8.3.
2 Nuclear Power
Notes and questions
As an alternative to fossil fuel generation, nuclear power has had a controversial press. It has
become a major source of energy in many counties across the world and the U.K., U.S.A. and
France, for example, could not meet their current energy supply targets without it. The use of nuclear
power to generate electrical energy is fairly widespread.
Much has been made of the potential for nuclear power to generate increased amounts of electricity
without further adding to greenhouse gas emissions. However there are strong arguments to
increase the use of renewable energy sources, particularly wind power, in order to meet our electrical
needs without compromising the climate. But is it safe?
After this lesson you should be able to;
Describe how neutrons produced in a fission reaction may be used to initiate further fission
reactions (chain reaction).
Distinguish between controlled nuclear fission (power production) and uncontrolled nuclear
fission (nuclear weapons).
Describe what is meant by fuel enrichment.
Describe the main energy transformations that take place in a nuclear power station.
Discuss the role of the moderator and the control rods in the production of controlled fission in
a thermal fission reactor.
Discuss the role of the heat exchanger in a fission reactor.
Describe how neutron capture by a nucleus of uranium-238 (238U) results in the production of
a nucleus of plutonium-239 (239Pu).
Describe the importance of plutonium-239 (239Pu) as a nuclear fuel.
Discuss safety issues and risks associated with the production of nuclear power.
Solve problems on the production of nuclear power.
Nuclear fission
235
Uranium is currently the fuel of choice for most reactors in current use. The nuclide 92 U undergoes
induced fission when neutrons are introduced into the uranium fuel, usually in the form of uranium
oxide. The reaction is described by the equation below.
235 1 141 92 1
U+92 0 n→ 56 Ba+36 Kr+30 n
You will know from atomic physics that the sum of mass and atomic numbers must balance on each
side of the equation. For example;
Mass numbers; 235 + 1 = 141 + 92 + (3 x 1)
Atomic numbers; 92 + 0 = 56 + 36 + (3 x 0)
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8.3.2 Nuclear Power
You may well have realised by now that several different pairs of fission fragments are possible as
long as the total mass number and atomic number are conserved. Another possible fission reaction
is;
235 1 93 141 1
92 U+ 0 n→ 37 Rb+ 55 Cs+2 0 n
The average amount of energy liberated in each 235U fission (E) can be calculated by considering the
mass deficit, the difference in actual mass (m) between the reactants and products, and by using the
equation; ΔE=Δ mc 2
Data Question
e = 1.60 x 10-19 C
NA = 6.02 x 1023 mol-1
mp = 1.673 x 10-27 kg
mn = 1.675 x 10-27 kg
The average amount of energy released when an atom of uranium-235 undergoes fission is 200 MeV.
Q1. Natural uranium contains 0.7% U-235. Calculate the maximum amount of energy available in
Joules when 1 kg of natural uranium completely undergoes fission.
Q2. Compare this with the maximum thermal energy produced when 1 kg of carbon 12 is burnt in
air. (1 mole of Carbon 12 produces 0.39 MJ of energy when burnt in air)
Q3. Comment on your answer and consider the significance in terms of energy production
planning.
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8.3.2 Nuclear Power
The enrichment process
Most naturally occurring uranium ores contain a mixture of two isotopes: uranium-235 and uranium-
238. 99.3% of the ore is uranium-238 and the uranium-235 required for fission only makes up 0.7%.
Modern reactors require enriched uranium containing up to 3.5 % of the isotope uranium-235.
In the enrichment of uranium the gas, uranium fluoride, is fed into a centrifuge. This contains a
series of evacuated cylinders, each with a rotor between one and two meters long with a diameter of
15-20 cm. The mixture of isotopes is spun round at rates of up to 70,000 revolutions per minute (rpm).
The heavier uranium-238 requires a larger centripetal force to stay in a circular path and thus moves
to the outside of the centrifuge. The uranium-235 requires a smaller force and collects together,
closer to the centre. The uranium-238 can then be removed, as depleted uranium, and the
remaining mixture is then centrifuged several more times, in a cascade of centrifuges, before the
concentration of uranium-235 has increased to the required 3.5%. The whole process is complicated
and involves some very technical and challenging engineering, partly due to the tremendous forces
involved.
Cascade of gas centrifuges used to produce
enriched uranium. This photograph is of the Diagram to illustrate the structure of a uranium
gas centrifuge plant in from 1984. Source: centrifuge. The rotor spins around a vertical axis. The
USA Department of Energy. uranium-235 collects towards the axis and the uranium-
238 towards the outer wall of the rotor.
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8.3.2 Nuclear Power
Data Questions
Data
Mass of U235 = 235.044 x 10-27 kg
Mass of F19 = 19.004 x 10-27 kg
Q4 Estimate the mass of one molecule of Uranium Hexafluoride, UF6 in kg.
(relative atomic mass U = 238, F = 19.0, 1 a.m.u. = 1.66 x 10-27 kg)
assume the starting conditions are as follows;
Initial orbital radius = r = 1.5 m
Rate of rotation = 70,000 rpm.(revolutions per minute)
Q5 Calculate (i) the number of revolutions per second, (ii) the period of rotation and (iii) the
angular velocity.
Q6 Calculate (i) the centripetal force on one molecule of uranium hexafluoride and (ii) the ratio
of the centripetal force on one molecule to the molecular weight . (iii) comment on this
answer - calculate the force experienced by a 50 kg student rotating at the same rate for
comparison.
Moderation and control In order for a nuclear reactor to continue to release thermal energy at a
steady rate, the reaction must be self-sustaining. For every one neutron that successfully collides
with a uranium-235 atom, another one has to be produced which will definitely induce another fission.
If too many neutrons are available for further fissions it is possible that the rate of production of
thermal energy in the reactor will increase in such a way that the reaction may become uncontrollable,
which may lead to an explosion. A great many precautions are used to ensure that this does not
happen. However this thermal runaway or uncontrolled fission is the mechanism by which a nuclear
bomb works.
The nuclear energy spectrum below illustrates that most neutrons produced in a reactor are fast
neutrons in the range 1 -2 MeV. These have too much energy to cause further uranium-235 fission
and are far more likely to be captured by uranium-238. Thermal neutrons are more likely to cause
further fission. These neutrons have energies of about 0.02 eV. Moderators are used to “slow” down
these fast neutrons to thermal energies to increase the probability of further fission. Control rods are
used to remove any excess neutrons to ensure the reaction continues safely.
Probability
Neutron energy spectrum from a fission reactor core
Scattering cross sections and probability The fission equations used on page1 show that for
every inducing neutron which has a successful collision with a nucleus of uranium-235, two or three
neutrons are produced in the resulting fission. In fact, the mean overall number of neutrons resulting
from each fission is about 2.5. These neutrons may:
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8.3.2 Nuclear Power
leave the fuel rod through the external surface
collide inelastically with a uranium-238 nucleus and be absorbed
collide inelastically with a uranium-235 nucleus inducing fission
collide elastically with either nuclide or the moderator and control rod molecules, transferring
energy only
The laws of probability are used to determine the chance of each outcome occurring. These
calculations enable appropriate conditions to be set up within the reactor to ensure criticality – a self-
sustaining fission reaction – is maintained. As we are discussing many billions of events, the laws of
probability work very well.
The concept of scattering cross sectional area is used. A large scattering cross sectional area
implies a large probability a particular the event occurring.
Scattering cross sections for uranium nuclides.
The curves are rather complicated but show that
the scattering cross section and hence the probability of a fission for uranium-235 increases
as the neutron energy is reduced.
the scattering cross section for uranium-238 neutron capture is particularly large in the 10 –
100 eV energy range. The sharp peaks in this energy range are known as resonances.
The uranium-235 and uranium-238 nuclides present a similar geometric cross sectional area to a
neutron but their scattering cross sections depend on the neutron energy.
Q7 Consider a neutron moving along a tube of area, A, towards a nuclide of area, a, as shown
below. Write down the probability of the neutron colliding with the nuclide. (You can assume
the neutron is a point object)
area, a
area, A
area,
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b
area, A
8.3.2 Nuclear Power
Q8. Now assume that the tube contains a different nuclide of area, b. Write down the probability
of a collision with the second nuclide.
Q9 (i) Write down the ratio of your answer to Q7 to your answer to Q8 and (ii) explain what this
answer means in terms of probabilities.
Q10 Assume the neutron is a thermal neutron of energy 0.01 eV. Using the graph above
determine the ratio of the probability of uranium-235 fission to uranium-238 capture.
Q11 Repeat Q10 for a fast neutron of energy 10eV.
Critical mass The concept of critical mass is used in calculations to determine the ideal shape and
mass of the uranium fuel rods used in nuclear reactors. The critical mass of uranium is defined as the
mass which just allows a self-sustaining nuclear reaction to continue without adding any more
neutrons from an external source.
For simplicity we will assume that the uranium is in the shape of a sphere,
though usually the fuel rods are cylindrical and are arranged in a hexagonal
formation within the reactor core.
It is reasonable to assume for a spherical piece of Uranium that the total
number of neutrons produced per second in the reactor core, NP is
4
π
proportional to the uranium volume, 3 r3, and the total number of
neutrons lost per second from the outer fuel rods surface, NL is proportional
to the uranium surface area, 4 π r2
3 2
N P ∝r and N L ∝r
so
NP
∝r
NL
As the radius of the uranium sphere increases so does the number of neutrons produced
compared to those lost. In this simple model:
If the uranium is below a certain critical size then NP/NL < 1 and the reaction will die out.
If the uranium is above this critical size then NP/NL > 1 and uncontrolled nuclear fission will
occur and the reactor may become dangerous.
The ideal ratio, where NP/NL = 1, needs to be maintained in order to ensure a self-sustaining
nuclear reaction. This condition is called criticality.
This is partly achieved by calculating the exact mass and shape of the uranium fuels needed, but in
the real world there are other factors to consider which means a more sophisticated model is
required.
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8.3.2 Nuclear Power
Nuclear waste
One of the greatest concerns, is the management of waste left over from the fission process.
Although much of the waste, notably the fission products, has a relatively short half life, some material
will be significantly hazardous for many generations to come and as such it is the responsibility of the
nuclear industry (and the governments who run it) to ensure that a reliable method for the safe
disposal of waste is used.
The major constituents of nuclear wastes are listed below.
1. Fission fragments, which are generally beta decay emitters with a half lives up to 10 years.
2. Transuranic elements are elements beyond uranium in the periodic table. These include
neptunium, plutonium and americium and are formed as shown in the decay chains below:
238 1 239
92 U + 0 n→ 92 U
239 239 0
92 U → 93 Np+ −1 e+ν e
239 239 0
93 Np→ 94 Pu+ −1 e +ν e
Further neutron capture can produce plutonium-241
239 1 240
94 Pu+ 0 n → 94 Pu
240 1 241
94 Pu+ 0 n → 94 Pu
this is unstable and decays into americium-241
241 241 0
94 Pu→ 95 Am+ −1 e +ν e
These elements decay with half-lives up to 1000 years or more.
Between them the transuranic elements and fission products account for up to 6% of the thermal
energy produced in the reactor.
3. Activation products are radioisotopes produced by the absorption of neutrons of any other
material including the steel containment vessel, coolant and moderator. These may include Tritium, a
form of Hydrogen – Hydrogen-3.
Once the spent fuel rods are removed from the reactor they will continue to emit thermal energy, due
to radioactive decay, at a rate of about 10 kW per tonne but this falls to about 1 kW per tonnes after
10 years. During this time the waste is stored under water in large cooling ponds.
Solidification processes have been developed in France, UK, US and Germany over the past 35
years. Liquid high-level wastes are evaporated, mixed with glass-forming materials, melted and
poured into robust stainless steel canisters which are then sealed by welding.
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