General Physics (PHY 2140)

Lecture 21Lecture 21Modern 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

PreviouslyPreviously……

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 atomsNext, atoms had electrons and a nucleusNext, atoms had electrons and a nucleusThe nucleus is composed of neutrons and The nucleus is composed of neutrons and protonsprotonsWhatWhat’’s next?s next?

30.5 The Fundamental Forces in Nature30.5 The Fundamental Forces in NatureStrong ForceStrong Force

Short range ~ 10Short range ~ 10--1515 m (1 m (1 fermifermi))Responsible for binding of quarks into neutrons and protonsResponsible for binding of quarks into neutrons and protonsGluonGluon

Electromagnetic ForceElectromagnetic Force1010--2 2 as strong as strong forceas strong as strong force1/r1/r2 2 force lawforce lawBinding of atoms and moleculesBinding of atoms and moleculesPhotonPhoton

Weak forceWeak force~ 10~ 10--66 times as strong as the strong forcetimes as strong as the strong forceResponsible for beta decay, very short range ~10Responsible for beta decay, very short range ~10--1818 mmWW++, W, W-- and Zand Z0 0 bosonsbosons

Gravitational ForceGravitational Force1010--4343 times as strong as the strong forcetimes as strong as the strong forceAlso 1/rAlso 1/r2 2 force lawforce lawGravitonGraviton

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:

Λ, Σ, Ξ, Λ, Σ, Ξ, ΩΩ all are heavier than the protonall are heavier than the protonDecay into end products that include a proton Decay into end products that include a proton

Particle Classification Particle Classification –– cont.cont.

LeptonsLeptonsSmall or light weight particlesSmall or light weight particlesAre point like particles Are point like particles –– no internal structure no internal structure (yet)(yet)6 leptons 6 leptons Electron eElectron e, , muonmuon μ, μ, tautau ττand their associated neutrinos: and their associated neutrinos: ννee, , ννμμ, , ννττ

Also, their antiparticlesAlso, their antiparticlesNeutrinos 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, B = +1 for baryons, --1 for anti1 for anti--baryonsbaryonsEgEg. Proton, neutron have B = +1. Proton, neutron have B = +1

, antiparticles have B = , antiparticles have B = --11B = 0 for all other particles (nonB = 0 for all other particles (non--baryons)baryons)p, n

More Conservation LawsMore Conservation Laws

Lepton numberLepton numberL = +1 for leptons, L = +1 for leptons, --1 for anti1 for anti--leptonsleptonsL = 0 for nonL = 0 for non--leptonsleptons

Example for electrons:Example for electrons:Electron e, electron neutrino Electron e, electron neutrino ννee have Lhave Lee = +1= +1Anti electron and antineutrino have LAnti electron and antineutrino have Lee = = --11Other leptons have LOther leptons have Lee = 0 = 0 BUTBUT have their own lepton have their own lepton numbers, Lnumbers, Lμμ, L, Lττ

Refer to tableRefer to table 30.230.2

Example neutron decayExample neutron decay

Consider the decay of the neutronConsider the decay of the neutron

Before: B = +1, LBefore: B = +1, Lee = 0= 0After: B = +1, LAfter: B = +1, Lee = +1 = +1 --1 = 01 = 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 + pn p + e +

μ e + + ν

π μ +ν

ν

ν

→

→

→

→

Quiz 30.2 Quiz 30.2 -- answeranswer

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

Q = +2 Q = +2 →→ Q = +1Q = +1

Baryon number is also not conserved:Baryon number is also not conserved:B = +2 B = +2 →→ B = +2B = +2--1 = +11 = +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 pairspairsππ-- + p+ p++ →→ KK00 + + ΛΛ0 0 but notbut not ππ-- + p+ p++ →→ KK00 + n+ n

Decay is slow (indicative of weak interaction Decay is slow (indicative of weak interaction rather than strong) Halfrather than strong) Half--lives of order of 10lives of order of 10--1010

to 10to 10--88 secsec

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

More StrangenessMore Strangeness

Explanation lies in the addition of a new Explanation lies in the addition of a new conservation law conservation law –– Strangeness, SStrangeness, SOne of the pair of strange particles gets One of the pair of strange particles gets S=+1 the other S=S=+1 the other S=--1. All other particles 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=+1Before S=0; After S=+1--1 = 01 = 0Second reaction violates strangenessSecond reaction violates strangeness

Example 30.6: Strangeness ConservationExample 30.6: Strangeness Conservation

Consider:Consider: ππ-- + n + n →→ KK++ + + ΣΣ--

Before: S=0+0=0 (no strange particles)Before: S=0+0=0 (no strange particles)After: After: KK++ has S=+1, has S=+1, ΣΣ-- has S = has S = --1 thus the 1 thus the net strangeness S = +1net strangeness S = +1--1 = 01 = 0So 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))

GellGell--Mann (1961) proposed hadrons have 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/3Three types u, d, s: up, down, strangeThree types u, d, s: up, down, strangeMesons were made of 2 quarks: q, qMesons were made of 2 quarks: q, qBaryons were made of 3 quarksBaryons were made of 3 quarks

¯̄

But that But that wasnwasn’’ enough!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, cAnd three more conservation laws: C, B, T for And three more conservation laws: C, B, T for charm, charm, bottomnessbottomness and and topnesstopness

Properties of Quarks and Properties of Quarks and AntiquarksAntiquarks

Fundamental Particles: PropertiesFundamental Particles: Properties

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

uu 360 360 MeVMeV +2/3+2/3

dd 360 360 MeVMeV --1/31/3

cc 1500 1500 MeVMeV +2/3+2/3

ss 540 540 MeVMeV --1/31/3

tt 173 173 MeVMeV +2/3+2/3

bb 5 5 GeVGeV --1/31/3

Quarks

Size of quark: < 10-18 m

Fundamental Particles Properties Fundamental Particles Properties continuedcontinued

ParticleParticle Rest EnergyRest Energy ChargeCharge

ee-- 511 511 keVkeV --ee

μμ-- 107 107 MeVMeV --ee

ττ-- 1784 1784 MeVMeV --ee

ννee < < 30 30 eVeV 00

ννμμ << 0.5 0.5 MeVMeV 00

ννττ << 250 250 MeVMeV 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 (all quarks are spin ½½ particles) canparticles) can’’t have t have three of the same particles occupying the three of the same particles occupying the same state.same state.Example: Example: ΩΩ-- is (is (ssssss) so need three ) so need three different yet strange quarksdifferent yet strange quarksSo colored quarks were proposedSo colored quarks were proposed

CCoolloor r continuedcontinued

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

AndAnd……three antithree anti--colorscolorsantiredantired, , antigreenantigreen and and antiblueantiblue: : rr, , gg, , bb

Mesons have a color Mesons have a color anticoloranticolor pairpairSpin 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 colorsSpin is Spin is ½½ so have 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 Quantum ChromodynamicsChromodynamics

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 the result of color force –– 8 colored gluons.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 calculateOpposite colors attract, redOpposite colors attract, red--antiredantired, in analogy , in analogy with electromagnetism.with electromagnetism.Different colors also attract though less stronglyDifferent colors also attract though less stronglyResidual color force is responsible for nuclear Residual color force is responsible for nuclear force that bind force that bind protronsprotrons and neutrons.and neutrons.

Interactions in the Yukawa Interactions in the Yukawa pionpion and and quarkquark--gluon modelsgluon 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 universeEdwin 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 fromthe 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 lawthe superposition principle

The electric field

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

Potential and potential energyPotential and potential energyelectrostatic force is conservativeelectrostatic force is conservativepotential (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

Mini ReviewMini Review

1 22e

q qF k

r=

0

FE

q=

cosneto

QEA θε

Φ = =∑

B APEV V Vq

ΔΔ = − =

EquipotentialEquipotential surfacessurfacesThey are defined as a surface in space on which They are defined as a surface in space on which 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 equipotentialequipotential surface is perpendicular to the surface is perpendicular to the surfacesurface

Capacitance and capacitorsCapacitance and capacitorsCapacitors with dielectrics (CCapacitors with dielectrics (C↑↑ if k if k ↑↑))

Current and resistanceCurrent and resistanceCurrent and drift speedCurrent and drift speed

Resistance and OhmResistance and Ohm’’s laws lawI is proportional to VI is proportional to V

Resistivity Resistivity material propertymaterial property R A

lρ =

QIt

Δ=

ΔdI nqv A=

V IR=

0 0,AC C Cd

κε κ= =

221 1

2 2 2QU QV CVC

= = =

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

KirchoffKirchoff’’ss rulesrules

RC circuitRC circuit

( )1o oR R T Tα⎡ ⎤= + −⎣ ⎦

( )22 V

P I V I RR

Δ= Δ = =

V IrΔ = −E1 2 3

1 2 3

1 1 1 1eq

eq

R R R R

R R R R

= + + +

= + +

1 10, 0

n n

i ii i

I V= =

= =∑ ∑

( )/

/

1 t RC

t RC

q Q e

q Qe

−

−

= −

=

Charging

Discharging

MagnetismMagnetismMagnetic fieldMagnetic fieldMagnetic force on a moving particleMagnetic force on a moving particleMagnetic force on a currentMagnetic force on a currentTorque on a current loopTorque on a current loopMotion in a uniform fieldMotion in a uniform fieldApplication of magnetic forcesAmpere’s lawCurrent loops and solenoids

Induced voltages and inductionMagnetic fluxGenerators and motorsSelf-inductionEnergy in magnetic fields

AC circuitsResistors, capacitors, inductors in ac circuitsPower in an AC circuit

sinF qvB θ=sinF BIl θ=

sinF NBIA θ=/r mv qB=

oB l IμΔ =∑

cosB A BA θ⊥Φ = =ILt

Δ= −

ΔE NL

IΦ

=

( )22L CZ R X X= + − tan L CX X

Rφ −

=1 , 2

2C LX X fLfC

ππ

= =

212LPE LI=

AC circuitsAC circuitsResonance in RLC circuitsResonance in RLC circuitsTransformersTransformersElectromagnetic WavesElectromagnetic Waves

Modern physicsModern physicsIntroductionIntroductionGallileanGallilean relativityrelativityMichelsonMichelson--Morley ExperimentMorley ExperimentRelativityRelativity

Time dilation, length contractionTime dilation, length contractionRelativistic energy, momentumRelativistic energy, momentumRelativistic addition of velocitiesRelativistic addition of velocities

01

2f

LCπ=

22 1

1

NV VN

Δ = Δ

81 2.99792 10o o

c m sμ ε

= = ×( )sin 2mv V ftπ φΔ = Δ +

2 21pt

tv c

ΔΔ =

−2 21pL L v c= −

2 21mvp mvv c

γ≡ =−

21

ad dbab

ad db

v vv v vc

+=

+KE = KE = γγmc2 mc2 –– mc2mc2

Quantum physicsQuantum physicsBlackbody radiationBlackbody radiationPlanckPlanck’’s hypothesiss hypothesisPhotoelectric effectPhotoelectric effectXX--raysrays

Wave functionWave functionUncertainty relationsUncertainty relationsAtomic DescriptionsAtomic DescriptionsAtomic SpectraAtomic SpectraBohrBohr’’s Atomic Theorys Atomic TheoryQuantum MechanicsQuantum MechanicsQuantum NumbersQuantum Numbers

KE hf= − Φ

2max 0.2898 10T m Kλ −= × ⋅

, 1,2,3,...nE nhf n= =

( )minhc

e Vλ =

Δ

2hE tπ

Δ Δ ≥2hx pπ

Δ Δ ≥

i fE E hf− =, 1,2,3,...em vr n n= =

2 2

1 1 1H

f i

Rn nλ

⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠

2 , 1,2,3,...r n nπ λ= =

Quantum physicsQuantum physicsElectron Clouds (Electron Clouds (OrbitalsOrbitals))The Pauli Exclusion PrincipleThe Pauli Exclusion PrincipleCharacteristic XCharacteristic X--RaysRaysAtomic Energy LevelsAtomic Energy LevelsLasers and HolographyLasers and Holography

Nuclear physicsNuclear physicsNuclear propertiesNuclear propertiesBinding energyBinding energyRadioactivityRadioactivityThe Decay ProcessThe Decay ProcessNatural RadioactivityNatural RadioactivityNuclear ReactionsNuclear ReactionsMedical ApplicationsMedical ApplicationsRadiation DetectorsRadiation Detectors

AZ X

1/30r r A=

2

2

4 ek Zedmv

=

Nuclear Energy, Elementary ParticlesNuclear Energy, Elementary ParticlesNuclear Reactors, Fission, FusionNuclear Reactors, Fission, FusionFundamental ForcesFundamental ForcesClassification of Particles Classification of Particles –– Making sense of the particle zooMaking sense of the particle zooConservation LawsConservation Laws

Remember:Remember:Electricity:Electricity:

Electric field and electric potential are different thingsElectric field and electric potential are different thingsMoreover, 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 Remember that formulas for capacitors and resistors are ““reversedreversed””

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 velocitirelativistic formulas for momentum, energy, addition of velocitieses

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!