nuclear energy: how it works
Chemistry is based on atoms. Here is a cartoon of an atom
It shows that an atom consists of a cloud of electrons surrounding a nucleus. However, this
cartoon is misleading in some important respects. In particular, the nucleus is 100,000 times
smaller than the atom.
The physics of the nucleus
The nucleus has two important properties:
*charge, which determines the number of electrons it can attract, and corresponds to the
atomic number Z of the element. Chemically different elements have different values for Z.
*mass. Most of the mass (99.9%!)of the atom is in the nucleus. It is almost an integer multiple
of the "atomic mass unit."
Here are some examples
Symbol Name
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H
2
H
C
14
C
12
14
N
O
117
Sn
235
U
238
U
16
Ordinary
Hydrogen
Heavy hydrogen
Carbon
Radioactive
carbon
Nitrogen
Oxygen
Tin
Uranium
Uranium
Charge
Z
1
N
Mass
0
Mass parameter
A
1
1
6
6
1
6
8
2
12
14
2.014102
7
8
50
92
92
7
8
67
143
146
14
16
117
235
238
14.00307
15.9949
116.90
235.04
238.05
1.007825
12.0000
14.00324
Note that it is possible for the same chemical element (like carbon, with Z = 6) to have several
isotopes with different masses (C-12, C-13, C-14 are all found in the environment).
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We can explain this table (and all of the other kinds of nuclei that are not included) if we assume
1) The nuclei are made of two particles, "proton" and "neutron". They have these properties:
Symbol Name
Charge Z N
Mass
mass
parameter A
n
Neutron
0
1
1
1.0078
p
proton
1
0
1
1.0087
The nucleus of an ordinary hydrogen atom is a single proton. Any other kind of nucleus is a ball
of neutrons and protons stuck together. If it contains Z protons and N neutrons; the mass
parameter A is the total number of particles Z + N.
2) The mass of a nucleus is slightly less than sum of the masses of the protons and neutrons it
contains. For example, 12C (ordinary carbon) contains 6 protons and 6 neutrons and has mass
12.0000, which is less than 6*1.0078 + 6* 1.0087. According to Einstein, there is an energy
associated with mass given by E = m c2 . When we combine protons and neutrons to make a
nucleus, some energy is given off, and this decreases the mass of the result. Because “c” is a
very large number, the small mass difference between a nucleus and the protons and neutrons
that make it up implies that a very large amount of energy is involved (large compared to what
happens in a chemical reaction, like exploding dynamite).
3) Neutrons can turn into protons (or protons into neutrons) if this decreases the energy (which
we can detect as a decrease in mass). This is the most common kind of radioactivity (it is called
“Beta decay”). The release of energy is large relative to the rearrangement of electrons that
takes place in chemical reactions; a single nuclear transition can cause hundreds of thousands of
chemical changes in the surrounding atoms.
This model explains the following properties of the table of isotopes:
* there can be more than one "isotope" of the same element (same Z, but different N and A). Z
tells you the number of protons, and now you can put in various numbers of neutrons. But only
a few of these isotopes are stable, because a neutron can turn into a proton if this lowers the
energy.
*for light stable elements, the number of neutrons N is equal to (or almost equal to) the charge
parameter Z, but for heavy elements N is 50% more than Z.
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This diagram shows whether a nucleus with Z protons (vertical axis) and N neutrons (horizontal
axis) is stable or not.
Nuclei in the blue regions are so unstable that they can’t be observed; they fall apart or turn into
something else immediately.
Nuclei in the white zone have been created in the laboratory. They are unstable (radioactive)
isotopes. By turning a neutron into a proton (or a proton into a neutron) these eventually
become stable nuclei (the black dots in the center of the diagram).
The mass of the elements is less than the mass parameter A all the way to tin, but for the really
heavy elements such as uranium, the mass is slightly larger than A. This means that adding
protons and neutrons to light nuclei lowers the energy, and we can extract energy by merging
two light nuclei into a heavier one. This process is called fusion; it is the mechanism that keeps
the sun hot, and is the basis for the hydrogen bomb.
Nuclear fusion
Theoretically we could be producing energy on earth by controlled fusion of hydrogen. We
have all the fuel we could ever want in the oceans of the world. But despite a lot of research,
scientists haven't quite figured out how to do it. For fusion to occur we have to get the nuclei
close enough together that they touch. But the normal limit on how close nuclei can get is
determined by the size of the atom, which is 100,000 times too large. The only method that
works to get the nuclei close together is to make the material very hot – millions of degrees!! –
which causes the nuclei to bang into each other. In the sun and in the fireball of a nuclear
explosion it gets hot enough to make this happen. How to maintain a gas at a million degrees
on earth is an unsolved problem.
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Nuclear fission
There is another way to get energy from nuclear reactions. Very heavy nuclei have larger
energy density than the lighter ones; we can also extract energy by breaking them up. This
time, nature has provided a way to do it, because certain isotopes will spontaneously break into
pieces when they absorb a neutron. This table explains the process:
Process step
name
Z
N
mass
Combine a
n
0 1
1.008
neutron and a
U-235
92 143 235.04
Uranium nucleus
result
unstable nucleus
92 144 236.04
Emit two neutrons
92 142 234.03
and split in two
red X on the diagram 46 71 117.02
Turn 4 neutrons
Into protons and
release energy
Sn-117
50 67 116.90
Energy released
234.03 – 2*116.90 = 0.23
= 0.001 x 235.04
The result is that one thousandth of the mass has been turned into energy. So if we start with
a kilogram of U-235 and fission all of it, we will get
E = (decrease in m) c^2 = 0.001 x 1 Kg x (3 x 10^8)^2 = 9 x 10^13 Joules
This is about the same size as the energy released by burning 1,000,000 Kg of gasoline (a
kiloton).
We needed a neutron to start the fission process, but the result of fissioning the U-235 has way
too many neutrons, and a few free neutrons will be emitted. In the example above, one
neutron went in and two came out. If both of these go on to cause fission, we will have 4, and
then 8, ... ... a "chain reaction." The time between doublings is the time it takes for the
neutron to move to the next nucleus – a few millionths of a second – which implies that the
entire 9 x 10^13 J will be released in a thousandth of a second. That describes an atom bomb.
Actually making a nuclear weapon is more complicated than that description suggests, because
if we have a small piece of uranium the neutrons will escape before they encounter another
nucleus (so we need a “critical mass”), and because the energy released will push the uranium
apart (so we need a way to rapidly assemble enough fissionable material, and keep it together
long enough to have a lot of fission take place).
It was also assumed that we had the U-235. Uranium is already not a very common material;
and in natural uranium only 0.7% is U-235; most is U-238. Natural uranium will not sustain a
chain reaction, because the U-238 absorbs neutrons without fissioning. Separating the U-235 is
a difficult technological problem, because it is almost identical to U-238 by any physical or
chemical test.
The first successful separation technique was gaseous diffusion. The compound UF6 (uranium
hexafluoride) is a gas at ordinary temperature. Because the mass is smaller, UF6 containing U-
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235 can get through a small hole slightly faster than the molecules containing U-238, thus giving
a slight enrichment. By repeating this thousands of times, nearly pure U-235 can be made. The
facility at Oak Ridge, TN was built to produce U-235 by this process. Later it was discovered
that in a centrifuge (a rapidly rotating container), the U-238 gas concentrated slightly towards
the outside. The facility at Portsmouth, OH makes U-235 this way.This technology has been
used by many countries.
A completely different route to making fissionable material is to build a nuclear reactor (which
does not require pure U-235) and run it for a while. Some of the neutrons get absorbed by the
U-238, which then turns into Plutonium-239. This can be separated by chemical means, and is
fissionable. A facility at Hanford, WA produced plutonium for the Nagasaki nuclear weapon
and many of the US nuclear weapons of the cold war era. India, Pakistan, and North Korea built
their nuclear weapons using plutonium from reactors; they previously had claimed the reactors
were for “research.” This is why Iran’s ambition to start a nuclear technology is regarded as
suspicious.
At least 8 countries have figured out how to do this and made nuclear weapons; there are now
over 20,000 nuclear weapons in the world (but 20 years ago there were 70,000).
Nuclear weapons have been used only twice in history, at the end of World War II. It seems
much less likely today that there will be a nuclear war than it was 40 years ago; you may hope
that this is a part of the this course that you don't need to know about.
Nuclear power
Nuclear reactions are being used to generate energy. To do so, we need to modify the chain
reaction so that it can be controlled. In the description above, it was assumed that 1 neutron
becomes two after a fission. But if one of them escapes or is absorbed without causing a
fission, the reaction could be self-sustaining with the fissions taking place at a constant rate.
By putting in neutron absorbers, the system can be tuned so that 1000 neutrons generate 1001
(or 999) neutrons after a round of fissions, and then the fission rate will increase (or decrease)
more slowly, with the number of neutrons doubling every thousandth of a second (instead of
every millionth of a second). By itself, this would not make a nuclear reactor controllable: it
would have to be adjusted every 0.001 second. But now there are other features of fission that
make control possible:
*uranium is much more likely to absorb neutrons if they are moving slowly. The neutrons start
out moving very fast, and slow down by bouncing off of other atoms. This takes a few
thousandths of a second. So the reactor is designed so that it won't work with rapidly moving
neutrons. This increases the time scale by a factor of a thousand.
*when a nucleus fissions, several neutrons are released. Not all of them are released
immediately; about 1% appear 1 second after the fission event. So the reactor is designed so
that every last neutron is needed to keep the chain reaction going. This changes the time scale
from a thousandth of a second to several seconds. That's how often you alter the steering
wheel when you are driving a car.
With a time scale of many seconds, the reactor becomes easy to control. For example, the
reactors in nuclear submarines are made of materials that change size when they get hot, in
such a way that this makes it easier for the neutrons to escape. The result is that the reactor
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maintains a constant temperature; if too much energy is produced, the reactor gets too hot, and
this turns off the nuclear reactions.
Here is a cartoon showing the components of a nuclear reactor.
The red bars represent the fuel rods, made of
uranium. The fissions take place inside the
fuel rods. The neutron leaves the fuel rod
before it slows down.
The orange represents the moderator. The
neutrons are slowed down by bumping into the
nuclei. Some of them escape from the reactor,
and some are absorbed by the control rods.
Just enough make it back into a fuel rod to
cause another fission, to keep the reactor
going.
The energy of the fission is delivered to the
moderator, and then to the blue water in the
pipe, which gets boiling hot and is used in the
turbine.
An important role in the reactor design is played by the "moderator" – the material that slows
down the neutrons. The best materials for slowing down a neutron are nuclei with small mass.
However, it is also important that the moderator won't absorb neutrons. Then there are four
choices:
*ordinary water can be used. The hydrogen atoms are very effective at slowing down the
neutrons. Almost all US nuclear power plants use water as the moderator. A drawback is that
some of the neutrons are absorbed, turning the hydrogen into deuterium (heavy hydrogen).
For this reason, these reactors require "enriched" uranium, with at least 3% U-235.
*heavy water (deuterium oxide) absorbs neutrons much less, making possible a reactor that will
work with ordinary unenriched uranium. The government of Canada developed reactors of this
sort, but apparently they have not been a commercial success.
*the first reactors used graphite (a form of carbon) as the moderator. This was the moderator
in the Chernobyl reactor, and may have played a role in the resulting disaster. It has not been
used very much in US power plants.
*helium will not absorb neutrons at all. It would also allow operation at very high
temperatures, which gives higher efficiency (according to the Second Law of Thermodynamics).
A few reactors using helium for the moderator have been built. However, helium is only a gas,
which means that it isn't very dense. The neutrons go too far before they are stopped.
Here is a diagram that shows how US nuclear power plants work.
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The reactor is the big red thing in the middle. It contains the uranium fuel, in the form of long
thin rods. It is a large tank containing water under pressure. The neutrons created in fission
collide with the water molecules, which slows down the neutrons (allowing them to cause
another fission) and transfers their energy to the water (making hot water, which will be used to
generate electricity). The water has chemicals dissolved in it that absorb some of the neutrons.
The water that has been inside the reactor is very radioactive, and so it is kept inside the reactor
building. At the steam generator, this hot water is used to warm water from outside. This hot
water is sent to the turbines, which drive the generators. After the turbine there is a
condenser, which cools the steam coming out (this makes the pressure low on the back side of
the turbine: this is a necessary part of the process). The condensed water goes back into the
reactor building to be heated up again. The condenser is cooled by yet another stream of
water, which gets warm; it is sent to the cooling tower to be cooled back down. The cooling
tower plays the same role as the radiator in your car.
A typical nuclear power plant produces 1200 Megawatts of electrical power, releases 2400
Megawatts of heat to the environment, and contains 170 tons of fuel which is replaced on a 4
year cycle.
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