Content check — University Physics 3, Chapter 11: Particle Physics and Cosmology

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 11: Particle Physics and Cosmology

53 problems · 2 figures

Check Your Understanding 11.1 §11.2 source ↗

What is the baryon number of a hydrogen nucleus?

Answer

Check Your Understanding 11.2 §11.2 source ↗

What is the lepton number of an electron-positron pair?

Answer

Check Your Understanding 11.3 §11.2 source ↗

What is the strangeness number of a muon?

Answer

Check Your Understanding 11.4 §11.3 source ↗

What is the baryon number of a pion?

Answer

Check Your Understanding 11.5 §11.4 source ↗

How much energy does an electron receive in accelerating through a 1-V potential difference?

Answer

1 eV

Check Your Understanding 11.6 §11.4 source ↗

A charged particle of a certain momentum travels in an arc through a uniform magnetic field. What happens if the magnetic field is doubled?

Answer

The radius of the track is cut in half.

Check Your Understanding 11.7 §11.4 source ↗

Why is a symmetric collider “symmetric?”

Answer

The colliding particles have identical mass but opposite vector momenta.

Check Your Understanding 11.8 §11.6 source ↗

The light of a galaxy that moves away from us is “redshifted.” What occurs to the light of a galaxy that moves toward us?

Answer

blueshifted

Check Your Understanding 11.9 §11.7 source ↗

Compare the abundance of helium by mass 10,000 years after the Big Bang and now.

Answer

about the same

11-1 §11.1 source ↗

What are the four fundamental forces? Briefly describe them.

Answer

Strong nuclear force: interaction between quarks, mediated by gluons. Electromagnetic force: interaction between charge particles, mediated photons. Weak nuclear force: interactions between fermions, mediated by heavy bosons. Gravitational force: interactions between material (massive) particle, mediate by hypothetical gravitons.

11-3 §11.1 source ↗

List the quark and lepton families

Answer

electron, muon, tau; electron neutrino, muon neutrino, tau neutrino; down quark, strange quark, bottom quark; up quark, charm quark, top quark

11-5 §11.2 source ↗

What are six particle conservation laws? Briefly describe them.

Answer

Conservation energy, momentum, and charge (familiar to classical and relativistic mechanics). Also, conservation of baryon number, lepton number, and strangeness—numbers that do not change before and after a collision or decay.

11-7 §11.2 source ↗

Why might the detection of particle interaction that violates an established particle conservation law be considered a good thing for a scientist?

Answer

It means that the theory that requires the conservation law is not understood. The failure of a long-established theory often leads to a deeper understanding of nature.

11-9 §11.3 source ↗

What is the general quark composition of a baryon? Of a meson?

Answer

3 quarks, 2 quarks (a quark-antiquark pair)

11-11 §11.3 source ↗

Why do baryons with the same quark composition sometimes differ in their rest mass energies?

Answer

Baryons with the same quark composition differ in rest energy because this energy depends on the internal energy of the quarks

(m = E / c^{2})

. So, a baryon that contains a quark with a large angular momentum is expected to be more massive than the same baryon with less angular momentum.

11-13 §11.4 source ↗

Describe the basic components and function of a typical colliding beam machine.

Answer

the “linac” to accelerate the particles in a straight line, a synchrotron to accelerate and store the moving particles in a circular ring, and a detector to measure the products of the collisions

11-15 §11.4 source ↗

What is the advantage of a colliding-beam accelerator over one that fires particles into a fixed target?

Answer

In a colliding beam experiment, the energy of the colliding particles goes into the rest mass energy of the new particle. In a fix-target experiment, some of this energy is lost to the momentum of the new particle since the center-of-mass of colliding particles is not fixed.

11-17 §11.5 source ↗

What is the Standard Model? Express your answer in terms of the four fundamental forces and exchange particles.

Answer

The Standard Model is a model of elementary particle interactions. This model contains the electroweak theory and quantum chromodynamics (QCD). It describes the interaction of leptons and quarks though the exchange of photons (electromagnetism) and bosons (weak theory), and the interaction of quark through the exchange of gluons (QCD). This model does not describe gravitational interactions.

11-19 §11.5 source ↗

What is the motivation behind grand unification theories?

Answer

To explain particle interactions that involve the strong nuclear, electromagnetic, and weak nuclear forces in a unified way.

11-21 §11.5 source ↗

If the Higgs boson is discovered and found to have mass, will it be considered the ultimate carrier of the weak force? Explain your response.

Answer

No, however it will explain why the W and Z bosons are massive (since the Higgs “imparts” mass to these particles), and therefore why the weak force is short ranged.

11-23 §11.6 source ↗

What is meant by cosmological expansion? Express your answer in terms of a Hubble graph and the red shift of distant starlight.

Answer

Cosmological expansion is an expansion of space. This expansion is different than the explosion of a bomb where particles pass rapidly through space. A plot of the recessional speed of a galaxy is proportional to its distance. This speed is measured using the red shift of distant starlight.

11-25 §11.6 source ↗

Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can be observed individually and that have absolute brightnesses at a standard distance that are well known. Explain how the measured brightness would vary with distance, as compared with the absolute brightness.

Answer

With distance, the absolute brightness is the same, but the apparent brightness is inversely proportional to the square of its distance (or by Hubble’s law recessional velocity).

11-27 §11.7 source ↗

Describe two pieces of evidence that support the Big Bang model.

Answer

The observed expansion of the universe and the cosmic background radiation spectrum.

11-29 §11.7 source ↗

If some unknown cause of redshift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect would that have on cosmology?

Answer

If light slow down, it takes long to reach Earth than expected. We conclude that the object is much closer than it really is. Thus, for every recessional velocity (based on the frequency of light, which we assume is not disturbed by the slowing), the distance is smaller than the “true” value, Hubble’s constant is larger than the “true” value, and the age of the universe is smaller than the “true” value.

11-31 §11.1 source ↗

How much energy is released when an electron and a positron at rest annihilate each other? (For particle masses, see Table 11.1.)

Table 11.1 Particles and their Properties in the book ↗

	Particle name	Symbol	Antiparticle	Mass $(MeV/ c^{2})$	Average lifetime (s)
Leptons
	Electron	$e^{−}$	$e^{+}$	0.511	Stable
	Electron neutrino	$υ_{e}$	$\overset{—}{υ_{e}}$	$\approx 0$	Stable
	Muon	$μ^{−}$	$μ^{+}$	105.7	$2.20 \times 10^{−6}$
	Muon neutrino	$υ_{μ}$	$\overset{—}{υ_{μ}}$	$\approx 0$	Stable
	Tau	$τ^{−}$	$τ^{+}$	1784	$< 4 \times 10^{−13}$
	Tau neutrino	$υ_{τ}$	$\overset{—}{υ_{τ}}$	$\approx 0$	Stable
Hadrons
Baryons	Proton	p	$\overset{−}{p}$	938.3	Stable
	Neutron	n	$\overset{−}{n}$	939.6	920
	Lambda	$Λ^{0}$	$\overset{—}{Λ^{0}}$	1115.6	$2.6 \times 10^{−10}$
	Sigma	$Σ^{+}$	$Σ^{−}$	1189.4	$0.80 \times 10^{−10}$
	Xi	$Ξ^{+}$	$Ξ^{−}$	1315	$2.9 \times 10^{−10}$
	Omega	$Ω^{+}$	$Ω^{−}$	1672	$0.82 \times 10^{−10}$
Mesons	Pion	$π^{+}$	$π^{−}$	139.6	$2.60 \times 10^{−8}$
	$π$ -Zero	$π^{0}$	$π^{0}$	135.0	$0.83 \times 10^{−16}$
	Kaon	$K^{+}$	$K^{−}$	493.7	$1.24 \times 10^{−8}$
	k-Short	$K_{S}^{0}$	$\overset{—}{K_{S}^{0}}$	497.6	$0.89 \times 10^{−10}$
	k-Long	$K_{L}^{0}$	$\overset{—}{K_{L}^{0}}$	497.6	$5.2 \times 10^{−8}$
	J/ $ψ$	J/ $ψ$	J/ $ψ$	3100	$7.1 \times 10^{−21}$
	Upsilon	$Υ$	$Υ$	9460	$1.2 \times 10^{−20}$

Answer

1.022 MeV

11-33 §11.1 source ↗

When both an electron and a positron are at rest, they can annihilate each other according to the reaction

$e^{−} + e^{+} \to γ + γ .$

In this case, what are the energy, momentum, and frequency of each photon?

Answer

0.511 MeV,

2.73 \times 10^{−22} kg \cdot m / s

1.23 \times 10^{20} Hz

11-35 §11.2 source ↗

Which of the following decays cannot occur because the law of conservation of lepton number is violated?

$\begin{matrix} (a) n \to p + e^{−} & (e) π^{−} \to e^{−} + {\overset{−}{υ}}_{e} \\ (b) μ^{+} \to e^{+} + υ_{e} & (f) μ^{−} \to e^{−} + {\overset{−}{υ}}_{e} + υ_{μ} \\ (c) π^{+} \to e^{+} + υ_{e} + {\overset{−}{υ}}_{μ} & (g) Λ^{0} \to π^{−} + p \\ (d) p \to n + e^{+} + υ_{e} & (h) K^{+} \to μ^{+} + υ_{μ} \end{matrix}$

Answer

a, b, and c

11-37 §11.2 source ↗

Identify one possible decay for each of the following antiparticles:

(a) $\overset{−}{n}$ , (b) $\overset{—}{Λ^{0}}$ , (c) $Ω^{+}$ , (d) $K^{−}$ , and (e) $\overset{−}{Σ}$ .

Answer

{\overset{−}{p}}_{e}^{+} v e

; b.

\overset{−}{p} π^{+}

\overset{−}{p} π^{0}

; c.

\overset{—}{Ξ^{0}} π^{0}

\overset{—}{Λ^{0}} K^{+}

; d.

μ^{-} {\overset{−}{v}}_{μ}

π^{−} π^{0}

; e.

\overset{−}{p} π^{0}

\overset{−}{n} π^{−}

11-39 §11.3 source ↗

Based on quark composition of a proton, show that its charge is

+ 1

Answer

A proton consists of two up quarks and one down quark. The total charge of a proton is therefore

+

\frac{2}{3} +

\frac{2}{3} +

− \frac{1}{3} =

+

1 .

11-41 §11.3 source ↗

Argue that the quark composition given in Table 11.5 for the positive kaon is consistent with the known charge, spin, and strangeness of this baryon.

Table 11.5 Meson Quarks in the book ↗

Name	Symbol	Quarks	Charge (e)	Spin	Mass $(GeV/ c^{2})$
Positive pion	$π^{+}$	$u \overset{−}{d}$	1	0	0.140
Positive rho	$ρ^{+}$	$u \overset{−}{d}$	1	1	0.768
Negative pion	$π^{−}$	$\overset{−}{u} d$	$−1$	0	0.140
Negative rho	$ρ^{−}$	$\overset{−}{u} d$	$−1$	1	0.768
Neutral Pion	$π^{0}$	$\overset{−}{u} u$ or $\overset{−}{d} d$	0	0	0.135
Neutral eta	$η^{0}$	$\overset{−}{u} u$ , $\overset{−}{d} d$ or $\overset{−}{s} s$	0	0	0.547
Positive kaon	$K^{+}$	$u \overset{−}{s}$	1	0	0.494
Neutral kaon	$K^{0}$	$d \overset{−}{s}$	0	0	0.498
Negative kaon	$K^{−}$	$\overset{−}{u} s$	$−1$	0	0.494
J/Psi	$J/ψ$	$\overset{−}{c} c$	0	1	3.10
Charmed eta	$η_{^{0}}$	$c \overset{−}{c}$	0	0	2.98
Neutral D	$D^{0}$	$\overset{−}{u} c$	0	0	1.86
Neutral D	$D^{*0}$	$\overset{−}{u} c$	0	1	2.01
Positive D	$D^{+}$	$\overset{−}{d} c$	1	0	1.87
Neutral B	$B^{0}$	$\overset{−}{d} b$	0	0	5.26
Upsilon	$ϒ$	$b \overset{−}{b}$	0	1	9.46

Answer

The

K^{+}

meson is composed of an up quark and a strange antiquark (

u \overset{−}{s}

). Since the changes of this quark and antiquark are 2e/3 and e/3, respectively, the net charge of the

K^{+}

meson is e, in agreement with its known value. Two spin

−1 / 2

particles can combine to produce a particle with spin of either 0 or 1, consistent with the

K^{+}

meson’s spin of 0. The net strangeness of the up quark and strange antiquark is

0 + 1 = 1

, in agreement with the measured strangeness of the

K^{+}

meson.

11-43 §11.3 source ↗

Why can’t either set of quarks shown below form a hadron?

Figure a has three red circles, each labeled u subscript R. Figure b has a blue circle labeled d subscript B and a purple circle labeled u subscript G.

Answer

a. color; b. quark-antiquark

11-45 §11.3 source ↗

Express the

β

decays

n \to p + e^{−} + \overset{−}{ν}

and

p \to n + e^{+} + ν

in terms of

β

decays of quarks. Check to see that the conservation laws for charge, lepton number, and baryon number are satisfied by the quark

β

decays.

Answer

d \to

u +

e^{−} +

{\overset{−}{v}}_{e};

u \to

d +

e^{+} +

v_{e}

11-47 §11.4 source ↗

A proton track passes through a magnetic field with radius of 50 cm. The magnetic field strength is 1.5 T. What is the total energy of the proton?

Answer

965 GeV

11-49 §11.4 source ↗

Assume that beam energy of an electron-positron collider is approximately 4.73 GeV. What is the total mass (W) of a particle produced in the annihilation of an electron and positron in this collider? What meson might be produced?

Answer

According to Example 11.7,

W =

2 E_{beam} =

9.46 GeV,

M =

9.46 GeV/ c^{2} .

This is the mass of the upsilon (1S) meson first observed at Fermi lab in 1977. The upsilon meson consists of a bottom quark and its antiparticle

(b \overset{−}{b})

Example 11.7 Creating a New Particle in the book ↗

11-51 §11.4 source ↗

Suppose a

W^{−}

created in a particle detector lives for

5.00 \times 10^{−25} s

. What distance does it move in this time if it is traveling at 0.900c? (Note that the time is longer than the given

W^{−}

lifetime, which can be due to the statistical nature of decay or time dilation.)

Answer

0.135 fm; Since this distance is too short to make a track, the presence of the

W^{−}

must be inferred from its decay products.

11-53 §11.4 source ↗

The 3.20-km-long SLAC produces a beam of 50.0-GeV electrons. If there are 15,000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?

Answer

3.33 MV

11-55 §11.5 source ↗

Use the Heisenberg uncertainly principle to estimate the range of a weak nuclear decay involving a graviton.

Answer

The graviton is massless, so like the photon is associated with a force of infinite range.

11-57 §11.5 source ↗

Assuming conservation of momentum, what is the energy of each

γ

ray produced in the decay of a neutral pion at rest, in the reaction

π^{0} \to γ + γ

Answer

67.5 MeV

11-59 §11.5 source ↗

The primary decay mode for the negative pion is

π^{−} \to μ^{−} + {\overset{−}{ν}}_{μ} .

(a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the

π^{−}

is at rest when it decays? You may assume the muon antineutrino is massless and has momentum

p = E / c

, just like a photon.

Answer

a. 33.9 MeV; b. By conservation of momentum,

| p_{μ} | = | p_{ν} | = p

. By conservation of energy,

E_{ν} =

29.8 MeV,

E_{μ} =

4.1 MeV

11-61 §11.6 source ↗

If the speed of a distant galaxy is 0.99c, what is the distance of the galaxy from an Earth-bound observer?

Answer

(0.99) (299792 km / s) =

((70 \frac{km}{s}) / Mpc) (d),

d =

4240 Mpc

11-63 §11.6 source ↗

If a galaxy is 153 Mpc away from us, how fast do we expect it to be moving and in what direction?

Answer

1.0 \times 10^{4} km/s away from us .

11-65 §11.6 source ↗

Our solar system orbits the center of the Milky Way Galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note that this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.

Answer

2.26 \times 10^{8} y

11-67 §11.6 source ↗

(a) Calculate the approximate age of the universe from the average value of the Hubble constant,

H_{0} =

20 km/s \cdot Mly

. To do this, calculate the time it would take to travel 0.307 Mpc at a constant expansion rate of 20 km/s. (b) If somehow acceleration occurs, would the actual age of the universe be greater or less than that found here? Explain.

Answer

1.5 \times 10^{10} y =

15 billion years

; b. Greater, since if it was moving slower in the past it would take less more to travel the distance.

11-69 §11.6 source ↗

Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.

Answer

v = \sqrt{\frac{G M}{r}}

11-71 §11.AP source ↗

Each of the following reactions is missing a single particle. Identify the missing particle for each reaction.

$\begin{matrix} (a) p + \overset{−}{p} \to n + ? \\ (b) p + p \to p + Λ^{0} + ? \\ (c) π^{-} + p \to Σ^{−} + ? \\ (d) K^{−} + n \to Λ^{0} + ? \\ (e) τ^{+} \to e^{+} + ν_{e} + ? \\ (f) {\overset{−}{ν}}_{e} + p \to n + ? \end{matrix}$

Answer

\overset{−}{n}

; b.

K^{+}

; c.

K^{+}

; d.

π^{−}

; e.

{\overset{−}{ν}}_{τ};

e^{+}

11-73 §11.AP source ↗

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

Answer

14.002 TeV \approx

14.0 TeV

11-75 §11.AP source ↗

The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, so the neutron star spins rapidly. If the initial core radius is

5.0 \times 10^{5} km

and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the core’s angular velocity was originally 1 revolution per 30.0 days.

Answer

964 rev/s

11-77 §11.AP source ↗

(a) What Hubble constant corresponds to an approximate age of the universe of

10^{10}

y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of

10^{10}

y. (b) Similarly, what Hubble constant corresponds to a universe approximately

2 \times 10^{10}

years old?

Answer

H_{0} =

\frac{30 km/s}{1 Mly} =

30 km/s \cdot Mly;

H_{0} =

\frac{15 km/s}{1 Mly} =

15 km/s \cdot Mly

11-79 §11.CP source ↗

The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere. Suppose a cosmic ray particle having an energy of $10^{10} GeV$ converts its energy into particles with masses averaging $200 MeV/ c^{2}$ .

(a) How many particles are created? (b) If the particles rain down on a $1 {.00-km}^{2}$ area, how many particles are there per square meter?

Answer

5 \times 10^{10}

; b. divide the number of particles by the area they hit:

5 \times 10^{4} particles / m^{2}

11-81 §11.CP source ↗

Plans for an accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity

γ = \frac{1}{\sqrt{1 - v^{2} / c^{2}}}

be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?

Answer

a. 2.01; b.

2.50 \times 10^{−8} s

; c. 6.50 m

11-83 §11.CP source ↗

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.

Answer

\begin{matrix} \frac{m v^{2}}{r} & = & \frac{G M m}{r^{2}} \Rightarrow \\ v & = & {(\frac{G M}{r})}^{1 / 2} = [\frac{(6.67 \times 10^{−11} N \cdot m^{2} / {kg}^{2}) (3 \times 10^{41} kg)}{(30,000 ly) (9.46 \times 10^{15} m/ly)}] = 2.7 \times 10^{5} m/s \end{matrix}

11-85 §11.CP source ↗

(a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two

γ

rays of equal energy. What is the characteristic

γ

-ray energy you would look for if searching for evidence of proton-antiproton annihilation? (The fact that such radiation is rarely observed is evidence that there is very little antimatter in the universe.) (b) How does this compare with the 0.511-MeV energy associated with electron-positron annihilation?

Answer

a. 938.27 MeV; b.

1.84 \times 10^{3}

11-87 §11.CP source ↗

(a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of

10^{−43} s

. (b) Compare this energy with the

10^{19} GeV

unification-of-forces energy and discuss why they are similar.

Answer

3.29 \times 10^{18} GeV \approx

3 \times 10^{18} GeV

; b. 0.3; Unification of the three forces breaks down shortly after the separation of gravity from the unification force (near the Planck time interval). The uncertainty in time then becomes greater. Hence the energy available becomes less than the needed unification energy.

End of the book.

Problems and answers are adapted from University Physics Volume 3 by Samuel J. Ling, Jeff Sanny and William Moebs, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/university-physics-volume-3/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.