General Physics (PHY 2140)

Lecture 21Lecture 21 Modern Physics

Elementary ParticlesStrange Particles – StrangenessThe Eightfold WayQuarksColored QuarksElectroweak Theory – The Standard ModelThe Big Bang and Cosmology

Chapter 29

http://www.physics.wayne.edu/~alan/2140Website/Main.htm

Chapter 30Chapter 30

Previously…Previously…

Nuclear Energy, Elementary ParticlesNuclear Energy, Elementary Particles

Nuclear Reactors, Fission, FusionNuclear Reactors, Fission, Fusion

Fundamental Forces

Classification of Particles

Elementary ParticlesElementary Particles

First we studied atomsFirst we studied atoms Next, atoms had electrons and a nucleusNext, atoms had electrons and a nucleus The nucleus is composed of neutrons and The nucleus is composed of neutrons and

protonsprotons What’s next?What’s next?

30.5 The Fundamental Forces in Nature30.5 The Fundamental Forces in Nature

Strong ForceStrong Force Short range ~ 10Short range ~ 10-15-15 m (1 fermi) m (1 fermi) Responsible for binding of quarks into neutrons and protonsResponsible for binding of quarks into neutrons and protons GluonGluon

Electromagnetic ForceElectromagnetic Force 1010-2 -2 as strong as strong forceas strong as strong force 1/r1/r2 2 force lawforce law Binding of atoms and moleculesBinding of atoms and molecules PhotonPhoton

Weak forceWeak force ~ 10~ 10-6-6 times as strong as the strong force times as strong as the strong force Responsible for beta decay, very short range ~10Responsible for beta decay, very short range ~10-18-18 m m WW++, W, W-- and Z and Z0 0 bosonsbosons

Gravitational ForceGravitational Force 1010-43-43 times as strong as the strong force times as strong as the strong force Also 1/rAlso 1/r2 2 force lawforce law GravitonGraviton

30.8 Particle Classification30.8 Particle Classification((Classify the animals in the particle zoo)Classify the animals in the particle zoo)

Hadrons Hadrons (strong force interaction, composed of quarks)(strong force interaction, composed of quarks)

We already met the mesons (We already met the mesons (middlemiddle weights) weights) Decay into electrons, neutrinos and photonsDecay into electrons, neutrinos and photons

BaryonsBaryons, i.e. the proton and neutron (the , i.e. the proton and neutron (the heavyheavy particles) particles)

Still other more exotic baryons: Still other more exotic baryons: all are heavier than the protonall are heavier than the proton Decay into end products that include a proton Decay into end products that include a proton

Particle Classification – cont.Particle Classification – cont.

LeptonsLeptons Small or light weight particlesSmall or light weight particles Are point like particles – no internal structure Are point like particles – no internal structure

(yet)(yet) 6 leptons 6 leptons Electron eElectron emuonmuontautau and their associated neutrinos: and their associated neutrinos: ee, , , ,

Also, their antiparticlesAlso, their antiparticles Neutrinos have tiny mass, ~3 eV/cNeutrinos have tiny mass, ~3 eV/c22

Some members of the ZooSome members of the Zoo

Particle Physics Conservation LawsParticle Physics Conservation Laws

So far in Physics we have conservation of energy, So far in Physics we have conservation of energy, momentum (linear and angular), charge, spin. momentum (linear and angular), charge, spin. Now we add more to help balance particle Now we add more to help balance particle reactionsreactions

Baryon number:Baryon number: B = +1 for baryons, -1 for anti-baryonsB = +1 for baryons, -1 for anti-baryons Eg. Proton, neutron have B = +1Eg. Proton, neutron have B = +1 , antiparticles have B = -1, antiparticles have B = -1 B = 0 for all other particles (non-baryons)B = 0 for all other particles (non-baryons)

p, n

More Conservation LawsMore Conservation Laws

Lepton numberLepton number L = +1 for leptons, -1 for anti-leptonsL = +1 for leptons, -1 for anti-leptons L = 0 for non-leptonsL = 0 for non-leptons

Example for electrons:Example for electrons: Electron e, electron neutrino Electron e, electron neutrino ee have L have Lee = +1 = +1

Anti electron and antineutrino have LAnti electron and antineutrino have Lee = -1 = -1

Other leptons have LOther leptons have Lee = 0 = 0 BUTBUT have their own lepton have their own lepton

numbers, Lnumbers, L, L, L

Refer to tableRefer to table

Example neutron decayExample neutron decay

Consider the decay of the neutronConsider the decay of the neutron

Before: B = +1, LBefore: B = +1, Lee = 0 = 0

After: B = +1, LAfter: B = +1, Lee = +1 -1 = 0 = +1 -1 = 0

+ -en p + e + ν

Quiz 30.2Quiz 30.2

Which of the following cannot occur?Which of the following cannot occur? (a)(a)

(b)(b)

(c)(c)

(d)(d)

-e

- -e μ

- -μ

p + p p + p + p

n p + e +

μ e + + ν

π μ +ν

Quiz 30.2 - answerQuiz 30.2 - answer

The disallowed reaction is (a) becauseThe disallowed reaction is (a) because Charge is not conserved:Charge is not conserved:

Q = +2 Q = +2 Q = +1 Q = +1

Baryon number is also not conserved:Baryon number is also not conserved: B = +2 B = +2 B = +2-1 = +1 B = +2-1 = +1

p + p p + p + p

StrangenessStrangeness

Several particles found to have unusual Several particles found to have unusual (strange) properties:(strange) properties: Always produced in Always produced in pairspairs

-- + p + p++ K K00 + + 0 0 but notbut not -- + p + p++ K K00 + n + n Decay is slow (indicative of weak interaction Decay is slow (indicative of weak interaction

rather than strong) Half-lives of order of 10rather than strong) Half-lives of order of 10 -10-10 to 10to 10-8-8 sec sec

Members of the strange club: K, Members of the strange club: K, , ,

More StrangenessMore Strangeness

Explanation lies in the addition of a new Explanation lies in the addition of a new conservation law – Strangeness, Sconservation law – Strangeness, S

One of the pair of strange particles gets One of the pair of strange particles gets S=+1 the other S=-1. All other particles S=+1 the other S=-1. All other particles get S=0. So in the previous reaction, get S=0. So in the previous reaction, strangeness is conserved:strangeness is conserved:

Before S=0; After S=+1-1 = 0Before S=0; After S=+1-1 = 0 Second reaction violates strangenessSecond reaction violates strangeness

Example 30.6: Strangeness ConservationExample 30.6: Strangeness Conservation

Consider:Consider: -- + n + n K K++ + + - -

Before: S=0+0=0 (no strange particles)Before: S=0+0=0 (no strange particles) After: KAfter: K++ has S=+1, has S=+1, - - has S = -1 thus the has S = -1 thus the

net strangeness S = +1-1 = 0net strangeness S = +1-1 = 0 So reaction does not violate law of So reaction does not violate law of

conservation of strangeness, the reaction conservation of strangeness, the reaction is allowedis allowed

The Eightfold WayThe Eightfold Way

Consulting table 30.2, Take the first 8 Consulting table 30.2, Take the first 8 baryons and plot Strangeness vs. Charge. baryons and plot Strangeness vs. Charge. We get an interesting picture. A hexagonal We get an interesting picture. A hexagonal pattern emerges.pattern emerges.

If we do the same for the spin 0 mesons we If we do the same for the spin 0 mesons we also get a hexagonal pattern.also get a hexagonal pattern.

The Eightfold WayThe Eightfold Way

The Original Quark Model (in The Original Quark Model (in B/WB/W))

Gell-Mann (1961) proposed hadrons have Gell-Mann (1961) proposed hadrons have structure, i.e. composed of a more structure, i.e. composed of a more fundamental type of particle.fundamental type of particle.

Quarks have fractional charge e/3 or 2e/3Quarks have fractional charge e/3 or 2e/3 Three types u, d, s: up, down, strangeThree types u, d, s: up, down, strange Mesons were made of 2 quarks: q, qMesons were made of 2 quarks: q, q Baryons were made of 3 quarksBaryons were made of 3 quarks

¯̄

But that wasn’ enough!But that wasn’ enough!

Soon after, experimental discrepancies Soon after, experimental discrepancies required the addition of three more quarksrequired the addition of three more quarks Top, bottom and charm: t, b, cTop, bottom and charm: t, b, c And three more conservation laws: C, B, T for And three more conservation laws: C, B, T for

charm, bottomness and topnesscharm, bottomness and topness

Properties of Quarks and AntiquarksProperties of Quarks and Antiquarks

Fundamental Particles: PropertiesFundamental Particles: Properties

ParticleParticle Rest EnergyRest Energy Charge (e)Charge (e)

uu 360 MeV360 MeV +2/3+2/3

dd 360 MeV360 MeV -1/3-1/3

cc 1500 MeV1500 MeV +2/3+2/3

ss 540 MeV540 MeV -1/3-1/3

tt 173 MeV173 MeV +2/3+2/3

bb 5 GeV5 GeV -1/3-1/3

Quarks

Size of quark: < 10-18 m

Fundamental Particles Properties Fundamental Particles Properties continuedcontinued

ParticleParticle Rest EnergyRest Energy ChargeCharge

ee-- 511 keV511 keV -e-e

-- 107 MeV107 MeV -e-e

-- 1784 MeV1784 MeV -e-e

ee < < 30 eV30 eV 00

<< 0.5 MeV 0.5 MeV 00

<< 250 MeV 250 MeV 00

Leptons

Quarks in Mesons and BaryonsQuarks in Mesons and Baryons

We should still be in B/W!

CCoolloorr

Because of the Pauli exclusion principle Because of the Pauli exclusion principle (all quarks are spin ½ particles) can’t have (all quarks are spin ½ particles) can’t have three of the same particles occupying the three of the same particles occupying the same state.same state.

Example: Example: -- is (sss) so need three is (sss) so need three different yet strange quarksdifferent yet strange quarks

So colored quarks were proposedSo colored quarks were proposed

CCoolloor r continuedcontinued

Three Three color chargescolor charges were added were added Red, green blue: Red, green blue: rr, , gg, , bb

And…three anti-colorsAnd…three anti-colors antired, antigreen and antiblue: antired, antigreen and antiblue: rr, , gg, , bb

Mesons have a color anticolor pairMesons have a color anticolor pair Spin is either zero or 1 so can have Spin is either zero or 1 so can have ↑↑ or ↑↓↑↑ or ↑↓

Baryons must have three different colorsBaryons must have three different colors Spin is ½ so have Spin is ½ so have ↑↑↓↑↑↓ or or ↓↓↑↓↓↑

¯ ¯ ¯

Quarks combinations with colorQuarks combinations with color

Total spin is 0 or 1

Total spin is ½ or 3/2

Quantum ChromodynamicsQuantum Chromodynamics

In analogy with photons and the electromagnetic In analogy with photons and the electromagnetic force, an interaction between colored quarks is force, an interaction between colored quarks is the result of color force – 8 colored gluons.the result of color force – 8 colored gluons.

The general theory is complex but explains The general theory is complex but explains experimental results better.experimental results better.

Numerical results can be very hard to calculateNumerical results can be very hard to calculate Opposite colors attract, red-antired, in analogy Opposite colors attract, red-antired, in analogy

with electromagnetism.with electromagnetism. Different colors also attract though less stronglyDifferent colors also attract though less strongly Residual color force is responsible for nuclear Residual color force is responsible for nuclear

force that bind protrons and neutrons.force that bind protrons and neutrons.

Interactions in the Yukawa pion and Interactions in the Yukawa pion and quark-gluon modelsquark-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 ModelThe Standard Model

History of the UniverseHistory of the Universeand of the four forcesand of the four forces

Energy: 1028 1024 1021 1017 1013 1011 eV

Time: 0 10-40 10-35 10 -11 sec

Tim

e

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

Expansion of the universe Edwin Hubble's 1929 observation that galaxies were generally

receding from us provided the first clue that the Big Bang theory might be right.

Abundance of the light elements H, He, Li 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 The early universe should have been very hot. The cosmic

microwave background radiation is the remnant heat leftover from the Big Bang.

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.

Cosmic Microwave Background

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

Coulomb’s law the superposition principle

The electric field

Flux. Gauss’s law.Flux. Gauss’s law. simplifies computation of electric fieldssimplifies computation of electric fields

Potential and potential energyPotential and potential energy electrostatic force is conservativeelectrostatic force is conservative potential (a scalar) can be introduced as potential potential (a scalar) can be introduced as potential

energy of electrostatic field per unit chargeenergy of electrostatic field per unit charge

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the potential is the same for every point the potential is the same for every point (surfaces of constant voltage)(surfaces of constant voltage)

The electric field at every point of an The electric field at every point of an equipotential surface is perpendicular to the equipotential surface is perpendicular to the surfacesurface

Capacitance and capacitorsCapacitance and capacitors Capacitors with dielectrics (C↑ if k ↑)Capacitors with dielectrics (C↑ if k ↑)

Current and resistanceCurrent and resistance Current and drift speedCurrent and drift speed

Resistance and Ohm’s lawResistance and Ohm’s law I is proportional to VI is proportional to V

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Current and resistanceCurrent and resistance

Temperature dependence of resistanceTemperature dependence of resistance

Power in electric circuitsPower in electric circuits

DC CircuitsDC Circuits

EMFEMF

Resistors in series and parallelResistors in series and parallel

Kirchoff’s rulesKirchoff’s rules

RC circuitRC circuit

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MagnetismMagnetism Magnetic fieldMagnetic field Magnetic force on a moving particleMagnetic force on a moving particle Magnetic force on a currentMagnetic force on a current Torque on a current loopTorque on a current loop Motion in a uniform fieldMotion in a uniform field Application of magnetic forces Ampere’s law Current loops and solenoids

Induced voltages and induction Magnetic flux Generators and motors Self-induction Energy in magnetic fields

AC circuits Resistors, capacitors, inductors in ac circuits Power in an AC circuit

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AC circuitsAC circuits Resonance in RLC circuitsResonance in RLC circuits TransformersTransformers Electromagnetic WavesElectromagnetic Waves

Modern physicsModern physics IntroductionIntroduction Gallilean relativityGallilean relativity Michelson-Morley ExperimentMichelson-Morley Experiment RelativityRelativity

Time dilation, length contractionTime dilation, length contraction Relativistic energy, momentumRelativistic energy, momentum Relativistic addition of velocitiesRelativistic addition of velocities

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Quantum physicsQuantum physics Blackbody radiationBlackbody radiation Planck’s hypothesisPlanck’s hypothesis Photoelectric effectPhotoelectric effect X-raysX-rays

Wave functionWave function Uncertainty relationsUncertainty relations Atomic DescriptionsAtomic Descriptions Atomic SpectraAtomic Spectra Bohr’s Atomic TheoryBohr’s Atomic Theory Quantum MechanicsQuantum Mechanics Quantum NumbersQuantum Numbers

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Quantum physicsQuantum physics Electron Clouds (Orbitals)Electron Clouds (Orbitals) The Pauli Exclusion PrincipleThe Pauli Exclusion Principle Characteristic X-RaysCharacteristic X-Rays Atomic Energy LevelsAtomic Energy Levels Lasers and HolographyLasers and Holography

Nuclear physicsNuclear physics Nuclear propertiesNuclear properties Binding energyBinding energy RadioactivityRadioactivity The Decay ProcessThe Decay Process Natural RadioactivityNatural Radioactivity Nuclear ReactionsNuclear Reactions Medical ApplicationsMedical Applications Radiation DetectorsRadiation Detectors

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Nuclear Energy, Elementary ParticlesNuclear Energy, Elementary Particles Nuclear Reactors, Fission, FusionNuclear Reactors, Fission, Fusion Fundamental ForcesFundamental Forces Classification of Particles – Making sense of the particle zooClassification of Particles – Making sense of the particle zoo Conservation LawsConservation Laws

Remember:Remember: Electricity:Electricity:

Electric field and electric potential are different thingsElectric field and electric potential are different things Moreover, Moreover, field is a vectorfield is a vector while the while the potential is a scalarpotential is a scalar

Remember the difference between parallel and series Remember the difference between parallel and series connectionsconnections

Remember that formulas for capacitors and resistors are “reversed”Remember that formulas for capacitors and resistors are “reversed”

Magnetism:Magnetism: Use right hand rule properlyUse right hand rule properly

Special relativity:Special relativity: If the problem involves speeds close to the speed of light, use If the problem involves speeds close to the speed of light, use

relativistic formulas for momentum, energy, addition of velocitiesrelativistic formulas for momentum, energy, addition of velocities In particular, In particular, KE=mvKE=mv22/2/2 is a is a NONRELATIVISTIC NONRELATIVISTIC expression for KEexpression for KE

Atomic and nuclear physics:Atomic and nuclear physics: In the way of handling, nuclear reactions are very similar to In the way of handling, nuclear reactions are very similar to

chemical reactionschemical reactions

Good Luck on the Final Exam!Good Luck on the Final Exam!