General Physics (PHY 2140)

1. General Physics (PHY 2140) Lecture 20 • Modern Physics • Nuclear Energy and Elementary Particles • Fission, Fusion and Reactors • Elementary Particles • Fundamental Forces • Classification of Particles • Conservation Laws Chapter 30 Chapter 29 http://www.physics.wayne.edu/~alan/2140Website/Main.htm

2. General Physics (PHY 2140) Lecture 21 • Modern Physics • Elementary Particles • Strange Particles – Strangeness • The Eightfold Way • Quarks • Colored Quarks • Electroweak Theory – The Standard Model • The Big Bang and Cosmology Chapter 30 Chapter 29 http://www.physics.wayne.edu/~alan/2140Website/Main.htm

3. Previously… • Nuclear Physics • Nuclear Reactions • Medical Applications • Radiation Detectors Review Problem: A beam of particles passes undeflected through crossed electric and magnetic fields. When the electric field is switched off, the beam splits up in several beams. This splitting is due to the particles in the beam having different A. masses. B. velocities. C. charges. D. some combination of the above E. none of the above r=mv/qB

4. Processes of Nuclear Energy • Fission • A nucleus of large mass number splits into two smaller nuclei • Fusion • Two light nuclei fuse to form a heavier nucleus • Large amounts of energy are released in either case

5. Processes of Nuclear Energy • Fission • A nucleus of large mass number splits into two smaller nuclei • Fusion • Two light nuclei fuse to form a heavier nucleus • Large amounts of energy are released in either case

6. Nuclear Fission • A heavy nucleus splits into two smaller nuclei • The total mass of the products is less than the original mass of the heavy nucleus • First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi • Lisa Meitner and Otto Frisch soon explained what had happened • Fission of 235U by a slow (low energy) neutron • 236U* is an intermediate, short-lived state • X and Y are called fission fragments • Many combinations of X and Y satisfy the requirements of conservation of energy and charge

7. Sequence of Events in Fission • The 235U nucleus captures a thermal (slow-moving) neutron • This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to undergo violent oscillations • The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion • The nucleus splits into two fragments, emitting several neutrons in the process

8. Energy in a Fission Process • Binding energy for heavy nuclei is about 7.2 MeV per nucleon • Binding energy for intermediate nuclei is about 8.2 MeV per nucleon • Therefore, the fission fragments have less mass than the nucleons in the original nuclei • This decrease in mass per nucleon appears as released energy in the fission event • An estimate of the energy released • Assume a total of 240 nucleons • Releases about 1 MeV per nucleon • 8.2 MeV – 7.2 MeV • Total energy released is about 240 MeV • This is very large compared to the amount of energy released in chemical processes

9. QUICK QUIZ In the first atomic bomb, the energy released was equivalent to about 30 kilotons of TNT, where a ton of TNT releases an energy of 4.0 × 109 J. The amount of mass converted into energy in this event is nearest to: (a) 1 g, (b) 1 mg, (c) 1 g, (d) 1 kg, (e) 20 kilotons (c). The total energy released was E = (30 ×103 ton)(4.0 × 109 J/ton) = 1.2 × 1014 J. The mass equivalent of this quantity of energy is:

10. Chain Reaction • Neutrons are emitted when 235U undergoes fission • These neutrons are then available to trigger fission in other nuclei • This process is called a chain reaction • If uncontrolled, a violent explosion can occur • The principle behind the nuclear bomb, where 1 g of U can release energy equal to about 30000 tons of TNT

11. Nuclear Reactor • A nuclear reactor is a system designed to maintain a self-sustained chain reaction • The reproduction constant, K, is defined as the average number of neutrons from each fission event that will cause another fission event • The maximum value of K from uranium fission is 2.5 • Two 235U reactions, one yields 3 the other 2 neutrons • In practice, K is less than this • A self-sustained reaction has K = 1

12. Basic Reactor Design Cadmium • Fuel elements consist of enriched uranium (a few % 235U rest 238U) • The moderator material helps to slow down the neutrons • The control rods absorb neutrons • When K = 1, the reactor is said to be critical • The chain reaction is self-sustaining • When K < 1, the reactor is said to be subcritical • The reaction dies out • When K > 1, the reactor is said to be supercritical • A run-away chain reaction occurs D2O, graphite

13. Schematic of a Fission Reactor

14. Nuclear Fusion • When two light nuclei combine to form a heavier nucleus • Is exothermic for nuclei having a mass less than ~20 • (Iron is the limit, Z=26, A=56) • The sun is a large fusion reactor • The sun balances gravity with fusion energy

15. Sun’s Proton Cycle • First steps: • Followed by H – He or He – He fusion: • or • Total energy released is 25 MeV 2% of sun’s energyis carried by neutrinos

16. Net Result • 4 protons (hydrogen nuclei) combine to give • An alpha particle (a helium nucleus) • Two positrons • One or two neutrinos (they easily escape) • Some gamma ray photons (absorbed) • The two positrons combine with electrons to form more gamma photons • The photons are usually absorbed and so they heat the sun (blackbody spectrum)

17. Fusion Reactors • Enormous energy in a small amount of fuel • 0.06g of deuterium could be extracted from 1 gal of water • This represents the equivalent energy of ~6x109 J • Fusion reactor would most likely use deuterium and tritium

18. Advantages of fusion power • Fuel costs are relatively small • Few radioactive by-products of fusion reaction • (mostly helium-3 and helium-4) Disadvantages of fusion power • Hard to force two charged nuclei together • Reactor is complex and expensive • Need high temperatures and pressures to achieve fusion (~108 K) need a plasma

19. Plasma confinement • Plasma ion density, n • Plasma confinement time,  • In order to achieve a fusion reaction need to satisfy Lawson’s criterion: Deuterium- tritium reactor Deuterium- deuterium reactor So need 108 K for 1 second

20. Fusion Reactors - 1 • Inertial confinement • Inject fuel pellets and hit them with alaser (lots of lasers) or ion beams to heat them • Imploding pellet compresses fuel to fusion densities • Doesn’t require plasma confinement via magnetic fields • Requires large facility to house lasers and target chamber.

21. National Ignition Facility • the facility is very large, the size of a sports stadium • the target is very small, the size of a BB-gun pellet • the laser system is very powerful, equal to 1,000 times the electric generating power of the United States • each laser pulse is very short, a few billionths of a second

22. The beams are generated in the laser bay

23. and deliverd to the target bay.

24. The National Ignition Facility

25. The target chamber

26. Fusion Reactors - 2 • Magnetic field confinement • Tokamak design – a toroidal magnetic field • First proposed by Russian scientists

27. Fusion Reactors – cont. • Tokamak Fusion Test Reactor – ITER

28. ITER’s proposed site layout

29. 30.4 Elementary Particles • First we studied atoms • Next, atoms had electrons and a nucleus • The nucleus is composed of neutrons and protons • What’s next?

30. Elementary particle interactions The scattering of two electrons via a coulomb force This virtual photon is said to mediate the electromagnetic force. The virtual photon can never be detected because it only lasts for a vanishing small time. An simple example of a Feynman diagram

31. Interactions continued • Can have similar diagrams with other particles and other forces • Strong force, weak force, gravity • Basic idea of exchange of a virtual particle is the common theme.

32. More examples of Feynman diagrams

33. 30.5 The Fundamental Forces in Nature • Strong Force • Short range ~ 10-15 m (1 fermi) • Responsible for binding of quarks into neutrons and protons • Gluon • Electromagnetic Force • 10-2 as strong as strong force • 1/r2 force law • Binding of atoms and molecules • Photon • Weak force • ~ 10-6 times as strong as the strong force • Responsible for beta decay, very short range ~10-18 m • W+, W- and Z0 bosons • Gravitational Force • 10-43 times as strong as the strong force • Also 1/r2 force law • Graviton

34. 30.6 Positrons and Antiparticles • Dirac proposed the positron to solve a negative energy problem (Dirac sea) • The general implication is that for every particle there is an antiparticle (symmetry) • Other antiparticles: • antiproton, antineutrino • Usually denoted with a bar over symbol • Some particles are their own antiparticles • photon, neutral pion: , 0

35. 30.7 Mesons • Part of an early theory to describe nuclear interactions • Mass between a electron and a proton • Flavors • Charged p meson: p+, p- ,mass 139.6 MeV/c2 • Netral p meson, p0 ,mass 135.0 MeV/c2 • Lifetimes 2.6x10-8 s for p+, p- 8.3x10-17 s for p0

36. More Mesons • Also have heavier mesons • Kaons ~500 MeV/c2 • Etas 548 and 958 MeV/c2 (note, mass of  is greater than proton mass)

37. 30.8 Particle Classification(Classify the animals in the particle zoo) Hadrons (strong force interaction, composed of quarks) • We already met the mesons (middle weights) • Decay into electrons, neutrinos and photons • Baryons, i.e. the proton and neutron (the heavy particles) • Still other more exotic baryons: • L, S, X,  all are heavier than the proton • Decay into end products that include a proton

38. Particle Classification – cont. • Leptons • Small or light weight particles • Are point like particles – no internal structure (yet) • 6 leptons (and their antiparticles 6 more) • Electron e, muon m, tau t • and their associated neutrinos: ne, nm, nt • Neutrinos have tiny mass, ~3 eV/c2

39. Some members of the Zoo

40. Particle Physics Conservation Laws So far in Physics we have conservation of energy, momentum (linear and angular), charge, spin. Now we add more to help balance particle reactions • Baryon number: • B = +1 for baryons, -1 for anti-baryons • Eg. Proton, neutron have B = +1 • , antiparticles have B = -1 • B = 0 for all other particles (non-baryons)

41. More Conservation Laws • Lepton number • L = +1 for leptons, -1 for anti-leptons • L = 0 for non-leptons • Example for electrons: • Electron e, electron neutrino ne have Le = +1 • Anti electron and antineutrino have Le = -1 • Other leptons have Le = 0 BUT have their own lepton numbers, Lm, Lt • Refer to table 30.2

42. Example neutron decay • Consider the decay of the neutron • Before: B = +1, Le = 0 • After: B = +1, Le = +1 -1 = 0

43. Quiz 30.2 • Which of the following cannot occur? • (a) • (b) • (c) • (d)

44. Quiz 30.2 - answer • The disallowed reaction is (a) because • Charge is not conserved: • Q = +2  Q = +1 • Baryon number is also not conserved: • B = +2  B = +2-1 = +1

45. Strangeness • Several particles found to have unusual (strange) properties: • Always produced in pairs p- + p+ K0 + L0 but notp- + p+ K0 + n • Decay is slow (indicative of weak interaction rather than strong) Half-lives of order of 10-10 to 10-8 sec • Members of the strange club: K, L, S

46. More Strangeness • Explanation lies in the addition of a new conservation law – Strangeness, S • One of the pair of strange particles gets S=+1 the other S=-1. All other particles get S=0. So in the previous reaction, strangeness is conserved: • Before S=0; After S=+1-1 = 0 • Second reaction violates strangeness

47. Example 30.6: Strangeness Conservation Consider: p- + n  K+ + S- • Before: S=0+0=0 (no strange particles) • After: K+ has S=+1, S- has S = -1 thus the net strangeness S = +1-1 = 0 • So reaction does not violate law of conservation of strangeness, the reaction is allowed

48. The Eightfold Way Consulting table 30.2, Take the first 8 baryons and plot Strangeness vs. Charge. We get an interesting picture. A hexagonal pattern emerges. If we do the same for the spin 0 mesons we also get a hexagonal pattern.

49. The Eightfold Way

50. The Original Quark Model (in B/W) • Gell-Mann (1961) proposed hadrons have structure, i.e. composed of a more fundamental type of particle. • Quarks have fractional charge e/3 or 2e/3 • Three types u, d, s: up, down, strange • Mesons were made of 2 quarks: q, q • Baryons were made of 3 quarks ¯