Transcript lecture30

Applications of Nuclear Physics
1. Nuclear Reactions and the Transmutation of Elements
A nuclear reaction takes place when a nucleus is struck by another nucleus or
particle.
If the original nucleus is transformed into another, this is called transmutation.
Example:
Generic reaction:
Laws of conservation:
•the total number of nucleons
•the total charge
•the energy
•the momentum
must be conserved in nuclear reactions.
Conservation of energy
For reaction:
•The reaction energy, or Q-value, is the sum of the initial masses less the sum
of the final masses, multiplied by c2
•If Q is positive, the reaction is exothermic, and will occur no matter how
small the initial kinetic energy is
•If Q is negative, there is a minimum initial kinetic energy that must be
available before the reaction can take place
Artificial transmutation. Transuranic elements
Neutrons are very effective in nuclear
reactions, as they have no charge and
therefore are not repelled by the nucleus.
2. Nuclear Fission. Nuclear Reactors
After absorbing a neutron, a uranium-235 nucleus
will split into two roughly equal parts.
One way to visualize this is to view the nucleus as
a kind of liquid drop.
The mass distribution of the fragments shows that
the two pieces are large, but usually unequal.
The energy release in a fission
reaction is quite large.
The chain reaction
Since smaller nuclei are stable with fewer neutrons,
several neutrons emerge from each fission as well.
These neutrons can be used to induce fission
in other nuclei, causing a chain reaction.
Neutrons that escape from the
uranium do not contribute to fission.
There is a critical mass below which
a chain reaction will not occur
because too many neutrons escape.
A moderator is needed to slow the neutrons;
otherwise their probability of interacting is too small.
Common moderators are heavy water and graphite.
Unless the moderator is heavy water, the fraction of
fissionable nuclei in natural uranium is too small to
sustain a chain reaction, about 0.7%. It needs to be
enriched to about 2-3%.
Nuclear Reactors
Control rods, usually cadmium or boron, that absorb neutrons can be
used for fine control of the reaction, to keep it critical but just barely.
An atomic bomb also
uses fission, but the
core is deliberately
designed to undergo a
massive uncontrolled
chain reaction when the
uranium is formed into a
critical mass during the
detonation process.
3. Nuclear Fusion
The lightest nuclei fuse to form heavier nuclei, releasing energy in the process.
Example1: the sequence of fusion processes that change hydrogen into helium
in the Sun.
The net effect is to transform four protons into a helium nucleus plus two
positrons, two neutrinos, and two gamma rays.
More massive stars can fuse heavier elements in their cores, all the way
up to iron, the most stable nucleus.
Example2: There are three fusion reactions that are being considered for
power reactors:
These reactions use very common fuels – deuterium or tritium – and release
much more energy per nucleon than fission does.
•A successful fusion reactor has not yet been achieved, but fusion, or
thermonuclear, bombs have been built.
•Several geometries for the containment of the incredibly hot plasma that
must exist in a fusion reactor have been developed – the tokamak, which is a
torus; or inertial confinement, which is tiny pellets of deuterium ignited by
powerful lasers.
http://news.yahoo.com/s/nm/20060420/sc_nm/energy_nuclear_usa_dc
Three Mile Island shows US nuclear risks, rewards
By Jon Hurdle Thu Apr 20, 6:35 AM ET
Pennsylvania (Reuters) - Four giant cooling
towers loom over the Three Mile Island
nuclear plant, reminders of the fears and
hopes surrounding an industry that may help
cut U.S. dependence on foreign oil.
Two towers stand quiet, idle since a partial meltdown in a reactor almost 30 years
ago in the nation's worst nuclear accident. Two others belch steam from an active
reactor, providing cheap electricity to 400,000 homes.
Unlike the Chernobyl disaster in Ukraine (April 26, 1986) no one died at Three Mile
Island. But critics of atomic power raise concerns over potential terrorist threats to
plants and say science has yet to provide an adequate solution for highly toxic
nuclear waste.
Nuclear Fission: Nuclear Power Plants
A controlled chain reaction
can be used to generate
electrical power.
The United States uses
103 nuclear power plants
to produce ~20% of our
electricity.
Worldwide about 400
nuclear power plants
produce about 1/6 of the
world’s electricity needs.
The nuclear reaction is
used to create heat;
the heat is converted to
mechanical energy and
used to create electricity.
Elementary Particles
1. High Energy Particles and Accelerators
We need accelerators because:
•As the momentum of a particle increases, its wavelength decreases (λ = h/p),
providing details of smaller and smaller structures
•If an incoming particle in a nuclear reaction has enough energy, new particles
can be produced
•This effect was first observed in cosmic rays; later particle accelerators were
built to provide the necessary energy.
•With additional kinetic energy more massive particles can be produced
Cyclotron:
•Charged particles are maintained in near-circular
paths by magnets
•An electric field accelerates them repeatedly.
The voltage is alternated so that the particles are
accelerated each time they traverse the gap
•The frequency of the applied voltage must equal
cyclotron frequency (frequency of circulations)
mv 2
 qvB 
r
1
v
qB
f  

T 2r 2m
KE  12 mv 2
2

qBr 

2m
Synchrotron:
•Here, the magnetic field is increased as the particles accelerate, so that the
radius of the path stays constant. This allows the construction of a narrow
circular tunnel to house a ring of magnets.
•Synchrotrons can be very large, up to several miles in diameter.
Synchrotron radiation (radiation due to the centripetal acceleration)
•Accelerating particles radiate; this causes them to lose energy.
•Particles in a circular path radiate due to the centripetal acceleration.
•For protons this is usually not a problem, but the much lighter electrons can
lose substantial amounts.
•One solution is to construct a linear accelerator for electrons
Linear accelerator: E = eV.
The largest is about 3 km long.
Collider:
Two beams of accelerated particles collide head-on.
Example: What is the wavelength, and hence the expected resolution, for
the beam of 1.3 GeV electrons?
Note!
me c 2  9.1094 10-31 kg  c 2  0.51100 MeV  1.3GeV
Comments:
E
For
For
m c    pc 
2 2
2
0
2 
2



1
pc
p
  m0 c 2 
pc  m0 c 2  E  m0 c 2 1 
 2 m c2 2 
2m0
0


pc  m0 c 2  E  pc  p  E c
h hc
 
p E


6.63 10 J  s 3.0 10 m / s   0.96 10

1.3 10 eV 1.6 10 J / eV 
34
9
8
19
1243 10 eV  m  1.243 10

1.3
1.3 10 eV 
9
9
15
15
m
m  0.96  10 15 m
2. Beginnings of Elementary Particle Physics – Particle Exchange
The today's model views quarks and leptons as basic constituents of ordinary mater.
The electromagnetic force acts over a distance – direct contact is not
necessary. How does that work?
Because of wave-particle duality, we can regard the electromagnetic force
between charged particles as due to:
1. an electromagnetic field, or
2. an exchange of photons
Feynman diagram for photon
exchange by electrons
The photon is emitted by one electron and
absorbed by the other.
It is never visible and is called a virtual photon.
The photon carries the electromagnetic force.
Feynman diagram for meson
exchange by nucleons
This is a crude analogy
for how particle
exchange would work to
transfer energy and
momentum.
The force can either be
attractive or repulsive.
Mesons
Originally, the strong force was thought to be carried by mesons.
The mesons have nonzero mass, which is what limits the range of the force, as
conservation of energy can only be violated for a short time.
The mass of the meson can be calculated, assuming the range, d, is limited
by the uncertainty principle:
Et  
E  mc 2
t  d / c
d  1.5 10 15 m size of a nucleon
d

c
c
2
mc 
 2.1 10 11 J  130 Mev
d
mc 2
This meson was soon discovered, and is called the pi meson, or pion, symbol π.
Pions are created in interactions in particle accelerators; here are two examples:
m 0  135.0MeV / c 2
m   139.6MeV / c 2
This table details the four known forces, their relative strength for
two protons in a nucleus, and their field particle.
•The weak nuclear force is also carried by particles; they are called the W+,
W-, and Z0. They have been directly observed in interactions.
•A carrier for the gravitational force, called the graviton, has been
proposed, but there is as yet no theory that will accommodate it.
•Every type of particle has its own antiparticle, with the same mass but most
quantum numbers being opposite.
•A few particles, such as the photon and the π0, are their own antiparticles,
as all the relevant quantum numbers are zero for them.
Particle Classification
As work continued, more and more particles of all kinds were
discovered. They have now been classified into different categories.
• Gauge bosons are the particles that mediate the forces
• Leptons interact weakly and (if charged) electromagnetically, but
not strongly
• Hadrons interact strongly; there are two types of hadrons, baryons
(B = 1) and mesons (B = 0).
Almost all of the particles that have been discovered are unstable
If they decay weakly, their lifetimes are around 10-13 s
If they decay electromagnetically, around 10-16 s; and if strongly, around 10-23 s
Strongly decaying particles do not travel far enough to be observed; their
existence is inferred from their decay products.
Quarks
Due to the regularities seen in the particle tables, as well as electron
scattering results that showed internal structure in the proton and neutron,
a theory of quarks was developed.
There are six different “flavors” of quarks; each has baryon number B = ⅓.
Hadrons are made of three quarks; mesons are a quark-antiquark pair.
Here are the quark compositions
for some baryons and mesons: