General Physics (PHY 2140)

Lecture 20Lecture 20 Modern 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

Previously…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 aboveE. none of the above

v = E/B

r=mv/qB

Processes of Nuclear EnergyProcesses of Nuclear Energy

FissionFission A nucleus of large mass number splits into A nucleus of large mass number splits into

two smaller nucleitwo smaller nuclei

FusionFusion Two 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

FissionFission A nucleus of large A nucleus of large

mass number mass number splitssplits into two smaller nucleiinto two smaller nuclei

FusionFusion Two 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 Fission A heavy nucleus splits into two smaller nucleiA heavy nucleus splits into two smaller nuclei The 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 nucleus First observed in 1939 by Otto Hahn and Fritz First observed in 1939 by Otto Hahn and Fritz

Strassman following basic studies by FermiStrassman following basic studies by Fermi Lisa Meitner and Otto Frisch soon explained what Lisa Meitner and Otto Frisch soon explained what

had happenedhad happened Fission of Fission of 235235U by a slow (low energy) neutronU by a slow (low energy) neutron

236236U* is an intermediate, short-lived stateU* is an intermediate, short-lived state X 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-moving) neutron (slow-moving) neutron This 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 oscillations The 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 distortion The nucleus splits into two fragments, emitting several neutrons in the The nucleus splits into two fragments, emitting several neutrons in the

processprocess

Energy in a Fission ProcessEnergy in a Fission Process

Binding energy for heavy nuclei is about 7.2 MeV per nucleonBinding energy for heavy nuclei is about 7.2 MeV per nucleon Binding energy for intermediate nuclei is about 8.2 MeV per nucleonBinding energy for intermediate nuclei is about 8.2 MeV per nucleon Therefore, the fission fragments have less mass than the nucleons Therefore, the fission fragments have less mass than the nucleons

in the original nucleiin the original nuclei This 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 event An estimate of the energy releasedAn estimate of the energy released

Assume a total of 240 nucleonsAssume a total of 240 nucleons Releases about 1 MeV per nucleonReleases about 1 MeV per nucleon

8.2 MeV – 7.2 MeV8.2 MeV – 7.2 MeV Total energy released is about 240 MeVTotal energy released is about 240 MeV

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 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:

1g ~ kg 103.1m/s) 100.3(

J 102.1 328

14

2

c

Em

Note: 1 gram TNT = 4184 J (exactly)

Chain ReactionChain Reaction Neutrons are emitted when Neutrons are emitted when 235235U undergoes fissionU undergoes fission These neutrons are then available to trigger fission in other nucleiThese neutrons are then available to trigger fission in other nuclei This process is called a This process is called a chain reactionchain reaction

If uncontrolled, a violent explosion can occurIf uncontrolled, a violent explosion can occur The principle behind the nuclear bomb, where 1 g of U can release The principle behind the nuclear bomb, where 1 g of U can release

energy equal to about 30000 tons of TNTenergy equal to about 30000 tons of TNT

11 Mt H-bomb11 Mt H-bomb

Nuclear ReactorNuclear Reactor

A A nuclear reactornuclear reactor is a system designed to is a system designed to maintain a maintain a self-sustained chain reactionself-sustained chain reaction

The 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 2.5

Two Two 235235U reactions, one yields 3 the other 2 neutronsU reactions, one yields 3 the other 2 neutrons In practice, K is less than thisIn practice, K is less than this

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

Basic Reactor DesignBasic Reactor Design Fuel 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 neutrons The The control rodscontrol rods absorb neutrons absorb neutrons When K = 1, the reactor is said to When K = 1, the reactor is said to

be be criticalcritical The chain reaction is self-The 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 out

When K > 1, the reactor is said to When K > 1, the reactor is said to be be supercriticalsupercritical A run-away chain reaction occursA run-away chain reaction occurs

D2O, 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 energy balances gravity with fusion energy

Sun’s Proton CycleSun’s Proton Cycle

First steps:First steps:

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

oror

Total energy released is 25 MeVTotal energy released is 25 MeV

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 photons

The 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 small Few radioactive by-products of fusion reactionFew radioactive by-products of fusion reaction

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

Disadvantages of fusion powerDisadvantages of fusion power

Hard to force two charged nuclei togetherHard to force two charged nuclei together Reactor is complex and expensiveReactor is complex and expensive Need 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, nn Plasma confinement time, Plasma confinement time, In order to achieve a fusion reaction need In order to achieve a fusion reaction need

to satisfy Lawson’s criterion: to satisfy Lawson’s criterion:

14 3

16 3

10 s/cm

10 s/cm

n

n

Deuterium- tritium reactor

Deuterium- deuterium reactor

So need 108 K for 1 second

Fusion Reactors - 1Fusion Reactors - 1

Inertial confinementInertial confinement Inject fuel pellets and hit them with aInject fuel pellets and hit them with a laserlaser ( (lotslots

of lasers) or ion beams to heat themof lasers) or ion beams to heat them Imploding pellet compresses fuel to fusion Imploding pellet compresses fuel to fusion

densitiesdensities Doesn’t require plasma confinement via Doesn’t require plasma confinement via

magnetic fieldsmagnetic fields Requires 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 BB-the 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 - 2Fusion Reactors - 2

Magnetic field Magnetic field confinementconfinement Tokamak Tokamak

design – a design – a toroidal toroidal magnetic fieldmagnetic field

First proposed First proposed by Russian by Russian scientistsscientists

Fusion Reactors – cont.Fusion Reactors – cont.

Tokamak Fusion Test Reactor – ITERTokamak Fusion Test Reactor – ITER

International Thermonuclear Experimental Reactor

To be constructed in Cadarache in the South of France.

ITER’s proposed site layoutITER’s proposed site layout

30.4 Elementary Particles30.4 Elementary 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?

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 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

30.6 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, antineutrino Usually denoted with a bar over symbolUsually denoted with a bar over symbol Some particles are their own antiparticlesSome particles are their own antiparticles

photon, neutral pion: photon, neutral pion: , , 00

30.7 Mesons30.7 Mesons

Part of an early theory to describe nuclear Part of an early theory to describe nuclear interactionsinteractions

Mass between a electron and a protonMass between a electron and a proton FlavorsFlavors

ChargedCharged meson: meson: mass 139.6 MeV/cmass 139.6 MeV/c22

NetralNetralmesonmeson,mass 135.0 MeV/c,mass 135.0 MeV/c22

Lifetimes 2.6x10Lifetimes 2.6x10-8-8 s for s for

8.3x10-17 s for 8.3x10-17 s for

More MesonsMore Mesons

Also have heavier mesonsAlso have heavier mesons Kaons ~500 MeV/cKaons ~500 MeV/c22

Eta’s 548 and 958 MeV/cEta’s 548 and 958 MeV/c2 2 (note, mass of (note, mass of is greater than proton mass) is greater than proton mass)