9.8
From Quanta to Quarks continued....
NOTE: This page is a continuation of the notes and
worksheets for topic 9.8 From Quanta To Quarks. Two separate pages were
used for this topic because of the large volume of material in the topic.
This will keep download time within acceptable limits.
PREPARED NOTES
NUCLEAR FISSION
Nuclear fission is the name
given to the process in which a heavy nucleus splits to form two lighter
nuclei, each of which is more stable than the original nucleus. The first artificially induced nuclear fission reaction was achieved
by Enrico Fermi in 1934, although at the time he did not realise that fission
had occurred. Fermi bombarded
uranium with neutrons and produced radioactive products that emitted b-particles.
Fermi assumed that he had produced a new isotope of uranium, U-239, and
that this had undergone beta decay to form an isotope of the first transuranic
element, atomic number 93, known today as neptunium-239.
Further transuranic elements could then be formed by further beta decays.
Two German chemists, Otto Hahn
and Fritz Strassman, repeated Fermi’s experiments in 1938 and used careful
isotopic half-life analysis to identify the products of the reaction.
To their surprise they found that not only was U-239 produced but also
various lighter elements, such as Ba-141, Kr-92, Ba-144, Kr-89, La-148, Br-85,
Xe-143 & Sr-90. Hahn and Strassman suspected that these lighter elements were
the products of the splitting of the uranium nucleus. This suspicion was confirmed in 1939 by two Austrian
physicists, Lise Meitner and Otto Frisch, who showed that when a U-235
nucleus absorbs a neutron, the nucleus splits into two smaller
nuclei and emits one, two or three neutrons in the process. Meitner & Frisch called the process nuclear fission.
In 1940, when the Manhattan
Project (to build an atomic bomb) was initiated in the USA, Fermi was placed
in charge of the development of the first ever nuclear reactor (or pile).
Fermi determined theoretically that a fission chain reaction, that
is a reaction where one reaction would lead to another and so on, could be
achieved using naturally occurring uranium.
Fermi designed his reactor so that the uranium fuel was spread
evenly throughout a pile of very high purity carbon blocks.
The carbon blocks were designed to slow (or moderate) the speed of
neutrons ejected from uranium nuclei, so that they could then produce
another fission reaction. Cadmium
rods were also inserted throughout the pile to capture neutrons and
thereby control the reaction. (Cadmium
is a good neutron absorber.)
Fermi’s reactor was built on the squash courts under
the football stadium at the University of Chicago. On December 2nd 1942, the cadmium control rods
were slowly, partially withdrawn from the pile.
The amount of radiation produced and the rate and magnitude of
temperature increase were in agreement with Fermi’s predictions.
The reactor ran at a steady rate, indicating that the control rods were
absorbing sufficient neutrons to maintain a chain reaction.
Fermi had demonstrated the first artificially created, controlled,
nuclear fission chain reaction.
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ENERGY FROM FISSION
The binding energy curve shows that a heavy nucleus has a binding energy
of about 7 MeV per nucleon, whereas nuclei of elements with roughly half the
mass number have average binding energies of about 8 MeV per nucleon.
Thus, when the heavy nucleus splits to form
two lighter nuclei, there is a release of about 1 MeV of energy per nucleon.
So, for a heavy nucleus of 200 nucleons, there would be a release of
about 200 MeV of energy from each fission.
Clearly, tremendous amounts of energy
can be produced from sustained fission reactions. For example, the fission of 1 kg of uranium releases about 9
x 1010 kJ of energy. Taking
a typical energy value for coal of about 30 kJ/g means that the fission of 1 kg
of uranium produces as much energy as the burning of about 3 million kg of coal.
An example of a typical fission reaction is:
We can calculate the energy released in this reaction
in a couple of different ways.
We can either determine the difference between the binding
energies of the products and reactants or we can find the difference
between the masses of the products and reactants and then convert this mass
difference into its energy equivalent using Einstein’s E = mc2
equation.
Note that as a
general rule, energy is released from a nuclear reaction when the binding energy
of the products is greater than that of the reactants.
Energy is released because some mass is converted to energy.
Cleary then, we can also say that energy is released from a nuclear
reaction when the mass of the products is less than that of the reactants.
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CHAIN REACTIONS & CRITICALITY
On average, 2.4 neutrons are
produced by every fission of U-235. A
fission chain reaction is one where the neutrons produced in one fission
go on to produce another fission and so on.
In order for a fission chain reaction to occur, the sample of fissionable
material must have a certain minimum size referred to as its critical mass.
Otherwise neutrons escape from the sample before they have an opportunity
to strike a nucleus and cause fission. The
chain stops if enough neutrons are lost. The
reaction is then said to be subcritical.
As an example, critical mass for weapons grade plutonium-239 is about 4
to 6 kg depending on shape. For
weapons grade (highly enriched) U-235 it is even less.
If the mass is large enough to
maintain the chain reaction with a constant rate of fission, the reaction is
said to be critical. This
situation results if only one neutron from each fission is subsequently
successful in producing another fission. Such
a reaction is controllable. See diagram below.
If the mass is larger still, few of the neutrons
produced are able to escape. If
one fission produces two neutrons, these two neutrons can cause two fissions.
The four neutrons thereby released produce four fissions and so on.
The number of fissions and their associated energies quickly increase and
if unchecked the result is a violent explosion.
Such branching chain reactions are said to be supercritical
and the reaction is uncontrollable.
See diagram below.
An excellent example of a controlled
nuclear fission reaction occurs in a fission reactor.
We will examine the basic workings of fission reactors in the next
section of this topic. An excellent example of an uncontrolled nuclear fission
reaction occurs in an atomic bomb.
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THE FISSION BOMB (ATOMIC BOMB)
In the U-235 atomic bomb,
two subcritical masses of U-235 are held well apart at opposite ends of a tube
(referred to as the gun barrel). On
detonation these two masses are imploded together by a conventional explosive
charge (TNT), so that criticality is attained suddenly.
In this way the chain reaction spreads throughout the combined mass
before it breaks up into subcritical fragments.
The result is an uncontrollable fission reaction.
As shown in the diagram below, the
two subcritical masses of U-235 each have a hollow cut into their centres.
The hollows are lined with beryllium, a good source of neutrons.
When the two hemispheres come together, the hollows close around a ball
of polonium, a good source of a-particles.
The a-particles hit the Be and
produce a huge flux of neutrons, which then cause the supercritical fission
reaction that leads to the explosion of the device.
The first such atomic bomb consisted of only a few
kilograms of U-235, but had an explosive force of 20000 tons of TNT. U-235 was
used in the bomb dropped on Hiroshima (August 6 1945).
Pu-239 was used in that dropped on Nagasaki.
Together, these relatively small devices killed well in excess of 100 000
people and caused massive devastation to both cities.
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NUCLEAR FISSION REACTORS
The purpose of a nuclear
fission reactor is to release nuclear energy at a controlled rate.
Fission reactors can be classified as either Thermal Reactors
where the neutrons producing the fission have energies comparable to gas
molecules at room temperatures (thermal neutrons, KE < 1
eV) or Fast Reactors
where the neutrons producing the fission have high energies (fast neutrons,
KE > 1 keV).
Most commercial reactors are Thermal Reactors.
In a Thermal Reactor, fuel
(fissionable material) is bombarded by neutrons, which have been slowed
down to thermal velocities by moderator material, and undergoes fission,
which releases heat energy. Control
rods containing neutron-absorbing material are used to control the rate of
reaction. The heat produced is
absorbed by a coolant material and can be transferred via a series of
heat exchangers to boil water, to produce steam to drive turbines and produce
electricity. Let us now have a
closer look at the basic components of a thermal fission reactor.
FUEL: Thermal reactors are fuelled with natural
uranium or more commonly with enriched fuel.
Enriched fuel is natural uranium, which has been processed by gaseous
diffusion or centrifuge techniques to raise the percentage of fissile U-235 in
it to between 3 and 7 percent, instead of the 0.7% in nature.
U-235 is fissionable with thermal neutrons, whereas U-238 and
U-234, the other isotopic components of natural uranium, are not.
Pure U-235 is never used in a reactor.
The fuel is converted to UO2
pellets and packed into zirconium or stainless steel tubes called fuel rods.
MODERATORS: The reactor core is not just a
mass of fuel. The fuel rods are
spaced out and surrounded by another material called the moderator. Its
purpose is to slow down the neutrons released by fission from high speeds to
thermal speeds. This is done for two reasons: (a) thermal neutrons are more
efficient at fissioning U-235; and (b) fast neutrons are more likely to be
captured by U-238 than to fission U-235.
The moderator must contain light
atoms so that when the fast neutrons collide with the moderator atoms, they move
them and thus give away some of their kinetic energy.
If they collided with heavy atoms such as lead, they would simply bounce
off with their original energies. Commonly
used moderator materials include ordinary water (in reactors using enriched
fuel), heavy water (deuterium oxide D2O), and graphite. Beyond
carbon, the atoms are too heavy to do the job efficiently.
CONTROL RODS: These are used to ensure the
chain reaction does not accelerate into an uncontrollable state.
They are made of neutron absorbing material such as boron or cadmium
encased in steel. As soon as the
temperature within the core rises above the acceptable value, the control rods
are lowered into the spaces between the fuel rods.
There they absorb neutrons and slow down the chain reaction.
COOLANT: Most of the energy released in a
fission reaction is carried away as the kinetic energy of the fission products.
These products collide with other atoms in the vicinity and produce heat.
The heat from the reactor core is collected by the coolant. The
coolant may be ordinary water, heavy water, liquid sodium, gas (eg CO2
or air) or certain liquid organic compounds.
The coolant is in a closed system to lessen the risk of radiation leaks.
RADIATION SHIELDS: There are usually two
shields: (a) A shield to protect the walls of the reactor from radiation damage
and at the same time reflect neutrons back into the core; and (b) A Biological
Shield used to protect people and the environment. It consists of many centimetres of very high density
concrete.
The following diagram shows the
basic structure of a thermal reactor.
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NEUTRON SCATTERING
One of the advantages of fission reactors is that they can be used to
produce large numbers of neutrons for all sorts of research applications. Neutrons
are ideal for probing the inner structure of matter because of the following
properties:
u
They are neutral and can therefore penetrate deeply into
matter.
u
The de Broglie wavelength of thermal neutrons is comparable to
the spacing of the atoms in an atomic lattice.
u
The energy of thermal neutrons is similar to the energies of
the lattice vibrations in solids.
u
They scatter well from protons, making them useful in
determining the structure of solids containing hydrogen bonds (eg organic
molecules).
Neutrons are directed from a reactor core onto a sample of
material. The neutrons collide
with atomic nuclei and scatter in directions determined by the neutron’s
wavelength and the structure of the material under study.
From the diffraction patterns obtained, physicists can deduce the
internal structure of the material.
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APPLICATIONS OF RADIO-ISOTOPES
Another advantage of fission
reactors is that they can be used to produce radioactive isotopes for a
number of special applications. The
radioisotopes are produced by bombarding appropriate elements with
neutrons in the reactor. Alternatively,
radioisotopes can be produced by bombarding appropriate elements with various
sub-atomic particles in a particle accelerator (which we will discuss
soon).
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MEDICAL APPLICATIONS
Radioisotopes are used in medicine
in both diagnosis and therapy. In
diagnosis, the principle use is to locate abnormal tissue such as tumours. In
therapy, radioisotopes are used to destroy abnormal cells within the body.
In diagnosis, a drug
containing the radioisotope to be used is taken orally or intravenously.
The drug carries the radioisotope to the organ(s) under study.
Radiation detectors are then used to measure the concentration and
distribution of the radioisotope and this can in turn result in the detection of
abnormalities. The radioisotopes
used must be short lived to minimise harm to the body. Most diagnostic radioisotopes are gamma emitters,
since gamma radiation is the only natural radiation with sufficient penetrating
power to escape from the body in detectable quantities.
A typical example of a diagnostic
radioisotope is technetium-99m, 99mTc. This
metastable (or excited) form of the Tc-99 isotope has a half-life of only a few
hours and decays to stable Tc-99 via gamma ray
emission.
Hospitals are sent Tc-99m generators, consisting of the molybdenum-99
isotope, which decays with a half-life of 67 hours to Tc-99m.
The Tc-99m so obtained is then
injected into the body and used to scan for brain, bone, liver, spleen,
kidney or lung cancer, as well as for blood flow anomalies.
As the Tc-99m de-excites to Tc-99, the emitted gamma radiation is
recorded and measured using a gamma ray camera.
In radiotherapy,
high-energy radiation is used to cause localised radiation damage to cancerous
cells and kill them. A typical
example is the use of cobalt-60, which kills cancer cells by the release of gamma
radiation. The cobalt-60 can be
implanted in the tumour in the form of a thin wire so that it can release the
gamma radiation over a period of time. Alternatively,
the gamma radiation from the Co-60 source can be directed onto the tumour from
outside the body.
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INDUSTRIAL APPLICATIONS
There are many industrial
applications of radioisotopes. Three
examples are given here.
Various sources of radiation (eg Co-60) are used to measure the thickness of metal, plastic, glass,
paper and so on, during manufacture. This
is done by measuring the amount of radiation passing through the material, which
is related to the thickness of the material.
If the material becomes too thick or thin, the detector senses the change
in radiation and the machine’s control circuits can then adjust the
machine’s settings to ensure the correct thickness.
Smoke detectors use americium-241,
an alpha emitter. The Am-241
ionises the air between two parallel plates and the flow of ions (current)
between the plates is constantly monitored.
If there is smoke in the air, smoke particles are attracted to ions in
the air, making them heavier. This
changes the flow of ions between the plates, which in turn sets off the alarm.
All radioisotopes generate heat as
they decay. Radioisotopic-powered
thermoelectric generators (RTG's) use the heat from the radioisotope plutonium-238
to generate the electricity that runs certain types of cardiac pacemakers.
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AGRICULTURAL APPLICATIONS
Phosphorus-32 is used in agriculture for tracking a plant's uptake of
fertilizer from the roots to the leaves. The phosphorus-32 is added to
soil water. As it has a half-life of 14.3 days and emits b-particles,
its passage through the plant can be traced and the tagged fertilizer's uptake
mapped. b-particles have sufficient
penetration power to emerge from root systems and from inside plant
tissues. They can be detected by Geiger-Muller tubes. Only small,
safe amounts need to be used in this process.
Try the sites below for more information on isotopes used in agriculture.
Phosphorus-32
Food
Irradiation
Agriculture
& Food Irradiation
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WORKSHEET
1 ON NUCLEAR PHYSICS
1.
In the deuterium nucleus, protons have a mass of 1.67 x 10-27
kg, a charge of 1.6 x 10-19 C and are separated by a distance of
about 2.5 x 10-15 m. Calculate
the sizes of the electrostatic and gravitational forces between these protons.
Comment on the relative sizes of these forces.
2.
Use Einstein’s E = mc2 equation to calculate the energy
equivalent of 1 atomic mass unit. Give
your answer in mega electron volts. Take the speed of light as 2.997 925 x 108 m/s.
(1 u = 931.5 MeV)
3.
Determine the mass defect, the binding energy and the binding energy per
nucleon of the
He-4
(a-particle)
nucleus. The experimentally
obtained mass of the alpha particle is 4.002604 u.
Ignore the masses of any electrons around the nucleus.
4.
In 1919 Rutherford bombarded N-14 with alpha particles and achieved the
first artificial transmutation. One of the two products of the reaction was a proton ejected
from the nucleus. Write a balanced
nuclear equation to determine the other product.
5.
When a deuterium nucleus (deuteron) collides with a N-14 nucleus, the
products are N-15 and a proton. Write a balanced nuclear equation for this reaction and then
calculate the mass difference* between the reactants and products and the total
energy in MeV liberated in this reaction. (Masses
of nuclei: N-14 = 14.003074 u, H-2 = 2.014102 u, N-15 = 15.000108 u & proton
= 1.007825 u.)
6.
For the following fission reaction, determine the mass difference*
between the reactants and products and hence calculate the energy released in
MeV.
(Masses: U-235 = 235.044 u, La-148
= 147.915 u, Br-85 = 84.911 u & neutron = 1.009 u.)
7.
Consider a fission reaction where U-235 fissions to produce Ba-141 &
Kr-92. Write a balanced equation to
represent this reaction. Calculate
the energy released in this reaction. (Masses:
U-235 = 235.0439 u, Ba-141 = 140.9139 u, Kr-92 = 91.8973 u & neutron =
1.008665 u.)
*NOTE:
The Syllabus uses the term “mass defect” to refer to the difference in mass
between reactants & products in a nuclear reaction.
So be prepared to read questions asking you to “calculate the mass
defect” in a particular reaction. Strictly
speaking the term “mass defect” refers ONLY to the mass equivalent of the
binding energy of the nucleus – that is the difference between the measured
mass of the nucleus and the theoretical mass determined by adding up the masses
of all protons & neutrons in the nucleus.
It does not refer traditionally to the difference in mass between the
reactants & products of a nuclear reaction.
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PARTICLE
ACCELERATORS
The
Synchrotron:
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The
Linear Accelerator (Linac):
This is a particle accelerator in which electrons or protons are
accelerated along a straight evacuated chamber by an electric field of
constant radio frequency. In
older machines cylindrical electrodes called drift tubes are aligned
coaxially with the chamber. Keeping
in phase with the radio frequency supply, the charged particles are accelerated
in the gaps between the electrodes. In
other words, initially, the tube in front of the particles has an opposite
charge to that of the particles, and hence attracts the particles. Once in the tube, the polarity of the tube changes.
The particles are repelled from the tube and attracted to the next tube,
and so on. Since the frequency of
the electric field is constant and the particles increase in speed, the tubes
get progressively longer to ensure that the particles spend the same amount of
time in each tube and therefore keep in phase with the electric field. See
diagram below.
Modern high-energy linacs are usually travelling wave accelerators in
which particles are accelerated by the electric component of a travelling wave
set up in a waveguide. No drift
tubes are used, the radio frequency being boosted at regular intervals along the
chamber by means of klystrons (electron tubes used for the amplification
or generation of high frequency waves). Only
a small magnetic field, supplied by magnetic lenses between the radio frequency
cavities is required to focus the particles and keep them in a straight line. Typical rates of energy gain in a linac are 7 MeV per metre
for electrons and 1.5 MeV per metre for protons.
The linac at Stanford University in USA is over 3 km long and can
accelerate electrons up to 99.99% of the speed of light.
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THE
STANDARD MODEL OF MATTER
Bosons:
Quarks:
For every quark, there is a corresponding anti-quark,
represented in the usual way with a bar above the symbol.
Quarks are never found in isolation, because the strong force that binds
them together is such that it increases in strength with increasing distance.
So quarks act as the constituents of other particles.
Leptons:
Success
of the Standard Model:
PARTICLE
PHYSICS & COSMOLOGY -
Not Examinable
FURTHER
THEORETICAL DEVELOPMENTS
- Not Examinable
WORKSHEET
2 ON NUCLEAR PHYSICS
1.
Perform a first-hand investigation or gather secondary information to
observe radiation emitted from a nucleus using a Wilson Cloud Chamber or similar
detection device. (In Class)
2.
Gather, process and analyse information to assess the significance of the
Manhatten Project to society. (Homework)
3.
Identify data sources, and gather, process and analyse information to
describe the use of a named isotope in: medicine, agriculture and engineering.
(Homework)
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From Quanta To Quarks
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