Solved: Particles and Accelerators(II) What strength of

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

Calculate the wavelength of 28-GeV electrons.

If particles are accelerated by the cyclotron of Example 322, what must be the frequency of the voltage applied to the dees?

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

What strength of magnetic field is used in a cyclotron in which protons make revolutions per second?

(a) If the cyclotron of Example 322 accelerated particles, what maximum energy could they attain? What would their speed be? (b) Repeat for deuterons (c) In each case, what frequency of voltage is required?

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

What is the wavelength resolvable size) of 7.0-TeV protons at the LHC?

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.)

A cyclotron with a radius of 1.0 m is to accelerate deuterons 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.

Show that the energy of a particle (charge e) in a synchrotron, in the relativistic limit is given by where B is the magnetic field and r is the radius of the orbit (SI units).

About how much energy is released when a decays to (See Table 322.)

How much energy is released in the decay See Table 322.

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

How much energy is required to produce a neutron antineutron pair?

Determine the total energy released when decays to and then to a proton.

Two protons are heading toward each other with equal speeds. What minimum kinetic energy must each have if a meson is to be created in the process? (See Table 322.)

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 pair in addition to themselves? (See Table 322.)

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

The cannot decay by the following reactions. What conservation laws are violated in each of the reactions?

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?

(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) \(p\ \rightarrow\ e^+ + v_e\) (e) \(\mu^+\ \rightarrow\ e^+ + \overline{v}_\mu\) (f) \(p\ \rightarrow\ n + e^+ + v_c\)

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?

In the rare decay what is the kinetic energy of the positron? Assume the decays from rest and .

For the decay calculate (a) the Q-value (energy released), and (b) the kinetic energy of the p and assuming the decays from rest. (Use relativistic formulas.)

Calculate the maximum kinetic energy of the electron when a muon decays from rest via [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.]

The mean life of the particle is What is the uncertainty in its rest energy? Express your answer in MeV.

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

The measured width of the meson is 88 keV. Estimate its mean life.

The meson is a quark combination. (a) Show that this is consistent for all quantum numbers. (b) What are the quark combinations for

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

Which of the following decays are possible? For those that are forbidden, explain which laws are violated.

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 of the virtual W, what is the expected lifetime of the W?

What quark combinations produce (a) a baryon and (b) a baryon?

What are the quark combinations that can form (a) a neutron, (b) an antineutron, (c) a (d

What particles do the following quark combinations produce: (a) uud

What is the quark combination needed to produce a

The meson has What quark combination would produce it?

Draw a possible Feynman diagram using quarks (as in Fig. 3217c) for the reaction

Draw a Feynman diagram for the reaction n + nm S p + m.

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

The mean lifetimes listed in Table 322 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?

(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 )

If protons moving at , with 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?

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?

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why

One decay mode for a is What would be the equivalent decay for a Check conservation laws

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 \(W^{\pm}\).

Calculate the Q-value for each of the reactions, Eq. 324, for producing a pion.

How many fundamental fermions are there in a water molecule?

The mass of a can be measured by observing the reaction 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 mass.

(a) Show that the so-called unification distance of in grand unified theory is equivalent to an energy of about Use the uncertainty principle, and also de Broglies wavelength formula, and explain how they apply. (b) Calculate the temperature corresponding to 1016 GeV

Calculate the Q-value for the reaction when negative pions strike stationary protons. Estimate the minimum pion kinetic energy needed to produce this reaction. [Hint: Assume and move off with the same velocity.]

A proton and an antiproton annihilate each other at rest and produce two pions, and What is the kinetic energy of each pion?

For the reaction where one of the initial protons is at rest, use relativistic formulas to show that the threshold energy is equal to three times the magnitude of the Q-value of the reaction, where is the proton mass. [Hint: Assume all final particles have the same velocity.]

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 of its true value? What are the corresponding wavelength and speed of the proton?

Use the quark model to describe the reaction

Identify the missing particle in the following reaction

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

Using the information in Section 321, show that the Large Hadron Colliders two colliding proton beams can resolve details that are less than 1/10,000 the size of a nucleus.

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

Estimate the lifetime of the Higgs boson from the width of the bump in Fig. 3219, using the uncertainty principle. [Note: This is not a realistic estimate because the underlying processes are very complicated.]

Problem 1 CQQ Physicists reserve the term “fundamental particle” for particles with a special property. What do you think that special property is? (a) Particles that are massless. (b) Particles that possess the minimum allowable electric charge. (c) Particles that have no internal structure. (d) Particles that produce no force on other objects.

Problem 1MCQ There are six kinds ( = flavors) of quarks: up, down, strange, charm, bottom, and top. Which flavors make up most of the known matter in the universe? (a) Up and down quarks. (b) Strange and charm quarks. (c) Bottom and top quarks. (d) All of the above.

Problem 1P (I) What is the total energy of a proton whose kinetic energy is 4.65 GeV?

Give a reaction between two nucleons, similar to Eq. 32–4, that could produce a \(\pi^{-}\) Equation Transcription: Text Transcription: \pi^-

Problem 1SL (a) What are the two major classes of particles that make up the matter of the universe? (b) Name six types, or flavors, of each class of particles. (c) What are the four known fundamental forces in the universe? (d) Name the particles that carry the forces in part c. Which force is much weaker than the other three?

Problem 2COQ The fundamental particles as we see them today, besides the long-sought-for Higgs boson, are (a) atoms and electrons. (b) protons, neutrons, and electrons. (c) protons, neutrons, electrons, and photons. (d) quarks, leptons, and gauge bosons (carriers of force). (e) hadrons, leptons, and gauge bosons.

Which of the following particles can not be composed of quarks? (a) Proton. (b) Electron. (c) \(\pi\) meson. (d) Neutron. (e) Higgs boson. Equation Transcription: Text Transcription: \pi

Problem 2P (I) Calculate the wavelength of 28-GeV electrons.

If a proton is moving at very high speed, so that its kinetic energy is much greater than its rest energy \(\left(m c^{2}\right)\), can it then decay via \(p_{\rightarrow} n+\pi^{+}\)? Equation Transcription: Text Transcription: (mc^2) p_{\rightarrow} n+\pi^{+}

Problem 2 SL (a) What property characterizes all hadrons? (b) What property characterizes all baryons? c) What property characterizes all mesons?

Problem 3 MCQ If gravity is the weakest force, why is it the one we notice most? (a) Our bodies are not sensitive to the other forces. (b) The other forces act only within atoms and therefore have no effect on us. (c) Gravity may be “very weak” but always attractive, and the Earth has enormous mass. The strong and weak nuclear forces have very short range. The electromagnetic force has a long range, but most matter is electrically neutral. (d) At long distances, the gravitational force is actually stronger than the other forces. (e) The other forces act only on elementary particles, not on objects our size.

(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? Equation Transcription: Text Transcription: \alpha

Problem 3Q What would an “antiatom,”made up of the antiparticles to the constituents of normal atoms, consist of? What might happen if antimatter, made of such antiatoms, came in contact with our normal world of matter?

Show that all conservation laws hold for all the decays described in Fig. 32–15 for the decays of the top quark.

Problem 4MCQ Is it possible for a tau lepton (whose mass is almost twice that of a proton) to decay into only hadrons? (a) Yes, because it is so massive it could decay into a proton and pions. (b) Yes, it could decay into pions and nothing else. (c) No, such a decay would violate lepton number; all of its decay products must be leptons. (d) No, its decay products must include a tau neutrino but could include hadrons such as pions. (e) No, the tau lepton is too massive to decay.

Problem 4P Particles and Accelerators (I) What is the time for one complete revolution for a very high-energy proton in the 1.0-km-radius Fermilab accelerator?

What particle in a decay signals the electromagnetic interaction?

The Higgs boson, Section 32–10, has very probably been detected at the \(C E R N L H C\). (a) If a Higgs boson at rest decays into two tau leptons, what is the kinetic energy of each tau? Follow the analysis of Example 32–5. See Table 32–2. (b) What are the signs of the electric charges of the two tau leptons? (c) Could a Higgs boson decay into two Z bosons (Table 32–2)? Equation Transcription: Text Transcription: CERN LHC

Many particle accelerators are circular because: (a) particles accelerate faster around circles. (b) in order to move in a circle, acceleration is required. (c) a circular accelerator has a shorter length than a square one. (d) the particles can be accelerated through the same potential difference many times, making the accelerator more compact. (e) a particle moving in a circle needs more energy than a particle moving in a straight line.

Problem 5P Particles and Accelerators (II) What strength of magnetic field is used in a cyclotron in which protons make 3.1 X 107revolutions per second?

Problem 5Q (a) Does the presence of a neutrino among the decay products of a particle necessarily mean that the decay occurs via the weak interaction? (b) Do all decays via the weak interaction produce a neutrino? Explain.

Problem 6MCQ Which of the following are today considered fundamental particles (that is, not composed of smaller components)? Choose as many as apply. (a) Atoms. (b) Electrons. (c) Protons. (d) Neutrons. (e) Quarks. (f) Photon. (g) Higgs boson.

\(\text { (II) }\) (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 \(\left({ }_{1}^{2} H\right)\) (c) In each case, what frequency of voltage is required? Equation Transcription: Text Transcription: (II) \alpha (1^ 2H)

Problem 6 Q Why is it that a neutron decays via the weak interaction even though the neutron and one of its decay products (proton) are strongly interacting?

Problem 6 SL What magnetic field is required for the 4.25-km-radius Large Hadron Collider (LHC) to accelerate protons to 7.0 TeV? [Hint: Use relativity, Chapter 26.]

Problem 7MCQ The electron’s antiparticle is called the positron. Which of the following properties, if any, are the same for electrons and positrons? (a) Mass. (b) Charge. (c) Lepton number. (d) None of the above.

Problem 7P Particles and Accelerators (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.

Problem 7 Q Which of the four interactions (strong, electromagnetic, weak, gravitational) does an electron take part in? A neutrino? A proton?

Problem 8 MCQ The strong nuclear force between a neutron and a proton is due to (a) the exchange of ? mesons between the neutron and the proton. (b) the conservation of baryon number. (c) the beta decay of the neutron into the proton. (d) the exchange of gluons between the quarks within the neutron and the proton. (e) Both (a) and (d) at different scales.

Problem 8 P Particles and Accelerators (II) What is the wavelength (= minimum resolvable size) of 7.0-TeV protons at the LHC?

Verify that charge and baryon number are conserved in each of the decays shown in Table 32–2.

Electrons are still considered fundamental particles (in the group called leptons). But protons and neutrons are no longer considered fundamental; they have substructure and are made up of (a) pions. (b) leptons. (c) quarks. (d) bosons. (e) photons.

Problem 9 P Particles and Accelerators (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.)

Which of the particle decays listed in Table 32–2 occur via the electromagnetic interaction?

Problem 10 MCQ Which of the following will interact via the weak nuclear force only? (a) Quarks. (b) Gluons. (c) Neutrons. (d) Neutrinos. (e) Electrons. (f) Muons. (g) Higgs boson.

Which of the particle decays listed in Table 32–2 occur by the weak interaction?

Problem 11P Particles and Accelerators (III) Show that the energy of a particle (charge e) in a synchrotron, in the relativistic limit (v ? C), is given by E (in eV) = Brcwhere B is the magnetic field and r is the radius of the orbit (SI units).

The \(\Delta\) baryon has spin \(\begin{array}{l}3 \\2\end{array}\) baryon number 1, and charge \(Q=2,+1,0, \text { or }-1\) Why is there no charge state \(Q=-2\) ? Equation Transcription: Text Transcription: \Delta 2 3 Q=2,+1,0, or -1 Q=-2

\((I)\) About how much energy is released when a \(\Lambda^{0}\) decays to \(n+\pi^{0}\)? (See Table 32–2.) Equation Transcription: Text Transcription: (I) \Lambda 0 n+\pi^0

Which of the particle decays in Table 32–4 occur via the electromagnetic interaction?

\(\text { (I) }\) How much energy is released in the decay \(\pi^{+} \rightarrow \mu^{+}+v_{\mu}\)? See Table 32–2. Equation Transcription: Text Transcription: (I) \pi^+ \rightarrow \mu^+ +v_\mu

Which of the particle decays in Table 32–4 occur by the weak interaction?

Problem 14Q Quarks have spin ½. How do you account for the fact that baryons have spin ½ or 3/2, and mesons have spin 0 or 1?

Problem 15P 32–2 to 32–6 Particle Interactions, Particle Exchange (I) How much energy is required to produce a neutron– antineutron pair?

Problem 15Q Suppose there were a kind of “neutrinolet” that was massless, had no color charge or electrical charge, and did not feel the weak force. Could you say that this particle even exists?

\(\text { (II) }\) Determine the total energy released when \(\Sigma^{0}\) decays to and then to \(\Lambda^{\circ}\) a proton. Equation Transcription: Text Transcription: (II) \sigma 0 \Lambda^{\circ}

Problem 16Q Is it possible for a particle to be both (a) a lepton and a baryon? (b) a baryon and a hadron? (c) a meson and a quark? (d) a hadron and a lepton? Explain.

\(\text { (II) }\) Two protons are heading toward each other with equal speeds. What minimum kinetic energy must each have if \(\pi^{\circ}\) a meson is to be created in the process? (See Table 32–2.) Equation Transcription: Text Transcription: (II) \pi^{\circ}

Using the ideas of quantum chromodynamics, would it be possible to find particles made up of two quarks and no antiquarks? What about two quarks and two antiquarks?

\(\text { (II) }\) 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.) Equation Transcription: Text Transcription: (II) K+K-

Problem 18Q Why can neutrons decay when they are free, but not when they are inside a stable nucleus?

Problem 19P 32–2 to 32–6 Particle Interactions, Particle Exchange (II) What are the wavelengths of the two photons produced when a proton and antiproton at rest annihilate?

Is the reaction \(e^- + p \rightarrow n + \overline v_c\) possible? Explain.

(II) The \(\Lambda^{0}\) cannot decay by the following reactions. What conservation laws are violated in each of the reactions? (a) \(\Lambda^{0} \rightarrow n+\pi^{-}\) (b) \(\Lambda^{0} \rightarrow p+K^{-}\) \(\Lambda^{0} \rightarrow \pi^{+}+\pi^{-}\) Equation Transcription: ? ? ? Text Transcription: Lambda^0 Lambda^0 \rightarrow n+\pi^- Lambda^0 \rightarrow p+K^- Lambda^0 \rightarrow \pi^+ +\pi^-

Occasionally, the \(\Lambda\) will decay by the following reaction: \(\Lambda^{0} \rightarrow p^{+}+e^{-}+v^{-} e\). Which of the four forces in nature is responsible for this decay? How do you know? Equation Transcription: Text Transcription: \Lambda \Lambda^{0} \rightarrow p^{+}+e^{-}+v^{-} e

Problem 21P 32–2 to 32–6 Particle Interactions, Particle Exchange (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?

(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) \(p \rightarrow e^{+}+v_{e}\) (e) \(\mu^{+} \rightarrow e^{+}+v_{\mu}^{-}\) (f) \(p \rightarrow n+e^{+}+v_{c}\) Equation Transcription: Text Transcription: \pi^-+p \rightarrow n+\eta^0 \pi^+n+p \rightarrow n+\pi^0 \pi^+ +p \rightarrow p+e^+ p \rightarrow e^+ +v_e p \rightarrow n+e^+ +v_c

(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? \(p+p \rightarrow p+p^{-}\) \(p+p \rightarrow p+p+p^{-}\) \(p+p \rightarrow p+p+p+p^{-}\) \)p+p \rightarrow p+e^{+}+e^{+}+p^{-}\) Equation Transcription: Text Transcription: p+pp+p- p+pp+p+p- p+pp+p+p+p- p+pp+e++e++p-

\(\text { (III) }\) In the rare decay \(\pi^{+} \rightarrow e^{+}+v_{e}\), what is the kinetic energy of the positron? Assume the \(\pi^{+}\) decays from rest and \(m_{v}=0\) Equation Transcription: Text Transcription: (III) \pi^+ \rightarrow e^+ +v_e \pi^+ mv=0

\(\text { (III) }\) Calculate the maximum kinetic energy of the electron when a muon decays from rest via \(\mu^{-} \rightarrow e^{-}+v^{-} e^{+} v_{\mu}\) [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. Equation Transcription: Text Transcription: (III) \mu^- \rightarrow e^- +v^- e^+ v_\mu

\(\text { (III) }\) For the decay \(\Lambda^{0} \rightarrow p+\pi^{-}\), calculate the \(Q \text {-value }\) (energy released), and (b) the kinetic energy of the \(p \text { and } \pi^{-}\), assuming the \(\Lambda^{0}\) decays from rest. (Use relativistic formulas.) Equation Transcription: Text Transcription: (III) \Lambda^0 \rightarrow p+\pi^- Q-value p and \pi^- \Lambda^0

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

\((I)\) The measured width of the \(\psi(3686)\) meson is about \(300 \mathrm{keV}\). Estimate its mean life. Equation Transcription: Text Transcription: (I) \psi(3686) 300 keV

\(\text { (I) }\) The measured width of the \(J / \psi\) meson is \(88 \mathrm{keV}\). Estimate its mean life. Equation Transcription: Text Transcription: (I) J/\psi 88keV

(I) The \(B^{-}\) meson is a bu quark combination. (a) Show that this is consistent for all quantum numbers. (b) What are the quark combinations for \(B^{+}, B^{0}, \bar{B}^{0}\)? Equation Transcription: Text Transcription: B^- B^+,B^0,\bar B^0

(I) What is the energy width (or uncertainty) of \(\eta^{0}\), and (b) \(\rho^{+}\) ? See Table . Equation Transcription: Text Transcription: \eta^0 \rho^+

(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) \(\Omega^{-} \rightarrow \Sigma^{0}+\pi^{-}+v\) (c) \(\Sigma^{0} \rightarrow \Lambda^{0}+\gamma+\gamma\) Equation Transcription: Text Transcription: \Xi^0 \rightarrow \Sigma^+ +\pi^- \Omega^- \rightarrow \Sigma^0+\pi^-+v \Sigma^0 \rightarrow \Lambda^0+\gamma+\gamma

Problem 32EB What effect does an increase in the mass of the virtual exchange particle have on the range of the force it mediates? (a) Decreases it; (b) increases it; (c) has no appreciable effect; (d) decreases the range for charged particles and increases the range for neutral particles.

EXERCISE C Return to the Chapter-Opening Questions, page 915, and answer them again now. Try to explain why you may have answered differently the first time. Equation Transcription: Text Transcription: \gamma Z^0 W^\pm H^0 \mu \tau v_e v_\mu v_\tau

Problem 32ED What is the quark composition of a K- meson?

(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? Equation Transcription: Text Transcription: W W \Delta E \approx W

(II) What quark combinations produce ( a) a \(\Xi^{0}\) baryon and a \(\Xi^{-}\) baryon? Equation Transcription: Text Transcription: \Xi^0 \Xi^-

(II) What are the quark combinations that can form (a) a neutron, (b) an antineutron, (c) a \(\Lambda^{0}\), (d) a \(\Sigma^{-0}\)? Equation Transcription: Text Transcription: \Lambda^0 \Sigma^-0

(II) What particles do the following quark combinations produce: (a) \(\text { uud }\) (b) \(\overline{u u s}\) (c) \(\bar{u} s\) (d) \(d \bar{u}\) (e) \(\bar{c}\)? Equation Transcription: Text Transcription: uud \overline uus \bar us d \bar u \bar c

Problem 37P 32–7 to 32–11 Resonances, Standard Model, Quarks, QCD, GUT (II) What is the quark combination needed to produce a D0 meson (Q = B = S = 0, c = +1)?

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

(II) Draw a possible Feynman diagram using quarks (as in Fig. ) for the reaction \(\pi^{-}+p \rightarrow \pi^{0}+n\) Equation Transcription: Text Transcription: \pi^-+p \rightarrow \pi^0+n

(II) Draw a Feynman diagram for the reaction \(n+v_{\mu} \rightarrow p+\mu^{-}\) Equation Transcription: Text Transcription: n+v_\mu \rightarrow p+\mu^-

Problem 41GP What is the total energy of a proton whose kinetic energy is 15 GeV? What is its wavelength?

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 \(950 \mathrm{MeV}\), how long would its track be as measured in the lab, on average, ignoring any collisions? Equation Transcription: Text Transcription: 950 MeV

(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 K E \approx 0 ) Equation Transcription: Text Transcription:

Problem 45GP 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?

Problem 44GP If 2 X 1014 protons moving at v ? 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?

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) \(K^{+} \rightarrow \pi^{0}+\pi^{0}+\pi^{+}\) Equation Transcription: Text Transcription: \pi^-+p \rightarrow K^0+p+\pi^0 K^-+p \rightarrow \Lambda^0+\pi^0 K^++n \rightarrow \Sigma^++\pi^0+\gamma K^+ \rightarrow \pi^0+\pi^0+\pi^+

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why. (a) \(\pi^{-}+p \rightarrow K^{+}+\sum^{-}\) (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) \(\pi^{-}+p \rightarrow p+e^{-}+v_{e}^{-}\) Equation Transcription: Text Transcription: \pi^- +p \rightarrow K^+ +\sum^- \pi^+ +p \rightarrow K^+ +\Sigma^+ \pi^- +p \rightarrow \Lambda^0+K^0+\pi^0 \pi^+ +p \rightarrow \Sigma^0+\pi^0 \pi^- +p \rightarrow p+e^-+v_e^-

Problem 48GP One decay mode for a ?+ is ?+ µ+ +v µ. What would be the equivalent decay for a ?-? Check conservation laws.

Symmetry breaking occurs in the electroweak theory at about \(10^{-8} \ \mathrm m\). Show that this corresponds to an energy that is on the order of the mass of the \(\mathrm W^\pm\).

Problem 50GP Calculate the Q-value for each of the reactions Eq. 32–4, for producing a pion. (I) What is the time for one complete revolution for a very high-energy proton in the 1.0-km-radiud Fermilab accelerator?

Problem 51GP How many fundamental fermions are there in a water molecule?

The mass of a \(\pi^{0}\) can be mcasurcd 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 \(0.60 \mathrm{MeV}\). Use conservation of energy and momentum to determine the \(\pi^{0}\) mass. Equation Transcription: Text Transcription: \pi^0 \pi^- +p \rightarrow \pi^0+n 0.60 MeV \pi^0

(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 \(10^{16}\ GeV\).

Calculate the \(Q \text {-value }\) 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 \(\Lambda^{0} \text { and } K^{0}\) move off with the same velocity.] Equation Transcription: Text Transcription: Q-value \pi^- +p \rightarrow \Lambda^0+K^0 \Lambda^0 and K^0

Problem 55GP A proton and an antiproton annihilate each other at rest and produce two pions, ?- and ?+What is the kinetic energy of each pion?

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

Problem 57GP 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?

Use the quark model to describe the reaction \(\bar{p}+n \rightarrow \pi^{-}+\pi^{0}\) Equation Transcription: Text Transcription: \bar p+n \rightarrow \pi^- +\pi^0

Problem 60GP What fraction of the speed of light c is the speed of a 7.0-TeV proton?

Identify the missing particle in the following reactions. (a) \(p+p \rightarrow p+n+\pi^{+}+?\) (b) \(p+? \rightarrow n+\mu^{+}\) Equation Transcription: Text Transcription: p+p \rightarrow p+n+ \pi^++? p+? \rightarrow n+ \mu^+

Problem 61GP 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.

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

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.]

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

Calculate the wavelength of 28-GeV electrons.

If particles are accelerated by the cyclotron of Example 322, what must be the frequency of the voltage applied to the dees?

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

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

(a) If the cyclotron of Example 322 accelerated particles, what maximum energy could they attain? What would their speed be? (b) Repeat for deuterons (c) In each case, what frequency of voltage is required?

(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.

What is the wavelength resolvable size) of 7.0-TeV protons at the LHC?

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.)

A cyclotron with a radius of 1.0 m is to accelerate deuterons 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.

Show that the energy of a particle (charge e) in a synchrotron, in the relativistic limit is given by where B is the magnetic field and r is the radius of the orbit (SI units).

About how much energy is released when a decays to (See Table 322.)

How much energy is released in the decay See Table 322.

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

How much energy is required to produce a neutron antineutron pair?

Determine the total energy released when decays to and then to a proton.

Two protons are heading toward each other with equal speeds. What minimum kinetic energy must each have if a meson is to be created in the process? (See Table 322.)

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 pair in addition to themselves? (See Table 322.)

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

The cannot decay by the following reactions. What conservation laws are violated in each of the reactions?

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?

Which of the following reactions and decays are possible? For those forbidden, explain what laws are violated.

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?

In the rare decay what is the kinetic energy of the positron? Assume the decays from rest and .

For the decay calculate (a) the Q-value (energy released), and (b) the kinetic energy of the p and assuming the decays from rest. (Use relativistic formulas.)

Calculate the maximum kinetic energy of the electron when a muon decays from rest via [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.]

The mean life of the particle is What is the uncertainty in its rest energy? Express your answer in MeV.

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

The measured width of the meson is 88 keV. Estimate its mean life.

The meson is a quark combination. (a) Show that this is consistent for all quantum numbers. (b) What are the quark combinations for

What is the energy width (or uncertainty) of (a) and (b) See Table 322.

Which of the following decays are possible? For those that are forbidden, explain which laws are violated.

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 of the virtual W, what is the expected lifetime of the W?

What quark combinations produce (a) a baryon and (b) a baryon?

What are the quark combinations that can form (a) a neutron, (b) an antineutron, (c) a (d

(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) \(\overline c\ s\)?

What is the quark combination needed to produce a

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

Draw a possible Feynman diagram using quarks (as in Fig. 3217c) for the reaction

Draw a Feynman diagram for the reaction n + nm S p + m.

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

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?

(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 )

If protons moving at , with 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?

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?

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why

Which of the following reactions are possible, and by what interaction could they occur? For those forbidden, explain why

One decay mode for a is What would be the equivalent decay for a Check conservation laws

Symmetry breaking occurs in the electroweak theory at about Show that this corresponds to an energy that is on the order of the mass of the

Calculate the Q-value for each of the reactions, Eq. 324, for producing a pion.

How many fundamental fermions are there in a water molecule?

The mass of a can be measured by observing the reaction 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 mass.

(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 \(10^{16}\ GeV\).

Calculate the Q-value for the reaction when negative pions strike stationary protons. Estimate the minimum pion kinetic energy needed to produce this reaction. [Hint: Assume and move off with the same velocity.]

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?

For the reaction where one of the initial protons is at rest, use relativistic formulas to show that the threshold energy is equal to three times the magnitude of the Q-value of the reaction, where is the proton mass. [Hint: Assume all final particles have the same velocity.]

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 of its true value? What are the corresponding wavelength and speed of the proton?

Use the quark model to describe the reaction

Identify the missing particle in the following reaction

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

Using the information in Section 321, show that the Large Hadron Colliders two colliding proton beams can resolve details that are less than 1/10,000 the size of a nucleus.

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

Estimate the lifetime of the Higgs boson from the width of the bump in Fig. 3219, using the uncertainty principle. [Note: This is not a realistic estimate because the underlying processes are very complicated.]