of this particle?
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Particles and interactions :MCQ 1. If a charged pion that decays in 10-8 second in its own rest frame is to travel 30 meters in the laboratory before decaying, the pion’s speed must be most nearly (A) 0.43 ¥ 108 m/s (B) 2.84 ¥ 108 m/s (C) 2.90 ¥ 108 m/s (D) 2.98 ¥ 108 m/s (E) 3.00 ¥ 108 m/s 2 The Lagrangian for a mechanical system is L=aq2+ bq4 where q is a generalized coordinate and a and b are constants. The equation of motion for this system is 3. The matrix shown above transforms the components of a vector in one coordinate frame S to the components of the same vector in a second coordinate frame S′. This matrix represents a rotation of the reference frame S by (A) 30° clockwise about the x-axis (B) 30° counterclockwise about the z-axis (C) 45° clockwise about the z-axis (D) 60° clockwise about the y-axis (E) 60° counterclockwise about the z-axis 4. The mean kinetic energy of the conduction electrons in metals is ordinarily much higher than kT because (A) electrons have many more degrees of freedom than atoms do (B) the electrons and the lattice are not in thermal equilibrium (C) the electrons form a degenerate Fermi gas (D) electrons in metals are highly relativistic (E) electrons interact strongly with phonons 5. An ensemble of systems is in thermal equilibrium with a reservoir for which kT = 0.025 eV. State A has an energy that is 0.1 eV above that of state B. If it is assumed the systems obey Maxwell-Boltzmann statistics and that the degeneracies of the two states are the same, then the ratio of the number of systems in state A to the number in state B is (A) e+4 (B) e+0.25 (C) 1 (D) e-0.25 (E) e-4 6. The muon decays with a characteristic lifetime of about 10-6 second into an electron, a muon neutrino, and an electron antineutrino. The muon is forbidden from decaying into an electron and just a single neutrino by the law of conservation of (A) charge (B) mass (C) energy and momentum (D) baryon number (E) lepton number 7. A particle leaving a cyclotron has a total relativistic energy of 10 GeV and a relativistic momentum of 8 GeV/c. What is the rest mass of this particle? (A) 0.25 GeV/c2 (B) 1.20 GeV/c2 (C) 2.00 GeV/c2 (D) 6.00 GeV/c2 (E) 16.0 GeV/c2 8. The neutrino belongs to the same family as A. Neutron B. Proton. C. Electron. D. Baryon 9. Hadrons doffer from other two families in that A. The mainly interact via electromagnetic force B. they mainly interact via the gravitational force C. they mainly interact via strong nuclear force. D. they mainly intercat via the weak interaction force. 10. A coil of 15 turns, each of radius 1 centimeter, is rotating at a constant angular velocity w = 300 radians per second in a uniform magnetic field of 0.5 tesla, as shown in the figure above. Assume at time t = 0 that the normal n� to the coil plane is along the y-direction and that the selfinductance of the coil can be neglected. If the coil resistance is 9 ohms, what will be the magnitude of the induced current in milliamperes? (A) 225p sinwt (B) 250p sinwt (C) 0.08p coswt (D) 1.7p coswt (E) 25p coswt 11. Pair production results when A. particles and antiparticles annihilate one another B. particle of sufficient energy pass close to a nucleus. C. gamma rays of sufficient energy pass close to a nucleus. D. gamma rays and particles annihilate one another. 12. pair production results when A. Particles annihilate one another B. particles of sufficient energy pass close to a nucleus. C. gamma rays of sufficient pass close to the nucleus D. gamma rays and particles annihilate one another. Particle accelerators and detectors Short Answers 1. This question is about particle accelerators. Particle accelerators may be used to accelerate protons. If the energy of the accelerated protons is high enough then, when these protons collide with stationary protons, different types of particles of large mass may be produced. (a) Explain why high energies are required to produce particles of large mass. ...................................................................... . ...................................................................... . ...................................................................... . ...................................................................... . (b) The diagram shows the basic structure of a cyclotron in which protons are accelerated. metal “D’s” path of proton Add labels to the diagram above to show the (i) magnets and their polarity. [1] (ii) points where the alternating electric potential difference is applied.[1] (c) Outline why the frequency of the alternating electric potential difference is made equal to the frequency of orbit of the protons. ....................................................................... ....................................................................... ....................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [2] 2. a) (i) Describe the operating principle of the bubble chamber. [2] .................................................................. .................................................................. .................................................................. .................................................................. (ii) Outline how two particle properties or characteristics are measured using a bubble chamber. [2] .............................................................. .............................................................. .............................................................. .............................................................. .............................................................. (b) The proportional wire spark chamber has now replaced the bubble chamber. Outline two advantages of this detector compared to the bubble chamber. [2] ................................................................... ................................................................... ................................................................... ................................................................... 3. A drift tube accelerator has an alternating potential difference of 50kV, with a frequency of 10 MHz applied to a row of tubular electrodes. Calculate the length of the drift tube if electrons are to arrive at the right time to be accelerated in the next gap ................................................................... ................................................................... ................................................................... 4. The synchrotron at Fermilab has a diameter of 2.0 km. Estimate the magnetic flux density needed to move a proton beam of 350 GeV. ................................................................... ................................................................... ................................................................... ................................................................... 5. A cyclotron is operated as an oscillator frequency of 15 MHz and has a dee radius of 0.50m. a) Calculate the magnetic flux density needed to accelerate protons in the cyclotron ................................................................... ................................................................... b) Determine the kinetic energy of the proton in MeV. ................................................................... ................................................................... 6. Calculate the total energy and the wavelength of a proton that has kinetic energy of 30 GeV. ................................................................... ................................................................... 7. Calculate the strength of a magnetic field use in a cyclotron in which a deuteron makes 1.5 x 107 revolutions per second. ................................................................... ................................................................... 8. A drift tube accelerator has an alternating potential difference of 30 kV, with a frequency of 15 MHz applied to a tow of tubular electrodes. Calculate the lengths of the first drift tube if electrons are to arrive at the right time to be accelerated in the next gap? ................................................................... ................................................................... ................................................................... ................................................................... 9. At CERN, protons are injected into a 200m Diameter 28 GeV synchrotron ring with an energy of 50 MeV. The tube is filled with protons which are injected with proton current of 100 MA for 6 uS. Ther are 14 acceleration point spaced evenly around the ring with a potential difference between the electrodes of each accelerator of 4 kV. The final energy of the proton is 28 Gev. If relvistive effets are ignored: a) Calculate the speed of the protons at injection ................................................................... ................................................................... b) Determine the time it takes to go around the ring at this speed. ................................................................... ................................................................... c) Calculate the momentum of the proton at injection. ................................................................... ................................................................... d) Determine the number of protons that were injected. ................................................................... ................................................................... e) Deduce by how much the energy of proton increases in each revolution of the synchrotron. ................................................................... ................................................................... f) Estimate the number of times a proton must go around the accelerator to obtain its final maximum energy. ................................................................... ................................................................... 10 An ion gun in an evacuated container consists of 2 parallel conducting plates separated by a distance of 2.0 cm. A potential difference of 50 kV is applied across the plates. Protons enter between the plates and drift with negligible speed into a region between the plates. The negative plate has a small hole where protons can be ejected. (a) Calculate the electric field strength between the plates. . (b) Determine the energy of the protons that are ejected through the hole of the negative plate. ................................................................... ................................................................ (c) Deduce that the speed of the protons ejected through the hole is approximately 3.1 x 10-6 ms’. ................................................................... . ................................................................ (d) Describe why the apparatus is evacuated. ................................................................... . ................................................................ 11. A cyclotron is operated at an oscillator frequency 15 MHz and has a dee radius 0.50 m. (a) Calculate the magnetic flux density needed to accelerate deuterons in the cyclotron. ................................................................... . ................................................................ (b) Determine the kinetic energy of the protons in MeV. ................................................................... . ................................................................ 12. Estimate the maximum resolving power that attainable using 370 GeV protons. ................................................................... . ................................................................ 13. The hadron track at CERN has a diameter of 8.5 km. Estimate the hint would take a high energy proton to make one revolution in the collider. ................................................................... . ................................................................ 14. the following figure sketch of the path of th epair production of an proton and antiproton. There is a magnetic field pointing out of the (a) Explain which of the tracks is due to the antiproton. A or B ................................................................... ................................................................ (b) Deduce whether the particles have the same energy. ................................................................... . ................................................................ 15. An ion gun in an evacuated container consists of 2 parallel conduction plates separated by a distance of 2.0 cm. A potential difference of 50 kVm. is applied across the plates. Protons enter between the plates and drift with negligible speed into a region between the plates. The negative plate has a small hole where protons can be ejected. (a) Calculate, the electric held strength between the plates. ................................................................... . ................................................................ (b) Determine the energy of the protons that are ejected through the hole of the negative plate. ................................................................... . ................................................................ (c) Deduce that the speed of the protons ejected through the hole is approximately 3.1 x 10-6 ms. ................................................................... . ................................................................ (d) Describe why the apparatus is evacuate ................................................................... . ................................................................ MCQ Questions 1-2 The sketch below shows a one-dimensional potential for an electron. The potential is symmetric about the V-axis. 1. Which of the following statements correctly describes the ground state of the system with one electron present? (A) A single electron must be localized in one well. (B) The ground state will accommodate up to four electrons. (C) The kinetic energy of the ground state will be one-half its potential energy. (D) The wave function of the ground state will be antisymmetric with respect to the V-axis. (E) The wave function of the ground state will be symmetric with respect to the V-axis. 2. A second electron is now added to the system. If the electrons do not interact, which of the following statements is correct? (A) The second electron must be localized in the well not previously occupied. (B) In the ground state of the system, each of the two electrons will have the same spatial wave function. (C) In the ground state of the system, one electron will be in a spatially symmetric state and one will be in a spatially antisymmetric state. (D) The second electron will not be bound. (E) Pair annihilation will occur. Questions 3-4 A particle with rest mass m and momentum mc/2 collides with a particle of the same rest mass that is initially at rest. After the collision, the original two particles have disappeared. Two other particles, each with rest mass m¢, are observed to leave the region of the collision at equal angles of 30° with respect to the direction of the original moving particle, as shown below. 3. What is the speed of the original moving particle? (A) c/5 (B) c/3 (C) c/ √7 (D) c/ √5 (E) c/2 4. What is the momentum of each of the two particles produced by the collision? (A) mc/5 (B) mc/2√ 3 (C) mc/ √5 (D) mc/2 (E) mc/√ 3 5. The nonconservation of parity in the decay p+®m++v can be verified by measuring the (A) Q-value of the decay (B) Longitudinal polarization of the m+ (C) Longitudinal polarization of the p+ (D) Angular correlation between the m+ and the v (E) Time dependence of the decay process Question 6-7 A long, thin, vertical wire has a net positive charge l per unit length. In addition, there is a current I in the wire. A charged particle moves with speed u in a straight-line trajectory, parallel to the wire and at a distance r from the wire. Assume that the only forces on the particle are those that result from the charge on and the current in the wire and that u is much less than c, the speed of light. 6. Suppose that the current in the wire is reduced to I/2. Which of the following changes, made simultaneously with the change in the current, is necessary if the same particle is to remain in the same trajectory at the same distance r from the wire? (A) Doubling the charge per unit length on the wire only (B) Doubling the charge on the particle only (C) Doubling both the charge per unit length on the wire and the charge on the particle (D) Doubling the speed of the particle (E) Introducing an additional magnetic field parallel to the wire 7. The particle is later observed to move in a straight-line trajectory, parallel to the wire but at a distance 2r from the wire. If the wire carries a current I and the charge per unit length is still l , the speed of the particle is (A) 4u (B) 2u (C) u (D) u/2 (E) u/4 30. An energy level of a certain isolated atom is split into three components by the hyperfine interaction coupling of the electronic and nuclear angular momenta. The quantum number j , specifying the magnitude of the total electronic angular momentum for the level, has the value j = 3/2. The quantum number i, specifying the magnitude of the nuclear angular momentum, must have the value (A) 1/2 (B) 1 (C) 3/2 (D) 2 (E) 3 31. An electron with energy E and momentum kj is incident from the left on a potential step of height V>E at x=0 . For x > 0 , the space part of the electron’s wave function has the form (A) eikx (B) e -ik x ¢ k < k ; ¢ (C) e-a x , where a is real and positive (D) sinkx (E) identically zero Quarks Short Answers 1. The Feynman diagram represents the electromagnetic interaction between two electrons. e– e– γ e– e– Another possible interaction between the electrons involves a neutral current. (a) (i) a Describe with reference to the interaction between the electrons, what is meant by neutral current. [2] ................................................................. . ................................................................. . ................................................................. . ................................................................. . (ii) the with reference to your answer in (a)(i), how experimental evidence supports standard model.[2] ................................................................. . ................................................................. . ................................................................. . ................................................................. . (b) Draw a Feynman diagram to show the production of an electron positron pair. [1] (c) According to the Big Bang theory, the production of electron positron pairs became possible when the universe had cooled to a temperature T. Determine, to the nearest power of ten, the value of T. [2] 2. The diagram below shows the2 eight spin ½ baryons made out of the three lightest quarks, the up (u), the down (d) and the strange (s). In this plot baryons belonging to the same horizontal line have the same strangeness (S) and those along the same slanted line have the same charge (Q). Q = –1 S=0 Q=0 Q=1 S = –1 S = –2 (a) (i) (ii) On the diagram above draw a circle around the point representing the neutron. State the quark content of the neutron. [1] ................................................................. . (b) The 0 baryon is unstable and decays according to the reaction . The quark content of the particles involved is du . ssd , 0 uds and [1 Worksheets State and explain whether the interaction involved in this decay is electromagnetic, strong or weak. ................................................................... ................................................................... ................................................................... MCQ Worksheets Leptons and the standard model Short Answers 1. 2 3 4 5 6 Worksheets 7 8 9 10 Worksheets MCQ 1 2 Worksheets Experimental evidence for the quark and standard models Short Answers MCQ Worksheets Cosmology and strings Short Answers (a) It is assumed that in the first 10–2 s after the Big Bang quarks behaved as free particles that could not bind into nucleons. Suggest a reason for this. ................................................................... .... ................................................................... .... ................................................................... .... [2] (b) At a time of 10–2 s after the Big Bang the average thermal energy per particle in the universe was approximately 50 MeV. Estimate the temperature of the universe 10–2 s after the Big Bang. ................................................................... .... ................................................................... .... [2] (c) In the very early universe it is thought that the total number of particles was only very slightly larger than the number of antiparticles. Explain why the matter in the present universe is made predominantly by particles and not antiparticles. ................................................................... .... ................................................................... .... ................................................................... .... [2] (d) Outline why physicists were led to consider string theories. Worksheets ................................................................... .... ................................................................... .... [2] (e) Many string theories suggest that space is 10 dimensional rather than the usual 3+1 dimensions (3 for space and 1 for time). Assuming that string theory is correct, explain why we are not aware of the extra dimensions. ................................................................... .... ................................................................... .... MCQ Worksheets Worksheets Activities Activity Three -- Rutherford's Discovery (Student Page) In this activity, you and your team members will use the methods pioneered by Ernest Rutherford in the early 1900s and still used by particle physicists in their accelerator experiments today. These methods enable scientists to identify the characteristics of particles that they cannot actually see. You will learn how precise your measurements must be when you can't see what you are studying. On your team's experiment table there is a large wooden board, under which your teacher has placed a flat shape. Your team's job is to identify the shape without ever seeing it. You can only roll marbles against the hidden object and observe the deflected paths that the marbles take. Your team will have five minutes to "observe" a shape. Place a piece of paper on top of the board for sketching the paths of the marbles. Then analyze this information to determine the object's actual shape. Draw a small picture of each shape you studied in the boxes below, and answer the following questions. 1. Can you tell the size of the object as well as its shape? _______________________________________________ 2. How could you find out whether the shape has features that are small compared to the size of your marbles? _______________________________________________ _______________________________________________ _______________________________________________ 3. Without looking, how can you be sure of your conclusions? _______________________________________________ _______________________________________________ _______________________________________________ Activity Two -- Psyching Out the System (Student Page) When scientists study any system they must ask two basic questions: 1) What are the basic objects, or "building blocks," from which this system is made? 2) What are the interactions between these objects? Worksheets The answer to these questions depends on the scale at which you study the system. Particle physics plays this game on the smallest possible scales -- seeking to discover the basic building blocks of all matter and the fundamental interactions between them. The connecting rules of these interactions, or basic forces, explain why some composite objects are observed and others are not observed. The basic forces are as important as the "building blocks" in explaining data, and what does not happen is as important a clue as what does. This puzzle shows the challenge that particle physicists face. Imagine that the puzzle presents information that was obtained about particles from an accelerator. The black figures represent objects that were observed, while the objects shown in white have not been observed. In this puzzle, "objects" are all two-dimensional shapes, and "interactions" are ways in which they can combine. The shapes that are not observed provide important clues to the answers. Write your answers in these spaces. Note that you need to answer both questions to explain why the objects that are not observed are not possible. The observed figures are constructed from: 1. ______________________________________ ______________________________________ 2. ______________________________________ ______________________________________ The rules for connecting these shapes are: 1. ______________________________________ ______________________________________ 2. ______________________________________ ______________________________________ [Puzzle adapted from Helen Quinn, "Of Quarks, Antiquarks, and Glue." The Stanford Magazine, Fall, 1983, p.29.] Worksheets Activity One -- Fundamentally Speaking (Student Page) "What is the world made of? What holds it together" Democritus (460-370 B.C.) People have asked these questions for thousands of years. But only recently has a clear picture of the "building blocks" of our universe been developed. The scientists who have developed this picture work in an exciting and challenging field called high-energy particle physics. Their discoveries are summarized in the chart, Standard Model of Fundamental Particles and Interactions. How much do you know about the latest theories and research on these ancient questions? You can find out by reading each of the statements below and placing a check mark in the proper box to indicate whether you agree or disagree.
