Physics: Principles with Applications

Douglas C. Giancoli

Chapter 32 ELEMENTARY PARTICLES - all with Video Answers

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Chapter Questions

00:50

Problem 1

(I) What is the total energy of a proton whose kinetic energy is 4.65 GeV?

Ren Jie Tuieng

Numerade Educator

06:05

Problem 2

(I) Calculate the wavelength of 28-GeV electrons.

Jeffrey Ormsby

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01:31

Problem 3

(I) If $\alpha$ particles are accelerated by the cyclotron of Example 32-2, what must be the frequency of the voltage applied to the dees?

Ren Jie Tuieng

Numerade Educator

01:25

Problem 4

(I) What is the time for one complete revolution for a very high-energy proton in the 1.0-km-radius Fermilab accelerator?

Ren Jie Tuieng

Numerade Educator

01:16

Problem 5

(II) What strength of magnetic field is used in a cyclotron in which protons make $3.1 \times 10^7$ revolutions per second?

Ren Jie Tuieng

Numerade Educator

07:47

(II) (a) If the cyclotron of Example 32-2 accelerated $\alpha$ particles, what maximum energy could they attain? What would their speed be? (b) Repeat for deuterons $(^{2}_{1}H)$. (c) In each case, what frequency of voltage is required?

Ren Jie Tuieng

Numerade Educator

04:26

Problem 7

(II) Which is better for resolving details of the nucleus: 25-MeV alpha particles or 25-MeV protons? Compare each of their wavelengths with the size of a nucleon in a nucleus.

00000 00000

Numerade Educator

00:58

Problem 8

(II) What is the wavelength ($=$ minimum resolvable size) of 7.0-TeV protons at the LHC?

Khoobchandra Agrawal

Numerade Educator

03:03

Problem 9

(II) The 1.0-km radius Fermilab Tevatron took about 20 seconds to bring the energies of the stored protons from 150 GeV to 1.0 TeV. The acceleration was done once per turn. Estimate the energy given to the protons on each turn. (You can assume that the speed of the protons is essentially c the whole time.)

Ren Jie Tuieng

Numerade Educator

09:18

Problem 10

(II) A cyclotron with a radius of 1.0 m is to accelerate deuterons $(^{2}_{1}H)$ to an energy of 12 MeV. (a) What is the required magnetic field? (b) What frequency is needed for the voltage between the dees? (c) If the potential difference between the dees averages 22 kV, how many revolutions will the particles make before exiting? (d) How much time does it take for one deuteron to go from start to exit? (e) Estimate how far it travels during this time.

Ren Jie Tuieng

Numerade Educator

01:30

Problem 11

(III) Show that the energy of a particle (charge $e$) in a synchrotron, in the relativistic limit $(\upsilon \approx c)$, is given by $E$ (in eV) $= Brc$, where $B$ is the magnetic field and $r$ is the radius of the orbit (SI units).

Khoobchandra Agrawal

Numerade Educator

01:33

Problem 12

(I) About how much energy is released when a $\Lambda^0$ decays to $n + \pi^0$? (See Table 32-2.)

Merlin Bacon

Numerade Educator

01:40

Problem 13

(I) How much energy is released in the decay $\pi^+ \rightarrow \mu^+ + \nu_\mu$ See Table 32-2.

Ren Jie Tuieng

Numerade Educator

01:59

Problem 14

(I) Estimate the range of the strong force if the mediating particle were the kaon instead of a pion.

Ren Jie Tuieng

Numerade Educator

01:13

Problem 15

(I) How much energy is required to produce a neutron-antineutron pair?

Ren Jie Tuieng

Numerade Educator

01:31

Problem 16

(II) Determine the total energy released when $\Sigma^0$ decays to $\Lambda^0$ and then to a proton.

Khoobchandra Agrawal

Numerade Educator

02:04

Problem 17

(II) Two protons are heading toward each other with equal speeds. What minimum kinetic energy must each have if a $\pi^0$ meson is to be created in the process? (See Table 32-2.)

Ren Jie Tuieng

Numerade Educator

02:31

Problem 18

(II) What minimum kinetic energy must a proton and an antiproton each have if they are traveling at the same speed toward each other, collide, and produce a $K^+K^-$ pair in addition to themselves? (See Table 32-2.)

Ren Jie Tuieng

Numerade Educator

01:02

Problem 19

(II) What are the wavelengths of the two photons produced when a proton and antiproton at rest annihilate?

Narayan Hari

Numerade Educator

04:09

Problem 20

(II) The $\Lambda^0$ cannot decay by the following reactions. What
conservation laws are violated in each of the reactions?
(a) $\Lambda^0 \nrightarrow n+ \pi^-$
(b) $\Lambda^0 \nrightarrow p+ K^-$
(c) $\Lambda^0 \nrightarrow \pi^+ + \pi^-$

Ren Jie Tuieng

Numerade Educator

06:28

Problem 21

(II) What would be the wavelengths of the two photons produced when an electron and a positron, each with 420 keV of kinetic energy, annihilate in a head-on collision?

William Liu

Numerade Educator

14:20

Problem 22

(II) Which of the following reactions and decays are possible? For those forbidden, explain what laws are violated.
(a) $\pi^- + p \rightarrow n + \eta^0$
(b) $\pi^+ + p \rightarrow n + \pi^0$
(c) $\pi^+ + p \rightarrow p + e^+$
(d) $p \rightarrow e^+ + \nu_e$
(e) $\mu^+ \rightarrow e^+ + \overline {\nu}_\mu$
(f) $p \rightarrow n + e^+ + \nu_e$

Daniel Sneed

Numerade Educator

02:38

Problem 23

(II) Antiprotons can be produced when a proton with sufficient energy hits a stationary proton. Even if there is enough energy, which of the following reactions will not happen?
$p + p \rightarrow p + \overline{p}$
$p + p \rightarrow p + p + \overline{p}$
$p + p \rightarrow p + p + p + \overline{p}$
$p + p \rightarrow p + e^+ + e^+ + \overline{p}$

Khoobchandra Agrawal

Numerade Educator

08:18

Problem 24

(III) In the rare decay $\pi^+ \rightarrow e^+ + \nu_e$, what is the kinetic energy of the positron? Assume the $\pi^+$ decays from rest
and $m_\nu = 0$.

Ren Jie Tuieng

Numerade Educator

01:05

Problem 25

(III) For the decay $\Lambda^0 \rightarrow p + \pi^-$, calculate (a) the $Q$-value (energy released), and (b) the kinetic energy of the p and $\pi^-$, assuming the $\Lambda^0$ decays from rest. (Use relativistic formulas.)

Khoobchandra Agrawal

Numerade Educator

09:46

Problem 26

(III) Calculate the maximum kinetic energy of the electron when a muon decays from rest via $\mu^- \rightarrow e^- + \overline{\nu} + \nu_\mu$. [$Hint$: In what direction do the two neutrinos move relative to the electron in order to give the electron the maximum kinetic energy? Both energy and momentum are conserved; use relativistic formulas.]

Ren Jie Tuieng

Numerade Educator

01:14

Problem 27

(I) The mean life of the $\Sigma^0$ particle is $7 \times 10^{-20}s$. What is the uncertainty in its rest energy? Express your answer in MeV.

Luis Mendoza

Numerade Educator

01:44

Problem 28

(I) The measured width of the $\psi$ (3686) meson is about 300 keV. Estimate its mean life.

Khoobchandra Agrawal

Numerade Educator

00:55

Problem 29

(I) The measured width of the $J/\psi$ meson is 88 keV. Estimate its mean life.

Luis Mendoza

Numerade Educator

01:42

Problem 30

(I) The $B^-$ meson is a $b \overline{u}$ quark combination. (a) Show that this is consistent for all quantum numbers. (b) What are the quark combinations for $B^+$, $B^0$, $\overline{B^0}$?

Luis Mendoza

Numerade Educator

02:16

Problem 31

(I) What is the energy width (or uncertainty) of (a) $\eta^0$ and (b) $\rho^+$? See Table 32-2.

Khoobchandra Agrawal

Numerade Educator

02:07

Problem 32

(II) Which of the following decays are possible? For those that are forbidden, explain which laws are violated.
(a) $\Xi^0 \rightarrow \Sigma^+ + \pi^-$
(b) $\Omega^- \rightarrow \Sigma^0 + \pi^- + \nu$
(c) $\Sigma^0 \rightarrow \Lambda^0 + \gamma + \gamma$

Luis Mendoza

Numerade Educator

03:40

Problem 33

(II) In ordinary radioactive decay, a W particle may be created even though the decaying particle has less mass than the W particle. If you assume $\Delta E \approx$ mass of the virtual W, what is the expected lifetime of the W?

Khoobchandra Agrawal

Numerade Educator

01:48

Problem 34

(II) What quark combinations produce (a) a $\Xi^0$ baryon and (b) a $\Xi^-$ baryon?

Luis Mendoza

Numerade Educator

02:01

Problem 35

(II) What are the quark combinations that can form (a) a neutron, (b) an antineutron, (c) a $\Lambda^0$ (d) a $\overline{\Sigma^0}$

Luis Mendoza

Numerade Educator

02:28

Problem 36

(II) What particles do the following quark combinations produce: (a) uud, (b) $\overline{u}$ $\overline{u}$ $\overline{s}$, (c) $\overline{u}s$, (d) $d \overline{u}$, (e) $\overline{c}s$?

Luis Mendoza

Numerade Educator

01:04

Problem 38

(II) The $D^{+}_{S}$ meson has $S=c=+1, B=0$. What quark combination would produce it?

Luis Mendoza

Numerade Educator

01:45

Problem 39

(II) Draw a possible Feynman diagram using quarks (as in Fig. 32-17c) for the reaction $\pi^- + p \rightarrow \pi^0 + n$.

Luis Mendoza

Numerade Educator

01:13

Problem 40

(II) Draw a Feynman diagram for the reaction $n + \nu_ \mu \rightarrow p + \mu^-$.

Luis Mendoza

Numerade Educator

05:56

Problem 41

What is the total energy of a proton whose kinetic energy is 15 GeV? What is its wavelength?

Merlin Bacon

Numerade Educator

02:27

Problem 42

The mean lifetimes listed in Table 32-2 are in terms of proper time, measured in a reference frame where the particle is at rest. If a tau lepton is created with a kinetic energy of 950 MeV, how long would its track be as measured in the lab, on average, ignoring any collisions?

Sarah Mccrumb

Numerade Educator

02:21

Problem 43

(a) How much energy is released when an electron and a positron annihilate each other? (b) How much energy is released when a proton and an antiproton annihilate each other? (All particles have $KE \approx 0$.)

Sarah Mccrumb

Numerade Educator

04:38

Problem 44

If $2 \times 10^{14}$ protons moving at , $\upsilon \approx c$ with $KE = 4.0 TeV$, are stored in the 4.3-km-radius ring of the LHC, (a) how much current (amperes) is carried by this beam? (b) How fast would a 1500-kg car have to move to carry the same kinetic energy as this beam?

Sarah Mccrumb

Numerade Educator

04:19

Problem 45

Protons are injected into the 4.3-km-radius Large Hadron Collider with an energy of 450 GeV. If they are accelerated by 8.0 MV each revolution, how far do they travel and approximately how much time does it take for them to reach 4.0 TeV?

Farnaz Mohseni

Numerade Educator

12:26

Problem 46

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why.
(a) $\pi^- + p \rightarrow K^0 + p + \pi^0$
(b) $K^- + p \rightarrow \Lambda^0 + \pi^0$
(c) $K^+ + n \rightarrow \Sigma^+ + \pi^0 + \gamma$
(d) $K^+ \rightarrow \pi^0 + \pi^0 + \pi^+$
(e) $\pi^+ \rightarrow e^+ + \nu_e$

Sarah Mccrumb

Numerade Educator

09:10

Problem 47

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why.
(a) $\pi^- + p \rightarrow K^+ + \Sigma^-$
(b) $\pi^+ + p \rightarrow K^+ + \Sigma^+$
(c) $\pi^- + p \rightarrow \Lambda^0 + K^0 + \pi^0$
(d) $\pi^+ + p \rightarrow \Sigma^0 + \pi^0$
(e) $\pi^- + p \rightarrow p + e^- + \overline{\nu}_e$

Sarah Mccrumb

Numerade Educator

02:50

Problem 48

One decay mode for a $\pi^+$ is $\pi^+ \rightarrow \mu^+ + \nu_\mu$. What would be the equivalent decay for a $\pi^-$? Check conservation laws.

Sarah Mccrumb

Numerade Educator

03:24

Problem 49

Symmetry breaking occurs in the electroweak theory at about $10^{-18}m$. Show that this corresponds to an energy that is on the order of the mass of the $W^\pm$.

Sarah Mccrumb

Numerade Educator

03:12

Problem 50

Calculate the $Q$-value for each of the reactions, Eq. 32-4, for producing a pion.

Sarah Mccrumb

Numerade Educator

02:09

Problem 51

How many fundamental fermions are there in a water molecule?

Vishal Gupta

Numerade Educator

07:02

Problem 52

The mass of a $\pi^0$ can be measured by observing the reaction $\pi^- + p \rightarrow \pi^0 + n$ with initial kinetic energies near zero. The neutron is observed to be emitted with a kinetic energy
of 0.60 MeV. Use conservation of energy and momentum to determine the $\pi^0$ mass.

Sarah Mccrumb

Numerade Educator

08:03

Problem 53

(a) Show that the so-called unification distance of $10^{-31} m$ in grand unified theory is equivalent to an energy of about $10^{16}$ GeV. Use the uncertainty principle, and also de Broglie's wavelength formula, and explain how they apply. (b) Calculate the temperature corresponding to $10^{16}$ GeV.

Sarah Mccrumb

Numerade Educator

06:15

Problem 54

Calculate the $Q$-value for the reaction $\pi^- + p \rightarrow \Lambda^0 + K^0$, when negative pions strike stationary protons. Estimate the minimum pion kinetic energy needed to produce this reaction. [Hint: Assume $\Lambda^0$ and $K^0$ move off with the same velocity.]

Sarah Mccrumb

Numerade Educator

03:00

Problem 55

A proton and an antiproton annihilate each other at rest and produce two pions, $\pi^-$ and $\pi^+$ What is the kinetic energy of each pion?

Ren Jie Tuieng

Numerade Educator

10:20

Problem 56

For the reaction $p + p \rightarrow 3p + \overline{p}$, where one of the initial protons is at rest, use relativistic formulas to show that the threshold energy is $6m_pc^2$, equal to three times the magnitude of the $Q$-value of the reaction, where $m_p$ is the proton mass. [$Hint$: Assume all final particles have the same velocity.]

Sarah Mccrumb

Numerade Educator

01:59

Problem 57

At about what kinetic energy (in eV) can the rest energy of a proton be ignored when calculating its wavelength, if the wavelength is to be within $1.0\%$ of its true value? What are the corresponding wavelength and speed of the proton?

Ren Jie Tuieng

Numerade Educator

03:04

Problem 58

Use the quark model to describe the reaction $\overline{p} + n \rightarrow \pi^- + \pi^0$.

Sarah Mccrumb

Numerade Educator

05:26

Problem 59

Identify the missing particle in the following reactions.
(a) $p + \rightarrow p + n + \pi^+ +$? (b) $p + ? \rightarrow n + \mu^+$

Sarah Mccrumb

Numerade Educator

03:03

Problem 60

What fraction of the speed of light c is the speed of a 7.0-TeV proton?

Sarah Mccrumb

Numerade Educator

04:15

Problem 61

Using the information in Section 32-1, show that the Large Hadron Collider's two colliding proton beams can resolve details that are less than 1/10,000 the size of a nucleus.

Sarah Mccrumb

Numerade Educator

05:47

Problem 62

Searches are underway for a process called $\textbf{neutrinoless double beta decay,}$ in which a nucleus decays by emitting two electrons. (a) If the parent nucleus is $^{96}_{40}Zr$, what would the daughter nucleus be? (b) What conservation laws would be violated during this decay? (c) How could $^{96}_{40}Zr$ decay to the same daughter nucleus without violating any conservation laws?

Sarah Mccrumb

Numerade Educator

02:43

Problem 63

Estimate the lifetime of the Higgs boson from the width of the "bump" in Fig. 32-19, using the uncertainty principle. [Note: This is not a realistic estimate because the underlying processes are very complicated.]

Sarah Mccrumb

Numerade Educator