General Physics PHY 2140 Lecture 20 Modern Physics

General Physics (PHY 2140) Lecture 20 Ø Modern Physics Nuclear Energy and Elementary Particles Fission, Fusion and Reactors Elementary Particles Fundamental Forces Classification of Particles Conservation Laws Chapter 2930 http: //www. physics. wayne. edu/~alan/2140 Website/Main. htm

General Physics (PHY 2140) Lecture 21 Ø Modern Physics Elementary Particles Strange Particles – Strangeness The Eightfold Way Quarks Colored Quarks Electroweak Theory – The Standard Model The Big Bang and Cosmology Chapter 2930 http: //www. physics. wayne. edu/~alan/2140 Website/Main. htm

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/q. B

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

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

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 235 U by a slow (low energy) neutron § 236 U* 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

Sequence of Events in Fission § The 235 U nucleus captures a thermal (slow-moving) neutron § This capture results in the formation of 236 U*, and the excess energy of this nucleus causes it to undergo violent oscillations § The 236 U* 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

Energy in a Fission Process § Binding energy for heavy nuclei is about 7. 2 Me. V per nucleon § Binding energy for intermediate nuclei is about 8. 2 Me. V 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 Me. V per nucleon § 8. 2 Me. V – 7. 2 Me. V § Total energy released is about 240 Me. V § This is very large compared to the amount of energy released in chemical processes

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:

Chain Reaction § Neutrons are emitted when 235 U 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

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 235 U reactions, one yields 3 the other 2 neutrons § In practice, K is less than this § A self-sustained reaction has K = 1

Basic Reactor Design § Fuel elements consist of enriched § § § Cadmium uranium (a few % 235 U rest 238 U) 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 selfsustaining § 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 D 2 O, graphite

Schematic of a Fission Reactor

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

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

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)

Fusion Reactors § Enormous energy in a small amount of fuel § 0. 06 g of deuterium could be extracted from 1 gal of water § This represents the equivalent energy of ~6 x 109 J § Fusion reactor would most likely use deuterium and tritium

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

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

Fusion Reactors - 1 § Inertial confinement § Inject fuel pellets and hit them with a laser (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.

National Ignition Facility § the facility is very large, the size of a sports stadium § the target is very small, the size of a BBgun 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

The beams are generated in the laser bay

and deliverd to the target bay.

The National Ignition Facility

The target chamber

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

Fusion Reactors – cont. § Tokamak Fusion Test Reactor – ITER

ITER’s proposed site layout

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?

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

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.

More examples of Feynman diagrams

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 force 1/r 2 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 Z 0 bosons § Gravitational Force § § § 10 -43 times as strong as the strong force Also 1/r 2 force law Graviton

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

30. 7 Mesons § Part of an early theory to describe nuclear interactions § Mass between a electron and a proton § Flavors § Charged meson: +, - , mass 139. 6 Me. V/c 2 § Netral meson, 0 , mass 135. 0 Me. V/c 2 § Lifetimes 2. 6 x 10 -8 s for +, 8. 3 x 10 -17 s for 0

More Mesons § Also have heavier mesons § Kaons ~500 Me. V/c 2 § Etas 548 and 958 Me. V/c 2 (note, mass of is greater than proton mass)

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

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 , tau t § and their associated neutrinos: e, , t § Neutrinos have tiny mass, ~3 e. V/c 2

Some members of the Zoo

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)

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 e have Le = +1 § Anti electron and antineutrino have Le = -1 § Other leptons have Le = 0 BUT have their own lepton numbers, L , Lt § Refer to table 30. 2

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

Quiz 30. 2 § Which of the following cannot occur? § (a) § (b) § (c) § (d)

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 -1 = +1

Strangeness § Several particles found to have unusual (strange) properties: § Always produced in pairs - + p+ K 0 + L 0 but not - + p+ K 0 + 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

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

Example 30. 6: Strangeness Conservation Consider: - + 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

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.

The Eightfold Way

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 2 e/3 § Three types u, d, s: up, down, strange § Mesons were made of 2 quarks: q, q¯ § Baryons were made of 3 quarks

But that wasn’ enough! § Soon after, experimental discrepancies required the addition of three more quarks § Top, bottom and charm: t, b, c § And three more conservation laws: C, B, T for charm, bottomness and topness

Properties of Quarks and Antiquarks

Fundamental Particles: Properties Quarks Particle Rest Energy Charge (e) u 360 Me. V +2/3 d 360 Me. V -1/3 c 1500 Me. V +2/3 s 540 Me. V -1/3 t 173 Me. V +2/3 b 5 Ge. V -1/3

Fundamental Particles Properties continued Leptons Particle Rest Energy Charge e- 511 ke. V -e - 107 Me. V -e t- 1784 Me. V -e e < 30 e. V 0 < 0. 5 Me. V 0 t < 250 Me. V 0

Quarks in Mesons and Baryons We should still be in B/W!

Co l o r § Because of the Pauli exclusion principle (all quarks are spin ½ particles) can’t have three of the same particles occupying the same state. § Example: - is (sss) so need three different yet strange quarks § So colored quarks were proposed

Color continued § Three color charges were added § Red, green blue: r, g, b § And…three anti-colors § antired, antigreen and antiblue: r¯, g¯, b¯ § Mesons have a color anticolor pair § Spin is either zero or 1 so can have ↑↑ or ↑↓ § Baryons must have three different colors § Spin is ½ so have ↑↑↓ or ↓↓↑

Quarks combinations with color Total spin is 0 or 1 Total spin is ½ or 3/2

Quantum Chromodynamics § In analogy with photons and the electromagnetic § § § force, an interaction between colored quarks is the result of color force – 8 colored gluons. The general theory is complex but explains experimental results better. Numerical results can be very hard to calculate Opposite colors attract, red-antired, in analogy with electromagnetism. Different colors also attract though less strongly Residual color force is responsible for nuclear force that bind protrons and neutrons.

Interactions in the Yukawa pion and quark-gluon models Yukawa’s pion model Quark QCD model In both cases a proton-neutron pair scatter off each other and exchange places.

The Standard Model

History of the Universe and of the four forces Energy: 1028 Time: 0 1024 10 -40 10 -35 1021 1017 1013 1011 10 -11 e. V sec

Time

Big Bang Model A broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. In the beginning, there was a Big Bang, a colossal explosion from which everything in the Universe sprung out.

Experimental Evidence of the Big Bang q Expansion of the universe q q Abundance of the light elements H, He, Li q q Edwin Hubble's 1929 observation that galaxies were generally receding from us provided the first clue that the Big Bang theory might be right. The Big Bang theory predicts that these light elements should have been fused from protons and neutrons in the first few minutes after the Big Bang. The cosmic microwave background (CMB) radiation q The early universe should have been very hot. The cosmic microwave background radiation is the remnant heat leftover from the Big Bang.

Cosmic Microwave Background 99. 97% of the radiant energy of the Universe was released within the first year after the Big Bang itself and now permeate space in the form of a thermal 3 K radiation field. COBE CMB Measurement

• CMB spectrum is that of a nearly perfect blackbody with a temperature of 2. 725 +/- 0. 002 K. • Observation matches predictions of the hot Big Bang theory extraordinarily well. • Deviation from perfect black body spectrum less than 0. 03 % • Nearly all of the radiant energy of the Universe was released within the first year after the Big Bang.

How did we get from there… … to here?

Let there be light: 400, 000 -700, 000 years