarrow e^{-}+$ ______ ; (b) $\tau^{+} \rightarrow e^{+}+$ ________ ; (c) $\tau^{-} \rightarrow$ $\mu^{-}+$ ________ ; (d) $\tau^{+} \rightarrow \mu^{+}+$ ________.
A $\mu^{-}$ and $\mu^{+}$ at rest annihilate to form two gamma rays, which emerge in opposite directions. Find the energy and wavelength of each gamma ray.
Fill in the following reactions with the missing particle or particles: (a) $\mathrm{K}^{-} \rightarrow \mu^{-}+$ ______ ; (b) $\Lambda \rightarrow n+$ _______ .
Fill in the following reactions with the missing particle or particles: (a) _______ $+p \rightarrow n+e^{+} ;(\mathrm{b}) \mathrm{K}^{+} \rightarrow \mu^{+}+$ __________ .
The neutral pion decays by emitting two gamma rays. If the pion is initially at rest, what are the energy and wavelength of the gamma rays?
Which of the following decays or reactions is allowed? For those that aren't allowed, explain why not. (a) $\Lambda \rightarrow p+\pi^{-}$; (b) $\pi^{+} \rightarrow \mu^{+}+n+\bar{\nu}_{\mu} ;$ (c) $p+\pi^{-} \rightarrow p+\Sigma^{+}$.
Which of the following decays or reactions is allowed? For those that aren't, explain why not. (a) $\Xi^{-} \rightarrow \Lambda+\pi^{-}$; (b) $e^{+}+\pi^{0} \rightarrow p+\nu_{e}$ (c) $\Xi^{0} \rightarrow \bar{p}+\pi^{-}$.
The $\Sigma^{+}$ particle decays via the reaction $\Sigma^{+} \rightarrow p+\pi^{0}$. For this reaction, discuss how the following conservation laws apply:electric charge, mass-energy, baryon number, lepton number, spin, strangeness.
Trace all possible decay sequences for the $\Omega^{-}$ baryon down to stable particles.
Consider the decay of the $\Omega^{-}$ particle via the reaction $\Omega^{-} \rightarrow \Lambda+\mathrm{K}^{-} .$ (a) If the omega was originally at rest, how much energy is available for the kinetic energy of the two products? (b) Which of the products gets more kinetic energy?
For the decay in the preceding problem, find the kinetic energy of each product.
The $\Omega^{-}$ particle has a quark configuration sss. What do you expect for the quark configuration of the $\Omega^{+} ?$
The $\Xi^{-}$ particle is a baryon with strangeness -2 that contains a down quark and a strange quark. (a) What must be the third quark? (b) What do you expect for the quark configuration and electric charge of the $\boldsymbol{\Xi}^{-}$ 's antiparticle?
The $\mathrm{D}^{0}$ meson has quark configuration $c \bar{u}$. (a) What's the quark configuration of the $\overline{\mathrm{D}}^{0}$ ? (b) Which properties are the same for the $\mathrm{D}^{0}$ and its antiparticle, and which are different?
The $\mathrm{D}_{S}^{-}$ meson has +1 for both strangeness and charm. What quark-antiquark combination produces this meson?
For the proton, $\Sigma^{0},$ and $\Delta^{+},$ show that the electric charge, baryon number, strangeness, and charm are all equal to the sums of the corresponding numbers for the constituent quarks.
Repeat the preceding problem for these particles: $\mathrm{K}^{+}, \mathrm{D}^{+}$, and $\mathrm{B}^{+}$.
Trace the evolution and transformation of quarks in the reaction $\Sigma^{+} \rightarrow p+\pi^{0}$ and the subsequent decay of the neutral pion.
Trace the evolution and transformation of quarks in the reaction $\Sigma^{-} \rightarrow n+\pi^{-}$ and the subsequent decay of the negative pion.
What are all possible quark configurations for baryons with charge (a) $2 e$ and $(\mathrm{b})-2 e ?$
Find the speed of 7 -TeV protons at the LHC accelerator at CERN.
Find and compare the speeds of (a) 1 -GeV electrons and (b) 1 -GeV protons.
Consider the formation of antiprotons via the reaction $p+p \rightarrow p+p+p+\bar{p} .$ Find the accelerator energies needed to initiate this reaction in (a) a colliding-beam experiment and(b) a stationary-target experiment.
The Alternating Gradient Synchrotron at Brookhaven National Laboratory in New York accelerates protons to a kinetic energy of $33 \mathrm{GeV}$. Find the time required for a proton to traverse the accelerator's 800 -m circumference.
When a $50-\mathrm{GeV}$ electron in the SLAC linear accelerator strikes a proton in a stationary target, how much energy is available to create new particles?
Compare the energy available between colliding-beam and stationary-target experiments with proton-proton collisions for each of these kinetic energies:(a) $1.0 \mathrm{GeV}$;(b) $10 \mathrm{GeV}$;(c) $100 \mathrm{GeV}$.
The cyclotron frequency is given by Equation 18.5 as $f_{\mathrm{c}}=|q| B / 2 \pi m,$ but this expression has to be corrected for relativistic particles to $f_{\mathrm{c}}=\frac{|q| B}{2 \pi m} \sqrt{1-\nu^{2} / c^{2}}$. Assuming a uniform 2.5-T magnetic field throughout a cyclotron, find the cyclotron frequency required for electrons (a) moving at $0.99 c$ and (b) with kinetic energy $1.0 \mathrm{GeV}$.
Find the temperature corresponding to a thermal energy of $7 \mathrm{TeV},$ the particle energy in the Large Hadron Collider.
Hydrogen atoms first appeared when the temperature of the universe had dropped to about $3000 \mathrm{~K}$. To what thermal energy does this correspond? Compare with hydrogen's ionization energy.
The median wavelength of the cosmic microwave background is $1.504 \mathrm{~mm} .$ Use Equation 23.2 to find the corresponding blackbody temperature.
The parsec, used in expressing the Hubble constant, is defined as the distance to an object such that the Earth-Sun distance would subtend an angle of 1 s $(1 / 3600$ of a degree $)$ when seen from the object. Use this definition to express the parsec in (a) light years and (b) meters.
The most distant objects observed are some 13 billion light years from Earth. How fast are they receding from us?
Find the distances to galaxies whose redshifts imply that they're moving away from us at(a) $2.5 \mathrm{Mm} / \mathrm{s}$;(b) $15 \mathrm{Mm} / \mathrm{s}$;(c) $0.20 c$;(d) $0.80 c$.
In the early universe, there was enough thermal energy to create neutrons via the reaction $e^{-}+p^{+} \rightarrow n+\nu_{e} .$ (a) Compute the minimum energy required to initiate this reaction. (b) Find the temperature corresponding to the energy you found in part (a), and use Figure 26.14 to estimate when in the history of the universe this process was most likely to occur.
Are either or both of these decay schemes possible for the tau particle: (a) $\tau^{-} \rightarrow e^{-}+\bar{\nu}_{e}+\nu_{\tau}$ and (b) $\tau^{-} \rightarrow \pi^{-}+\pi_{0}+\nu_{\tau} ?$
Is the interaction $p+p \rightarrow p+\pi^{+}$ allowed? If not, what conservation law does it violate?
The $\Sigma^{+}$ and $\Sigma^{-}$ particles have quark compositions uus and $d d s,$ respectively. Are the $\Sigma^{+}$ and $\Sigma^{-}$ each other's antiparticles? If not, give the quark compositions of their antiparticles.
The mass of the photon is assumed to be zero, but experiments put an upper limit of only $5 \times 10^{-63} \mathrm{~kg}$ on the photon's mass. What would be the range of the electromagnetic force if the photon mass were actually at this upper limit?
The Tevatron at Fermilab accelerates protons to $1 \mathrm{TeV}$ kinetic energy. (a) What's this in joules? (b) How far would a $1-\mathrm{g}$ mass have to fall near Earth's surface to gain this much energy?
(a) Find the relativistic factor $\gamma$ for a 7 -TeV proton in the Large Hadron Collider. (b) Find an accurate value for the proton's speed, in terms of $c$.
The neutral lambda particle has mass $1116 \mathrm{MeV} / \mathrm{c}^{2}$. (a) Find the minimum energy needed for colliding protons and antiprotons to produce a lambda-antilambda pair. (b) To what proton speed does this correspond?
A so-called muonic atom is a hydrogen atom with the electron replaced by a muon, with mass 207 times the electron's. Find (a) the size and (b) the ground-state energy of the muonic atom.
Astronomers describe redshifts in the spectra of distant objects using the quantity $Z$, defined as the shift in wavelength divided by the original wavelength $\lambda_{0}: Z=\left(\lambda-\lambda_{0}\right) / \lambda_{0} .$ Use the relativistic Doppler formula (Equation 20.9 ), along with the Hubble relation, to find distances to objects with redshifts $Z$ of (a) $0.50 ;$ (b) $1.5 ;$ (c) 7.0 , roughly the redshift of the most distant galaxies observed.