General Physics (PHY 2140)

Lecture 20Lecture 20Modern Physics

Nuclear Energy and Elementary ParticlesFission, Fusion and ReactorsElementary ParticlesFundamental ForcesClassification of ParticlesConservation Laws

Chapter 30

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

Chapter 30Chapter 30

PreviouslyPreviously……

Nuclear PhysicsNuclear ReactionsMedical ApplicationsRadiation 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 aboveE. none of the above

v = E/B

r=mv/qB

Processes of Nuclear EnergyProcesses of Nuclear Energy

FissionFissionA nucleus of large mass number splits into A nucleus of large mass number splits into two smaller nucleitwo smaller nuclei

FusionFusionTwo light nuclei fuse to form a heavier Two light nuclei fuse to form a heavier nucleusnucleus

Large amounts of energy are released in Large amounts of energy are released in either caseeither case

Processes of Nuclear EnergyProcesses of Nuclear Energy

FissionFissionA nucleus of large A nucleus of large mass number mass number splitssplitsinto two smaller nucleiinto two smaller nuclei

FusionFusionTwo light nuclei Two light nuclei fusefuse to to form a heavier nucleusform a heavier nucleus

Large amounts of Large amounts of energy are released in energy are released in either caseeither case

Fission

Fusion

Nuclear FissionNuclear FissionA heavy nucleus splits into two smaller nucleiA heavy nucleus splits into two smaller nucleiThe total mass of the products is less than the The total mass of the products is less than the original mass of the heavy nucleusoriginal mass of the heavy nucleusFirst observed in 1939 by Otto Hahn and Fritz First observed in 1939 by Otto Hahn and Fritz StrassmanStrassman following basic studies by Fermifollowing basic studies by FermiLisa Meitner and Otto Frisch soon explained what Lisa Meitner and Otto Frisch soon explained what had happenedhad happenedFission of Fission of 235235U by a slow (low energy) neutronU by a slow (low energy) neutron

236236U* is an intermediate, shortU* is an intermediate, short--lived statelived stateX and Y are called X and Y are called fission fragmentsfission fragments

Many combinations of X and Y satisfy the requirements of Many combinations of X and Y satisfy the requirements of conservation of energy and chargeconservation of energy and charge

neutronsYX*UUn 23692

23592

10 ++→→+

Sequence of Events in FissionSequence of Events in Fission

The The 235235U nucleus captures a U nucleus captures a thermalthermal (slow(slow--moving) neutronmoving) neutronThis capture results in the formation of This capture results in the formation of 236236U*, and the excess energy of this U*, and the excess energy of this nucleus causes it to undergo violent oscillationsnucleus causes it to undergo violent oscillationsThe The 236236U* nucleus becomes highly elongated, and the force of repulsion U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortionbetween the protons tends to increase the distortionThe nucleus splits into two fragments, emitting several neutronsThe nucleus splits into two fragments, emitting several neutrons in the in the processprocess

Energy in a Fission ProcessEnergy in a Fission Process

Binding energy for heavy nuclei is about 7.2 Binding energy for heavy nuclei is about 7.2 MeVMeV per nucleonper nucleonBinding energy for intermediate nuclei is about 8.2 Binding energy for intermediate nuclei is about 8.2 MeVMeV per nucleonper nucleonTherefore, the fission fragments have less mass than the nucleonTherefore, the fission fragments have less mass than the nucleons s in the original nucleiin the original nucleiThis decrease in mass per nucleon appears as released energy in This decrease in mass per nucleon appears as released energy in the fission eventthe fission eventAn estimate of the energy releasedAn estimate of the energy released

Assume a total of 240 nucleonsAssume a total of 240 nucleonsReleases about 1 Releases about 1 MeVMeV per nucleonper nucleon

8.2 8.2 MeVMeV –– 7.2 7.2 MeVMeVTotal energy released is about 240 Total energy released is about 240 MeVMeV

This is very large compared to the amount of energy released in This is very large compared to the amount of energy released in chemical processeschemical processes

QUICK QUIZIn 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 μg, (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:

1g ~ kg 103.1m/s) 100.3(

J 102.1 328

14

2−×=

××

==cEm

Note: 1 gram TNT = 4184 J (exactly)

Chain ReactionChain ReactionNeutrons are emitted when Neutrons are emitted when 235235U undergoes fissionU undergoes fissionThese neutrons are then available to trigger fission in other nuThese neutrons are then available to trigger fission in other nucleicleiThis process is called a This process is called a chain reactionchain reaction

If uncontrolled, a violent explosion can occurIf uncontrolled, a violent explosion can occurThe principle behind the nuclear bomb, where 1 g of U can releasThe principle behind the nuclear bomb, where 1 g of U can release e energy equal to about 30000 tons of TNTenergy equal to about 30000 tons of TNT

11 Mt H11 Mt H--bombbomb

Nuclear ReactorNuclear Reactor

A A nuclear reactornuclear reactor is a system designed to is a system designed to maintain a maintain a selfself--sustained chain reactionsustained chain reactionThe The reproduction constantreproduction constant, K, is defined as the , K, is defined as the average number of neutrons from each fission average number of neutrons from each fission event that will cause another fission eventevent that will cause another fission event

The maximum value of K from uranium fission is 2.5The maximum value of K from uranium fission is 2.5Two Two 235235U reactions, one yields 3 the other 2 neutronsU reactions, one yields 3 the other 2 neutronsIn practice, K is less than thisIn practice, K is less than this

A selfA self--sustained reaction has K = 1sustained reaction has K = 1

Basic Reactor DesignBasic Reactor DesignFuel elements consist of enriched Fuel elements consist of enriched uranium (a few % uranium (a few % 235235U rest U rest 238238U)U)The The moderator materialmoderator material helps to helps to slow down the neutronsslow down the neutronsThe The control rodscontrol rods absorb neutronsabsorb neutronsWhen K = 1, the reactor is said to When K = 1, the reactor is said to be be criticalcritical

The chain reaction is selfThe chain reaction is self--sustainingsustaining

When K < 1, the reactor is said to When K < 1, the reactor is said to be be subcriticalsubcritical

The reaction dies outThe reaction dies outWhen K > 1, the reactor is said to When K > 1, the reactor is said to be be supercriticalsupercritical

A runA run--away chain reaction occursaway chain reaction occurs

D2

O, graphite

Cadmium

SCRAM

= Safety Control Rod Axe Man

Schematic of a Fission ReactorSchematic of a Fission Reactor

Nuclear FusionNuclear Fusion

When two light nuclei combine to form a heavier nucleusWhen two light nuclei combine to form a heavier nucleus

Is exothermic for nuclei having a mass less than ~20Is exothermic for nuclei having a mass less than ~20(Iron is the limit, Z=26, A=56)(Iron is the limit, Z=26, A=56)

The sun is a large fusion reactorThe sun is a large fusion reactor

The The sunsun balances gravity with fusion energybalances gravity with fusion energy

SunSun’’s Proton Cycles Proton Cycle

First steps:First steps:

Followed by H Followed by H –– He or He He or He –– He fusion:He fusion:

oror

Total energy released is 25 Total energy released is 25 MeVMeV

1 1 2 +e1 1 1H + H H + e ν→ +

1 2 31 1 2H + H He + γ→

1 3 4 +2 e1 2H + He He + e ν→ +

3 3 4 1 12 2 2 1 1He + He He + H + H→

2% of sun’s energyis

carried

by neutrinos

Net ResultNet Result

4 protons (hydrogen nuclei) combine to give4 protons (hydrogen nuclei) combine to give•• An alpha particle (a helium nucleus)An alpha particle (a helium nucleus)•• Two positronsTwo positrons•• One or two neutrinos (they easily escape)One or two neutrinos (they easily escape)•• Some gamma ray photons (absorbed)Some gamma ray photons (absorbed)The two positrons combine with electrons to The two positrons combine with electrons to form more gamma photonsform more gamma photonsThe photons are usually absorbed and so The photons are usually absorbed and so they heat the sun (blackbody spectrum)they heat the sun (blackbody spectrum)

Fusion ReactorsFusion Reactors

Enormous energy in a small amount of fuelEnormous energy in a small amount of fuel

0.06g of deuterium could be extracted from 1 gal of water0.06g of deuterium could be extracted from 1 gal of water

This represents the equivalent energy of ~6x10This represents the equivalent energy of ~6x1099 J J

Fusion reactor would most likely use deuterium and tritiumFusion reactor would most likely use deuterium and tritium2 2 3 11 1 2 0H + H He + n, 3.27 MeVQ→ =2 2 3 11 1 1 1H + H H + H, 4.03 MeVQ→ =

2 3 4 11 1 2 0H + H He + n, 17.59 MeVQ→ =

Advantages of fusion powerAdvantages of fusion power

Fuel costs are relatively smallFuel costs are relatively smallFew radioactive byFew radioactive by--products of fusion reactionproducts of fusion reaction

(mostly helium(mostly helium--3 and helium3 and helium--4)4)

Disadvantages of fusion powerDisadvantages of fusion powerHard to force two charged nuclei togetherHard to force two charged nuclei togetherReactor is complex and expensiveReactor is complex and expensiveNeed high temperatures and pressures to Need high temperatures and pressures to achieve fusion (~10achieve fusion (~1088 K) need a K) need a plasmaplasma

Plasma confinementPlasma confinement

Plasma ion density, Plasma ion density, nnPlasma confinement time, Plasma confinement time, ττIn order to achieve a fusion reaction need In order to achieve a fusion reaction need to satisfy Lawsonto satisfy Lawson’’s criterion: s criterion:

14 3

16 3

10 s/cm10 s/cm

nnτ

τ

≥

≥

Deuterium-

tritium reactor

Deuterium-

deuterium reactor

So need 108 K for 1 second

Fusion Reactors Fusion Reactors -- 11

Inertial confinementInertial confinementInject fuel pellets and hit them with aInject fuel pellets and hit them with a laserlaser ((lotslotsof lasers) or ion beams to heat themof lasers) or ion beams to heat themImploding pellet compresses fuel to fusion Imploding pellet compresses fuel to fusion densitiesdensitiesDoesnDoesn’’t require plasma confinement via t require plasma confinement via magnetic fieldsmagnetic fieldsRequires large facility to house lasers and Requires large facility to house lasers and target chamber.target chamber.

National Ignition FacilityNational Ignition Facility

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

The beams are generated in the laser bay

and deliverd to the target bay.

The National Ignition Facility

The target chamberThe target chamber

Fusion Reactors Fusion Reactors -- 22

Magnetic field Magnetic field confinementconfinement

TokamakTokamakdesign design –– a a toroidaltoroidalmagnetic fieldmagnetic fieldFirst First proposed by proposed by Russian Russian scientistsscientists

Fusion Reactors Fusion Reactors –– cont.cont.

TokamakTokamak Fusion Test Reactor Fusion Test Reactor –– ITERITER

International Thermonuclear Experimental Reactor

To be constructed in Cadarache

in the South of

France.

ITERITER’’ss proposed site layoutproposed site layout

30.4 Elementary Particles30.4 Elementary 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?

Elementary particle interactionsElementary particle interactions

An simple example of a Feynman diagramAn simple example of a Feynman diagram

This This virtualvirtual photon is said to mediate the electromagnetic photon is said to mediate the electromagnetic force. The virtual photon can never be detected because it force. The virtual photon can never be detected because it only lasts for a vanishing small time.only lasts for a vanishing small time.

The scattering of two electrons via a coulomb forceThe scattering of two electrons via a coulomb force

Interactions continuedInteractions continued

Can have similar diagrams with other Can have similar diagrams with other particles and other forcesparticles and other forces

Strong force, weak force, gravityStrong force, weak force, gravity

Basic idea of exchange of a virtual particle Basic idea of exchange of a virtual particle is the common theme.is the common theme.

More examples of Feynman diagramsMore examples of Feynman diagrams

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

30.6 Positrons and Antiparticles30.6 Positrons and Antiparticles

Dirac proposed the positron to solve a Dirac proposed the positron to solve a negative energy problem (Dirac sea)negative energy problem (Dirac sea)The general implication is that for every The general implication is that for every particle there is an antiparticle (symmetry)particle there is an antiparticle (symmetry)Other antiparticles:Other antiparticles:

antiproton, antineutrinoantiproton, antineutrinoUsually denoted with a bar over symbolUsually denoted with a bar over symbolSome particles are their own antiparticlesSome particles are their own antiparticles

photon, neutral photon, neutral pionpion: : γγ, , ππ00

30.7 Mesons30.7 Mesons

Part of an early theory to describe nuclear Part of an early theory to describe nuclear interactionsinteractionsMass between a electron and a protonMass between a electron and a protonFlavorsFlavors

ChargedCharged ππ meson: meson: ππ++, π, π−− ,,mass 139.6 MeV/cmass 139.6 MeV/c22

NetralNetral π π mesonmeson, π, π0 0 ,,mass 135.0 MeV/cmass 135.0 MeV/c22

Lifetimes 2.6x10Lifetimes 2.6x10--88 s for s for ππ++, π, π−−

8.3x108.3x10--17 s for 17 s for ππ0 0

More MesonsMore Mesons

Also have heavier mesonsAlso have heavier mesonsKaonsKaons ~500 MeV/c~500 MeV/c22

EtaEta’’ss 548 and 958 MeV/c548 and 958 MeV/c2 2 (note, mass of (note, mass of η′η′ is greater than proton mass)is greater than proton mass)