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General Physics (PHY 2140)
Lecture 20
¾ Modern Physics
Nuclear Energy and Elementary Particles
Fission, Fusion and Reactors
Elementary Particles
Fundamental Forces
Classification of Particles
Conservation Laws
Chapter
Chapter
3030
Previously…
ƒ Nuclear Physics
ƒ Nuclear Reactions
ƒ Medical Applications
ƒ 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 above
E. none of the above
v = E/B
r=mv/qB
http://www.physics.wayne.edu/~alan/2140Website/Main.htm
Processes of Nuclear Energy
ƒ Fission
ƒ A nucleus of large mass number splits into
two smaller nuclei
ƒ Fusion
ƒ Two light nuclei fuse to form a heavier
nucleus
Processes of Nuclear Energy
ƒ Fission
ƒ A nucleus of large
mass number splits
into two smaller nuclei
ƒ Fusion
ƒ Two light nuclei fuse to
form a heavier nucleus
ƒ Large amounts of
Fission
Fusion
energy are released in
either case
ƒ Large amounts of energy are released in
either case
1
Nuclear Fission
Sequence of Events in Fission
ƒ A heavy nucleus splits into two smaller nuclei
ƒ The total mass of the products is less than the
original mass of the heavy nucleus
ƒ First observed in 1939 by Otto Hahn and Fritz
Strassman following basic studies by Fermi
ƒ Lisa Meitner and Otto Frisch soon explained what
had happened
ƒ Fission of 235U by a slow (low energy) neutron
1
0
236
n+ 235
92 U→ 92 U* → X + Y + neutrons
ƒ 236U* is an intermediate, shortshort-lived state
ƒ X and Y are called fission fragments
ƒ Many combinations of X and Y satisfy the requirements of
conservation of energy and charge
ƒ The 235U nucleus captures a thermal (slow(slow-moving) neutron
ƒ This capture results in the formation of 236U*, and the excess energy of this
nucleus causes it to undergo violent oscillations
ƒ The 236U* nucleus becomes highly elongated, and the force of repulsion
between the protons tends to increase the distortion
ƒ The nucleus splits into two fragments, emitting several neutrons in the
process
Energy in a Fission Process
ƒ Binding energy for heavy nuclei is about 7.2 MeV per nucleon
ƒ Binding energy for intermediate nuclei is about 8.2 MeV per nucleon
ƒ Therefore, the fission fragments have less mass than the nucleons
nucleons
in the original nuclei
QUICK QUIZ
In 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
ƒ This decrease in mass per nucleon appears as released energy in
the fission event
ƒ An estimate of the energy released
ƒ Assume a total of 240 nucleons
ƒ Releases about 1 MeV per nucleon
ƒ 8.2 MeV – 7.2 MeV
ƒ Total energy released is about 240 MeV
(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:
ƒ This is very large compared to the amount of energy released in
chemical processes
m=
E
1.2 × 1014 J
=
= 1.3 × 10−3 kg ~ 1g
2
8
2
c
(3.0 × 10 m/s)
Note: 1 gram TNT = 4184 J (exactly)
2
Chain Reaction
ƒ
ƒ
ƒ
11 Mt H-bomb
Neutrons are emitted when 235U undergoes fission
These neutrons are then available to trigger fission in other nuclei
nuclei
This process is called a chain reaction
ƒ If uncontrolled, a violent explosion can occur
ƒ The principle behind the nuclear bomb, where 1 g of U can release
release
energy equal to about 30000 tons of TNT
Nuclear Reactor
ƒ A nuclear reactor is a system designed to
maintain a selfself-sustained chain reaction
ƒ The reproduction constant,
constant, K, is defined as the
average number of neutrons from each fission
event that will cause another fission event
ƒ The maximum value of K from uranium fission is 2.5
ƒ Two 235U reactions, one yields 3 the other 2 neutrons
ƒ In practice, K is less than this
ƒ A selfself-sustained reaction has K = 1
Basic Reactor Design
ƒ Fuel elements consist of enriched
uranium (a few %
235U
rest
Cadmium
238U)
ƒ The moderator material helps to
slow down the neutrons
ƒ The control rods absorb neutrons
ƒ When K = 1, the reactor is said to
be critical
ƒ The chain reaction is selfselfsustaining
ƒ When K < 1, the reactor is said to
be subcritical
ƒ The reaction dies out
ƒ When K > 1, the reactor is said to
be supercritical
ƒ A runrun-away chain reaction occurs
SCRAM = Safety Control Rod Axe Man
D2O, graphite
3
Schematic of a Fission Reactor
Nuclear Fusion
ƒ When two light nuclei combine to form a heavier nucleus
ƒ Is exothermic for nuclei having a mass less than ~20
ƒ (Iron is the limit, Z=26, A=56)
ƒ The sun is a large fusion reactor
ƒ The sun balances gravity with fusion energy
Sun’s Proton Cycle
Net Result
ƒ First steps:
ƒ 4 protons (hydrogen nuclei) combine to give
H+ H →
2
1
H + e + νe
H + 21 H →
3
2
He + γ
H + 23 He →
4
2
He + e+ + ν e
1
1
1
1
1
1
+
2% of sun’s
energyis carried
by neutrinos
ƒ Followed by H – He or He – He fusion:
ƒ or
1
1
3
2
He + 23 He →
4
2
He + 11 H + 11 H
ƒ Total energy released is 25 MeV
•
•
•
•
An alpha particle (a helium nucleus)
Two positrons
One or two neutrinos (they easily escape)
Some gamma ray photons (absorbed)
ƒ The two positrons combine with electrons to
form more gamma photons
ƒ The photons are usually absorbed and so
they heat the sun (blackbody spectrum)
4
Fusion Reactors
ƒ Enormous energy in a small amount of fuel
ƒ 0.06g of deuterium could be extracted from 1 gal of water
Advantages of fusion power
ƒ Fuel costs are relatively small
ƒ Few radioactive byby-products of fusion reaction
ƒ (mostly heliumhelium-3 and heliumhelium-4)
ƒ This represents the equivalent energy of ~6x109 J
ƒ Fusion reactor would most likely use deuterium and tritium
2
1
H+ H →
2
1
3
2
He + n, Q = 3.27 MeV
1
0
H + H → H + 11 H, Q = 4.03 MeV
2
3
4
1
1 H + 1 H → 2 He + 0 n, Q = 17.59 MeV
2
1
2
1
3
1
Plasma confinement
ƒ Plasma ion density, n
ƒ Plasma confinement time, τ
ƒ In order to achieve a fusion reaction need
to satisfy Lawson’s criterion:
nτ ≥ 1014 s/cm3
Deuterium- tritium reactor
nτ ≥ 1016 s/cm3
Deuterium- deuterium reactor
So need 108 K for 1 second
Disadvantages of fusion power
ƒ
ƒ
ƒ
Hard to force two charged nuclei together
Reactor is complex and expensive
Need high temperatures and pressures to
achieve fusion (~108 K)
need a plasma
Fusion Reactors - 1
ƒ Inertial confinement
ƒ Inject fuel pellets and hit them with a laser (lots
of lasers) or ion beams to heat them
ƒ Imploding pellet compresses fuel to fusion
densities
ƒ Doesn’
Doesn’t require plasma confinement via
magnetic fields
ƒ Requires large facility to house lasers and
target chamber.
5
National Ignition Facility
ƒ the facility is very large, the size of a
sports stadium
ƒ the target is very small, the size of a BBgun pellet
ƒ the laser system is very powerful, equal to
1,000 times the electric generating power
of the United States
ƒ each laser pulse is very short, a few
billionths of a second
The beams are generated in the laser bay
and deliverd to the target bay.
The National Ignition Facility
6
The target chamber
Fusion Reactors - 2
ƒ Magnetic field
confinement
ƒ Tokamak
design – a
toroidal
magnetic field
ƒ First
proposed by
Russian
scientists
Fusion Reactors – cont.
ITER’s proposed site layout
ƒ Tokamak Fusion Test Reactor – ITER
International
Thermonuclear
Experimental
Reactor
To be constructed in
Cadarache in the South of
France.
7
30.4 Elementary Particles
ƒ First we studied atoms
ƒ Next, atoms had electrons and a nucleus
ƒ The nucleus is composed of neutrons and
Elementary particle interactions
The scattering of two electrons via a coulomb force
This virtual photon is said to mediate the electromagnetic
force. The virtual photon can never be detected because it
only lasts for a vanishing small time.
protons
ƒ What’s next?
An simple example of a Feynman diagram
Interactions continued
More examples of Feynman diagrams
ƒ Can have similar diagrams with other
particles and other forces
ƒ Strong force, weak force, gravity
ƒ Basic idea of exchange of a virtual particle
is the common theme.
8
30.5 The Fundamental Forces in Nature
ƒ Strong Force
ƒ
ƒ
ƒ
Short range ~ 10-15 m (1 fermi)
fermi)
Responsible for binding of quarks into neutrons and protons
Gluon
ƒ
ƒ
ƒ
ƒ
10-2 as strong as strong force
1/r2 force law
Binding of atoms and molecules
Photon
ƒ Electromagnetic Force
ƒ Weak force
ƒ ~ 10-6 times as strong as the strong force
ƒ Responsible for beta decay, very short range ~10-18 m
ƒ W+, W- and Z0 bosons
ƒ Gravitational Force
ƒ 10-43 times as strong as the strong force
ƒ Also 1/r2 force law
ƒ Graviton
30.6 Positrons and Antiparticles
ƒ Dirac proposed the positron to solve a
negative energy problem (Dirac sea)
ƒ The general implication is that for every
particle there is an antiparticle (symmetry)
ƒ Other antiparticles:
ƒ
ƒ
ƒ
antiproton, antineutrino
Usually denoted with a bar over symbol
Some particles are their own antiparticles
ƒ photon, neutral pion:
pion: γ, π0
30.7 Mesons
More Mesons
ƒ Part of an early theory to describe nuclear
ƒ Also have heavier mesons
ƒ Kaons ~500 MeV/c2
ƒ Eta’s 548 and 958 MeV/c2 (note, mass of
interactions
ƒ Mass between a electron and a proton
ƒ Flavors
η′ is greater than proton mass)
ƒ Charged π meson: π+, π− ,mass 139.6 MeV/c2
ƒ Netral π meson,
meson, π0 ,mass 135.0 MeV/c2
ƒ Lifetimes 2.6x10-8 s for π+, π−
8.3x108.3x10-17 s for π0
9