Post on 11-Jan-2016
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)