Transcript PHY313 - CEI544 The Mystery of Matter From Quarks to the

PHY313 - CEI544
The Mystery of Matter
From Quarks to the Cosmos
Spring 2005
Peter Paul
Office Physics D-143
www.physics.sunysb.edu PHY313
Peter Paul 02/24/05
PHY313-CEI544 Spring-05
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What have we learned last time I
•
•
•
We studied the nucleus. It is made up of a
dense package of neutrons and protons, i.e.
nucleons. The protons produce the positive
charge Z that identifies the element, the N
neutrons add to the mass number A = N+Z.
Nucleons interact by the strong force, which
is ~ 100 time stronger than the electromagnetic (EM) force. It has a range of only ~ 1
fm, about the same as the size of a nucleon.
Yukawa invented the concept of the force
being mediated by the exchange of specific
particles, in this case pi mesons. These
exchange particles are created out of
nothing, as virtual particles that live for a
time given by the Heisenberg Uncertainty
Relation
•
•
•
•
The nuclei derive their binding from the
combined effect of all the nucleons inside
the nucleus.
The nucleons are packed together like water
molecules in a liquid drop. Thus the volume
(size) of the nucleus increases linearly with
the number of nucleons, A, and the radius
goes like the cube root of A:
The binding energy increases as we add
more nucleons, to a peak of 8.8
MeV/nucleon at the Fe (Iron) nucleus. As
we add more protons the Coulomb repulsion
between protons diminishes the binding of
heavier nuclei.
In nuclei past Pb (lead) the large Coulomb
energy makes the nuclei prone to fission.
After Thorium nuclei are not stable
anymore.
t   / E   / m c2
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What have we learned last time II
• Nuclei can transform themselves
spontaneously by radioactive decay.
Beta decay is the emission of a negative
or positive electron and a neutrino. It
changes a neutron into a proton or vice
versa. It is mediated by the weak
interaction and thus the half lives are
quite long.
• Radioactive decay can be used for
radioactive dating, by comparing the
intensity left over after a given time to
that predicted by the half life of the
isotope.
• Positron emitters can be used for PET
scanning of isotope distribution inside a
human/animal body.
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• To produce new isotopes or new
elements one uses the fusion
reaction. In this reaction two nuclei
can be fused together, if they have
sufficient energy to overcome their
mutual Coulomb repulsion. This
normally requires an accelerator.
• Neutrons, because they are not
charged, can fuse with a nucleus at
very low energy.
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The Nucleus as Energy Source: Fission
• It was already realized before WW-II that the
fission process can provide a huge source of
energy.
• This energy is obtained without fossil fuel
combustion. It does not produce CO2 which
is the source for global warming.
• The challenges were at first considered
technical: Produce a controlled fission
reaction, in a safe vessel that contains all
radioactivity. Then find a a way to deposit
and safeguard the radioactive waste that has
life times of tens of thousands of years.
• Soon, however, the challenges were more a
matter of public acceptance and policy.
First electricity producing reactor
At INEEL in the U.S. 1951
Modern nuclear reactors
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The fission process
• The fission process for 235U:
*
144
89
n235U 236
U

Ba

92
56
36 Kr  3n
• http://lectureonline.cl.msu.edu/~m
mp/applist/chain/chain.htm
• This process releases 173 MeV
directly, and overall about 202 MeV,
per reaction.
• It also produces 3 neutrons for each
one that it used.
• More precisely, the neutron excess
for different nuclei is
 2.432 new neutrons
239Pu  2.874 new neutrons
235U
• These numbers are crucial for the
production of a chain reaction.
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Neutron cross sections
• Cross section area is a pictorial expression
1240MeVfm
4



28

10
fm
for the probability of a projectile
2
2mc En
interacting with a target nucleus.
• If we take about Rn ~ the cross
• A Boron nucleus has a size RB~ 2.6 fm
section can be A = 2400 bn
and a nucleon has a radius Rn ~ 1.2 fm
Thus we expect A ~ (RB+Rn)2 =
14 x10-26 cm2 = 0.14 bn
• A cross section area of = 10-24 cm2 is
called a barn (bn) because it is as easy for
neutrons to hit as a barn door.
• In fact Boron has a neutron capture cross
section at 0.1 eV of 3,800 bn = 35,000
times what one expects: Why??
• It follows from the wave nature of the
neutron that is important at low energies.
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Neutron reactions
• Neutron scattering as a function of
neutron energy
n12C  n12C
n12C  n'12 C  4.4MeV
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• Neutron capture shows distinct
resonances where the n is captures
into excited nuclear states.
n 235U 236U  fission
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Multiplication factor for chain reactions
• Neutron multiplication factor
k    f  p    PL
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•
•
•
•
•
•
•
•
If k =1 chain reaction is critical
If k< 1 chain reaction is sub critical
If k> 1 chain reaction is supercritical
Explanation of factors in the equation:
 = number of fission neutrons of any
energy per initial thermal neutron
absorbed in the fuel
f = fraction of thermal secondary
neutrons absorbed in the fuel
p = number of neutrons that escape from
being thermalized
 = fast fission enhancement factor
PL = neutron loss factor from volume
Peter Paul 02/24/05
• These values are for pure isotopes. For
natural uranium the 235U fraction is
0.72%; “weapons grade” uranium,
the235U is enriched to at least 3%
• Typical values for a 3% enriched
thermal-neutron reactor:
 = 1.65
f = 0.71
P = 0.87
 = 1.02
PL = 0.96
• The values produce k = 1
• For a chain reaction to build up k must
be > 1.
http://lectureonline.cl.msu.edu/~mmp/applist/ch
ain/chain.htm.
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Neutron Moderation
• In the fission process neutrons are
emitted with energies between 1 and 2
Me. They must be “moderated” down
to thermal energies
• This is done in elastic collisions with
so-called moderator material that
surrounds the Uranium.
• The energy loss  = final average
neutron energy/ initial neutron energy
• The lighter the scattering material is
the more energy the light neutron is
losing in the collision:
 = 0.5 for hydrogen, 0.86 for Carbon,
0.99 for Uranium
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• Thus light (H2O) and heavy (D2O) water
are the best moderators. However,
because of its propensity to absorb
neutrons light water is not very good,
D2O is in effect 100 time better,
Graphite is next.
• Light and heavy water can also be used
as a coolant, but not graphite.
• BNL heavy water- moderated HFBR
research reactor:
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Plutonium Breeding, Xenon Poisoning & Control Material
• n-capture on 238U can breed 239Pu,
which is an even better fission energy
source than 235U.
decay
n 238U 239U 
239 Pu
• Thus reactors produce their own fuel
while they produce energy.
• Materials that absorb neutrons very
effectively act either as poisons –
stopping the reactor, or as control
elements-keeping the power of the
chain reaction in check
• Xenon-135 was an early poison that
almost stopped the Pu production at the
Hanford reactors in 11943 ~ 7 hours
after its start. 135 Xe has a cross section
of 2.65 barns for slow neutrons.
• Good control materials are 10B (cross
section 3800 bn) and 113 Cd (20,000
bn). These materials serve in control
rods that are inserted into or withdrawn
from the core to absorb more or fewer
neutrons.
http://library.thinkquest.org/17940/texts/jav
a/Reaction.html
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Light-water reactors
• The most widely used reactor types
use water for cooling of the reactor
core during the fission reaction.
• The water is either boiling or under
pressure.
• In the BWR the steam
heated in the reactor core
directly drives the steam
turbine which produces the
Electricity.
• A typical reactor generates
about 1000 MW of electricity.
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http://www.ida.liu.se/~her/npp/demo.html
http://www.eia.doe.gov/cneaf/nuclear/page/
at_a_glance/reactors/states.html
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The core of the reactor is an engineering marvel
• But it is not physically complicated.
It has few moving parts, mainly the
control rods.
• They cannot ever be allowed to get
stuck in the pulled-out position or
the reactor could not be controlled
• The most critical parts are the
cooling water pumps. If the cooling
water stops the reactor will overheat
and the fuel rods can melt.
• Automatic safety precautions as
fallbacks are incorporated into the
reactor design, but these have not
always been effective
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Some facts about the fuel cycle
• Typically a reactor has about 280 fuel
• This requires ~ 200 tons of natural
rods in a bundle. Typically fuel rods
uranium. Present world demand for
are changed when they become
Uranium is ~ 60,000 tons/years,
“poisoned” and replaced with new
corresponding to a power production of
ones. The spent fuel can be re300 GW-years. The price of ~$260/kg
processed and Pu can be extracted.
or $260,000/ton.
• A modern reactor has a thermal
• Spent fuel can be re-processed, with
efficiency for the production of
99.8% extraction of Uranium and Pu.
electricity of ~32%. Thus a 1000 MWe • The remainder needs to be stored
reactor needs to produce 3100 MW of
somewhere to cool down thermally and
heat.
in terms of radiation.
• Uranium provides “burn-up” energy of
~ 40 GWd/ton at 3.75% enrichment
• 1 GWe-year requires 1.2 tons of 235U, Yukka Mountain
or 32 tons of total Uranium (3.75%
Repository
enrichment)
• Fuel is changes about 3 tomes/year
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Nuclear Reactors in the world
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Global warming
• production from burning fossil Energy
fuels produces CO2 which slowly
accumulates in the upper atmosphere.
• CO2 transmits the sun‘s radiation to
earth but absorbs the heat radiation
emitted from earth and reflects it back.
This leads to global warming.
• The emssion of CO2 could be
significantly reduced by use of nucler
enrgy production.
• Global warming has
happened before in the
Earth‘s history, but leads
to serious climate
changes
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The Three-Mile Island Accident
• 3MI reactor unit 2 (~800 MW) had a
serious accident on March 28, 1979
when the main cooling water pumps
stopped working. The reactor fuel
overheated and melted.
• Although the containment vessel was
not breached the publics faith in nuclear
power was badly shaken.
• The cause of the accident was human
error, design deficiencies and
component failures.
• Today the 3MI-II reactor is
defueled and decommissioned.
• Total cost of accident
~ $1 Billion
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• Time line:
March 1979: Accident happened
July 1980: 43,000 Ci of Krypton vented
July 1980: First human entry into reactor
building
Oct 1985: Defueling begun
Jan 1990: Defueling completed
April 1991: Evaporation of 2.23 Million
g of contaminated water begins
August 1993: Water removal completed
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Some commercial power statistics
Source
World (2001)
Fossil
346 86%
83.8
86%
Renewable
30
7.4%
5.8
6%
Nuclear
26
6.5%
8.1
8.3%
Total
397 100%
98
100%
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US(2002)
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World Growth of Nuclear Power
Gross
generation
(GWyr)
World
Western
Europe
Asia
US
France
Japan
1973
22
8.4
1.4
10
1.7
1.1
1980
71
24
11
30
7.0
9.5
1990
202
84
32
69
36
22
2000
260
102
57
89
47
37
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Next-Generation Reactors
• The U.S. Government is beginning a
program to design the next generation
nuclear reactors: Generation-IV program.
• This program is studying 6 reactor
concepts with the goal of having designs
ready for construction by 2030.
• It has dedicated the Idaho National
Laboratory to this reactor development.
• The Japanese are also developing
advanced concepts:
The Reduced Moderation Light water
Reactor: This reactor type leaves more
energetic neutrons in the core that “burn
away” heavy radioactive isotopes
• In addition there is development of
Thorium fueled reactors which do not
produce Pu and are thus proliferationproof.
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•
Gas-Cooled Fast Reactor (GFR)
features a fast-neutron-spectrum, helium-cooled reactor and
closed fuel cycle
INEEL contact: Kevan Weaver, [email protected]
•
Very-High-Temperature Reactor (VHTR)
a graphite-moderated, helium-cooled reactor with a oncethrough uranium fuel cycle
INEEL contact: Finis Southworth, [email protected]
•
Supercritical-Water-Cooled Reactor (SCWR)
a high-temperature, high-pressure water-wooled reactor
that operates above the thermodynamic critical point of
water
INEEL contact: Jacopo Buongiorno, [email protected]
•
Sodium-Cooled Fast Reactor (SFR)
features a fast-spectrum, sodium-cooled reactor and closed
fuel cycle for efficient management of actinides and
conversion of fertile uranium
INEEL contact: John Ryskamp, [email protected]
•
Lead-Cooled Fast Reactor (LFR)
features a fast-soectrum lead of lead/bismuth eutectic liquid
metal-cooled reactor and a closed fuel cycle for efficient
conversion of fertile uranium and management of actinides
INEEL contact: Kevan Weaver, [email protected]
•
Molten Salt Reactor (MSR)
produces fission power in a circulating molten salt fuel
mixture with an epithermal-spectrum reactor and a full
actinide recycle fuel cycle
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Reduced-Moderation Water Reactor (RMWR)
drier
• As a candidate of advanced light-water reactors, JAERI is now
developing RMWR.
• RMWR has a possibility of a high conversion ratio of more
than 1.0.
• Gap spacing between each fuel rod is required to be only about
1 mm.
• To attain the gap spacing of 1 mm, a tight-lattice core with
triangular fuel rod arrangement can be needed. This requires
very precise computer modeling
separator
core
control rod
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seed fuel
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blanket fuel
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Nuclear weapons
k    f  p    PL
• For a bomb the neutrons are not very
well contained; in addition one needs a
rapid build-up of the chain reaction,
before the material flies apart.
• For a nuclear bomb the uranium is
highly enriched in 235U, between 60%
and 90%.
• The minimum Uranium requirement is
between 10 and 25 kg. For Pu bomb
the minimum requirement is ~5 kg.
• If these “critical” amounts of material
are in close proximity the nuclear
reaction will explode.
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• Two types of assembly:
1.The gun-type where an explosive charge
drives a sub-critical mass into a second
sub-critical mass at high speed.
Uranium fuel
2.A compression type where a spherical
charge compresses the nuclear fuel from
a low density to a high density where it
becomes critical.
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Pu fuel
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Some archive pictures
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Energy from Fusion in the Sun
1
H 1H 2H  e  
e  e    
2
H  H  He  
1
3
3
1
H 1H 2H  e  
e  e    
2
H 1H 3He  
He3He4He1H 1H
4 1H + 2 e-  4He +2 n + 6  + 26.7 MeV
energy per reaction at ~ 100 Million K
temperature
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Fusion energy in the Laboratory
• The best fusion reaction is d + t   +n
with an energy output of 17.6 MeV.
• D and T present the lowest Coulomb
barrier to fusion, and thus the lowest
temperature. But it requires ~ the
temperature at the core of the sun, ~100
Million degrees. At this Temperature
the electrons separate from the nuclei: a
Plasma
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http://www.jet.efda.org/
• In a thermonuclear bomb (hydrogen
bomb, this temperature is produced
through a fission explosion which then
detonates the fusion reaction.
• For steady state operation the material
needs to be held in a magnetic bottle
• Both the ions and
the electrons in the
plasma can be held
by magnetic fields.
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Advantages and disadvantages of Fusion
• Deuterium is available from sea water,
about 10x 1012 tons. Tritium can be
produced from Li through the reaction:
n 7Li  T  
• Sea water contains thousands of years
supply of Li.
• No long-lives radioactive material is
created”: Tritium half life =32 years
• Fusion reactors could be continuously
loaded: no poisoning of fuel.
• Fuel consumption extremely low
because of huge energy production per
kg of fuel.
Disadvantage: The complexity of
plasma confinement and heating has
held back development for 40 years!
http://fire.pppl.gov/fire_program.htm
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10 - 20 keV
Is optimum
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Need
~ (plasma pressure)2
28 keV
10 atmospheres @ 10
Confinement of plasma particles by magnetic fields
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Toroidal Magnetic Confinement
“TOKAMAK”
Charged particles have helical orbits
in a magnetic field; they describe
circular orbits perpendicular to the
field with gyro-radius rl=v/Ω, where
Ω=qB/mc
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(Russian abbreviation for “toroidal
chamber” with magnetic fields);
includes an induced toroidal plasma
current to form, heat and confine the
plasma
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Product of fuel density, plasma lifetime and temperature is the “figure of merit”.
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As the step to ignition ITER ready to be build
500 MW of power in the plasma, plasma volume 840m3
Toroidal Field Coil
Nb3Sn, 18 coils
Vacuum Vessel
9 sectors
Port Plug
6 heating
3 test blankets
2 limiters
rem. diagnostics
Poloidal Field Coil
Nb-Ti, 6 coils
Central
Solenoid
Nb3Sn, 6
modules
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Blanket
Module
421
modules
Cryostat
24 m high x
28 m dia.
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Divertor
54 cassettes
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Cosmic Timeline for the Big Bang
deuterons
Quarks
proton, neutrons
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He nuclei( particles)
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How are the light elements produced in stars
• Three minutes after the Big Bang the
universe consisted of
75% Hydrogen,
25% 4He
less than 0.01% of D, 3He and 7Li.
• The sun began to burn the available H
into additional 4He, as we learned and
heated itself up.
• Once there was sufficient 4He available
the reaction
4He + 4He+ 4He  12 C + 8 MeV
became efficient. It heated the sun up
still further
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Energy from Fusion in the Sun
1
H 1H 2H  e  
e  e    
2
H  H  He  
1
3
3
1
H 1H 2H  e  
e  e    
2
H 1H 3He  
He3He4He1H 1H
4 1H + 2 e-  4He +2 n + 6  + 26.7 MeV
energy per reaction at ~ 100 Million K
temperature
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From Helium to Carbon
• When the start has used up its hydrogen, the
refraction stops and the star cools and contracts.
If the star is heavy enough the contraction will
produce enough heat near the core where the
4He has accumulated to start helium burning.
4
He 4He8Be;
8
Be 4He12C
• Because of gravity the heavier elements always
accumulate in the core of the star.
• The star now has 4 layers: at the center
accumulates the Carbon, surrounded by a He
fusion layer, surrounded by a hydrogen fusion
layer, surrounded by a dilute inert layer of
hydrogen
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The CNO Cycle
• Once sufficient 12C is available it uses H
nuclei to produce all the nuclei up to 16O
in a reaction cycle.
• When sufficient 16O is available and the
star has heated up muich more, the star
breaks out of the CNO cycle by capture
of a 4He or a proton. This forms all the
nuclei up to 56Fe.
• In this process energy is produced to
heat the star further because the binding
energy/ nucleon is still increasing.
• Hans Bethe (Cornell) and Willy Fowler
(Caltech) obtained Nobel Prizes for
these discoveries
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Relative Elemental Abundances of the Solar System
1.E+02
1.E+00
% abundance
1.E-02
1.E-04
1.E-06
1.E-08
1.E-10
1.E-12
0
10
20
30
40
50
60
70
80
90
100
Z
.At least 4 processes generate heavier elements.
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Supernova explosion produces heavy elements
• When a star has burned all
its light fuel, it cools and
contracts under the gravitational pressure. It then explodes. During
the explosion huge numbers
of neutrons are produced and
captured rapidly by the existing elements (r-process).
• Beta decay changes neutrons into protons
and fills in the elements
• The new elements are blasted into space
and are collected by newly formed stars.
• Binary stars which are very hot can also
produce the heavy elements.
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“normal”
donor star
Accretion disk
Neutron star
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Location of the r-process
in
the
nuclear
mass
table
“Magic”
Chart of the
Nuclei
neutron
numbers
...+126
“Magic” proton
numbers
2,8,20,28,50,82 N=Z
Z
The r-process works its way up
the mass table on the neutronrich side . There are other
processes on the proton rich side
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N
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•Heavy elements are also created in a slow neutron capture
process, called the “s” process.
•The site for this process is in specific stage of stellar evolution,
known as the Asymptotic Giant Branch(AGB) phase.
•It occurs just before an old star expels its gaseous envelope
into the surrounding interstellar space and sometime thereafter
dies as a burnt-out, dim "white dwarf“
•They often produce beautiful nebulae like the "Dumbbell
Nebula".
•Our Sun will also end its active life this way, probably some 7
billion years from now.
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Fifth Homework Set, due March 3, 2005
1. Which two nuclei are used most often in nuclear fission reactors. How
are these nuclei made to fission?
2. The most widely used reactor type is a lit-water reactor. What purposes
does the water serve in the operation of the reactor?
3. What reaction does a fusion reactor use to produce energy and what are
the principal advantages of a fusion reactor over a fission reactor that
follow from using this reaction?
4. What is a nuclear chain reaction; how can it be started and can it be
stopped?
5. How is the plasma in a fusion reactor kept away from the walls of the
reactor vessel? What is the shape of the “bottle” that holds the plasma ?
6. What fuel does the sun burn to produce its power, and what is the “ash”
left behind from the burning?
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