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Radioactivity and nuclear decay: presentation script
Pratap Singh, The Perse School
09/09/14
Slide: Title
Over the last year, I have been reading about and studying
the different types of radiation and how they are detected,
especially in the context of cosmic rays. This talk is about
radioactivity.
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Slide: Overview
Specifically: I will begin by giving a simple qualitative
description of some core physics “laws” or “principles”.
Then, based on these, I will describe the processes that
lead to the various types of radiation, and how and why
they interact with matter as we observed on Friday. I will
describe a very simple device that can detect ionizing
radiation - the Geiger-Müller tube that we used on Friday.
Finally, I will go over some examples of radioactivity - the
decay chain of uranium-238, the chain-reaction fission of
uranium-235, and the concept of critical mass (may be
skipped). In case I don’t give exactly correct
explanations because I don’t know something very well,
please jump in and correct me.
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Slide: Photoelectric effect
Let’s start with the physics principles. One of the most
fundamental principles of physics is the conservation of
energy. We know that a positively charged particle, like a
nucleus, and a negatively charged particle, like an
electron, will attract each other. So if we pull an electron
away from the nucleus, it must have more energy. And
when an electron falls back closer to the nucleus, it must
lose this excess energy in some way. The energy that is
released takes the form of a photon - a particle with no
mass and pure energy. This is the photoelectric effect.
The reverse process can also take place - when a
photon strikes an electron, it may be absorbed and
cause the electron to jump to a higher-energy state.
More generally, whenever an atom is in any kind of
excited state, if it returns to a lower-energy state the excess
energy will be radiated off as a photon.
This becomes important later in the discussion of gamma
rays, but we can also apply it to other interesting
observations. For example: Due to some other principles
which we don’t need to go into, electrons can only exist at
certain quantized energy states around the nucleus. So for
a photon to be absorbed, its energy must be greater than
or equal to the energy required by the electron to jump to
the next allowed energy state. Now we can see why glass
is transparent to visible light - photons of visible light do not
have enough energy to move any electron in the glass to
its next energy level, so all the photons can do is pass
straight through the glass. On the other hand, no electrical
conductor will be transparent - the delocalized electrons in
the metal can be excited by very small amounts of energy,
so virtually no photons will be able to pass through without
exciting an electron.
The full theoretical explanation of the photoelectric effect
was given by Albert Einstein in 1905, and won him a Nobel
Prize.
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Slide: Mass-energy equivalence
The next principle is one of the best-known equations in
physics, and was again given by Einstein - E = mc^2.
This equation states that mass and energy are actually
two sides of the same coin - if a particle gains some
energy, its mass increases. We will need this when
looking at the energy released in the fission examples.
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Slide: Fundamental forces
Now we come to the main principles involved in
radioactivity. Up until the start of the 20th century, all
observations in physics, chemistry, etc could be
explained by just two fundamental forces - gravity and
electromagnetism. But when we found out what the
inside of an atom looks like, a problem arose. The
nucleus of an atom contains many positively charged
protons, which all repel each other due to the
electromagnetic force. However, nuclei do not
spontaneously disintegrate and fly apart. So the question
is: what holds the nucleus together?
One idea is gravity - but gravity is just too weak. It is
actually 10^37 times weaker than the electromagnetic
repulsion between the protons.
Slide: Strong force
The question was eventually answered by a chain of
discoveries that led to the postulation of another
fundamental force, called the strong force. Nucleons (ie
protons and neutrons) are each made up of three smaller
particles called quarks, and the strong force is what
holds these quarks together to form a nucleon. The
strong force is, unsurprisingly, very strong: it binds
quarks together with so much force that they gain a very
high potential energy. From the mass-energy
equivalence, this means that nucleons have a mass
roughly 100 times greater than the sum of the masses of
the three component quarks.
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Slide: Residual strong force
However, the mathematics of the strong force predicts
that the effect of this attraction goes beyond the
boundaries of the nucleon: a small residual force, called
the residual strong force or the nuclear force, acts for a
very short distance outside the nucleon. The residual
strong force has a very strange behavior: when nucleons
are less than 0.7 femtometers (that is, 0.7 x 10^-15
meters) apart, the force repels them apart. But at 0.7
femtometers it becomes an attraction, and reaches the
maximum attraction at 0.9 femtometers. It then
exponentially decreases to negligible strength beyond
about 2.0 femtometers. The effect of this residual strong
force is to bind neighboring nucleons together, and
overcome the electromagnetic repulsion between
protons. This is the force that holds the nucleus together.
Slide: Why neutrons?
The residual strong force provides the answer to another
question: why are there neutrons? It turns out that if there
are only protons in the nucleus, they would be too close
together and the electromagnetic force would rip them
apart. Neutrons effectively separate out the protons in
the nucleus, and provide more attraction via the residual
strong force; they reach a point where the residual strong
force overcomes the electromagnetic repulsion and
holds the nucleus together.
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Slide: How many neutrons?
From this reasoning, we can see that if there are vastly
too many protons relative to the number of neutrons in a
nucleus - for example, oxygen-12, with 8 protons but
only 4 neutrons - a proton will just be ejected from the
nucleus, leaving us with nitrogen-11. This again turns out
to have too many protons, and will eject a proton to leave
carbon-10. Carbon-10 is still unstable but closer to
stability, so here something different happens - we’ll
come back to it. On the other hand, if there are vastly too
many neutrons, it turns out that neutrons will also be
ejected to reach a more stable state - for example,
oxygen-25, with 8 protons and 17 neutrons, will eject a
neutron to leave oxygen-24.
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Slide: Weak force
Nuclei such as carbon-10 and oxygen-24 are
unbalanced, but not so heavily that they will eject
protons and neutrons. They decay in a different way, and
to understand this, we actually need to introduce the
fourth and final fundamental force, known as the weak
force. I don’t know what the underlying mechanism of the
weak force is, but it has a simple high-level effect - if
there are too many neutrons, it causes some neutrons to
decay into protons; and if there are too many protons,
some decay into neutrons. This allows the nucleus to
move towards a more stable state, with the right ratio of
protons to neutrons. For example, four neutrons in the
oxygen-24 from earlier will decay in this way into protons,
turning into magnesium-24 (a stable isotope with 12
protons and 12 neutrons). On the other hand, one proton in
carbon-10 will decay into a neutron, leaving stable
boron-10.
Slide: Weak force: details
However, there is a problem with this explanation - if we
start with a neutron, with no charge, how can we be left
with a positively charged proton? In the actual
mechanism, which is called beta decay, an electron and
a very small neutral particle called a neutrino are also
ejected. We want to be able to represent this compactly,
so we write a sort of equation similar to a chemical
symbol equation. So the equation for a neutron’s beta
decay, called beta-minus decay, is as follows:
n —> p + e^- + v^-_e
where n is a neutron, p is a proton, e^- is an electron, and
v^-_e is an antineutrino.
Similarly, a proton decays into a neutron as follows via
beta-plus decay:
p —> n + e^+ + v_e
This time, we get e^+, which is the anti-particle of an
electron, called a positron. The neutrino is a regular
neutrino.
Slide: Beta decay
The positron, as it flies through normal matter, could
interact with a normal electron. They would annihilate
each other and release the energy as two high-energy
gamma rays; so this type of decay could lead to gamma
radiation. In both cases, the electron is radiated off with
very high energy, and so is detected as beta radiation.
So this process is the origin of the beta radiation we
observed on Friday.
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Slide: Summarizing forces
Let’s pause and summarize the roles of the four
fundamental forces in the nucleus.
Gravity - irrelevant. It is too weak to play a role in normal
matter.
Electromagnetism - behaves the same as on a
macroscopic scale. Causes protons to repel each other,
according to an inverse-square law.
The residual strong force - behaves in a very peculiar
way. Holds nucleons at a very precise distance from
each other, and binds the nucleus together - balancing
electromagnetic repulsion. No effect outside of the
nucleus.
The weak force - allows protons and neutrons to change
into one another releasing beta radiation, so that the
nucleus moves closer to a stable ratio of protons to
neutrons.
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Slide: alpha decay
We’ve seen what happens when the ratio of protons to
neutrons is unbalanced. However, this isn’t the only
criterion for nuclear stability. In very large nuclei, the
range of the residual strong force means that nucleons
are attracted only to their nearest neighbors. But the
protons are repelled by all of the other protons in the
nucleus. This explains why larger nuclei need more
neutrons than protons - they spread out the protons
further and provide extra attraction via the residual
strong force. Occasionally, a small part of the nucleus
may be attracted so weakly that it randomly falls off.
These chunks will move out of the range of the strong
force and will then be accelerated off by the
electromagnetic repulsion of the protons, leading to a new
sort of radiation. It turns out that in almost all cases, only
one particular type of chunk falls off - consisting of two
protons and two neutrons. This is known as the alpha
particle. Alpha particles are favored because they are very
stable - the helium nucleus is actually the most stable
nucleus of all. We can represent this in an equation as well.
Let’s take the example of uranium-238, the most common
type of uranium in nature. Since it has such a big nucleus,
it decays via alpha decay. Losing two protons and two
neutrons leaves an atom two places to the left in the
periodic table - thorium-234. Summarizing:
^238_92 U —> ^234_90 Th + \alpha
So alpha radiation arises when chunks of the nuclei of
large atoms fall off.
Slide: gamma decay
When these two types of decay occur, a large amount of
potential energy is converted into the kinetic energy of
the resultant particles. This leaves these particles in
higher-energy states. We know that due to the
photoelectric effect, when the particles return to their
lower-energy states, the excess energy will be radiated
off as a photon. Typically, there is so much energy that
the photon emitted is a high-energy gamma ray. This is
the most common source of gamma radiation. The other
source that I mentioned earlier is positron-electron
annihilation. This covers the mechanisms of the three
main types of nuclear decay, and the resulting radiation alpha, beta and gamma.
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Slide: Nuclide map
Let’s see what sorts of nuclei are produced by these
decay processes.
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Slide: zoomed-out nuclide map
The diagram on the screen is known as a nuclide map. It
shows all the different possible nuclei, with the number of
neutrons increasing from left to right, and the number of
protons increasing from bottom to top.
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Slide: zoomed-in nuclide map
Each box represents a nuclide (a particular type of
nucleus), and the colors represent how they decay.
Black boxes are stable - they do not undergo any decay.
All other nuclides want to decay into one of these black
boxes. The map nicely illustrates the roles of the different
types of decay.
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Slide: zoomed-out nuclide map (back one slide)
Alpha decay is shown by a yellow box - this causes the
nuclide to jump two boxes to the left and two down. We
can see that this happens mostly with very large nuclei,
as we predicted.
Beta-minus decay (with a neutron turning into a proton)
is shown in pink - this causes the nuclide to jump one
box left and one box up, as it gains a proton and loses a
neutron. We can see that this happens “below” the line of
stable nuclei, where there are more neutrons than required.
Beta-plus decay (with a proton turning into a neutron) is
shown in light blue - this causes the nuclide to jump one
box right and one box down. We can see that this happens
“above” the line of stable nuclei, where there are more
protons than required.
Around the edges of the chart, we see other types of
boxes. Those in orange have so many protons that they
decay simply by ejecting one; they move one box down.
Those in purple have the same problem but with neutrons they eject a neutron and move one box to the left.
The last color on the diagram is green - representing a
process called spontaneous fission. These nuclei are so
big and unstable that they don’t just eject alpha particles they spontaneously smash into several large and small
chunks. It is this process which can lead to a chain
reaction, and this process which is used to generate
nuclear power or build nuclear fission weapons.
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Slide: nuclide map zoomed with Am-241 in center
On Friday, we used three radioactive sources, one for
each type of radiation. The alpha source contained the
radioactive isotope americium-241, represented by the
yellow box in the center of the screen. Since this has a
very large nucleus, it is unstable and decays via alpha
decay, moving two boxes diagonally down and left in the
nuclide map to neptunium-237.
Slide: nuclide map zoomed with Sr-90 in center
The beta source contained strontium-90, represented by
the pink box in the center of the screen. Strontium-90 has
more neutrons than it needs, so via beta-minus decay,
one neutron decays into a proton emitting an electron.
The nuclide moves one box diagonally up and left on the
map, to give yttrium-90.
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Slide: nuclide map zoomed with Co-60 in center
The gamma source contained cobalt-60, shown by the
pink box in the center of the screen. The pink box tells us
that cobalt-60 decays via beta-minus decay, going to
nickel-60. However, the resulting nickel-60 nucleus is in
an excited state; so via the photoelectric effect it
releases its energy in the form of two photons. So much
energy is released that the photons are actually emitted
in the gamma-ray part of the electromagnetic spectrum.
If you remember, the gamma source had a bigger
container; this was to stop the beta particles emitted, so
we only detect the gamma rays.
Slide: Ionization
We have seen how the various forces at work in the
nucleus result in the three types of ionizing radiation. But
the next question is: why is this radiation known as
“ionizing”? How do alpha, beta, and gamma particles
ionize matter?
To understand this, we must divide the ionizing radiation
into two types - charged and neutral. Alpha and beta
particles are charged, and so will interact differently with
matter than the uncharged gamma-ray photons.
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Slide: Ionization by charged particles
An atom becomes ionized when an electron is knocked
loose. When a charged particle moves past an atomic
electron, their electric fields will interact. This results in
some energy being transferred from the more energetic
moving particle to the less energetic electron. When the
charged particle has high energy, such as an alpha or
beta particle resulting from nuclear decay, the energy
transferred is often enough to rip the electron away from
its nucleus. In this way, a charged particle can ionize an
atom simply by passing by it. So alpha and beta
radiation will ionize matter continuously along their path,
and lose energy continuously in this way. A beta particle
traveling at 96.7% the speed of light will ionize roughly 50
molecules per centimeter it travels through air. An alpha
particle, with twice the charge, will interact even more
strongly with matter and ionize many more molecules. The
energy lost in these interactions is what leads to the short
ranges of these particles, and is why they can be stopped
by very small amounts of matter as we saw on Friday alpha particles are “stopped” by cigarette paper, beta
particles by a thin sheet of aluminum.
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Slide: Ionization by uncharged gamma rays
Uncharged gamma-ray photons behave very differently.
Since they have no charge, they cannot interact with
electrons at a distance - they must collide head-on with
them. Since matter is mostly “nothing”, and only a tiny
fraction of the space is “occupied” by electrons or the
nucleus, the likelihood of a gamma ray striking a given
electron is very small. So the gamma ray must pass
through very many more atoms before it collides with an
electron. A gamma-ray photon with the same energy as
the beta particle from before (which ionized 50 air
molecules per centimeter it traveled) would travel, on
average, 170 meters before hitting an electron head-on
and transferring all or part of its energy. This is why
gamma rays are much more penetrating than alpha or beta
particles. The gamma ray gives up its energy via the
photoelectric effect. Usually, the electron is fully ejected
from the atom without using up all of the gamma ray’s
energy, in which case the gamma ray continues on as well
at a lower energy; this type of interaction is known as a
Compton scattering. As a result of this Compton scattering,
a gamma ray can produce a beta particle and a less
energetic gamma ray.
Slide: The GM tube
The common behavior of all these types of radiation is
that they can ionize matter. We can use this to build a
detector for ionizing radiation. There are many types of
detectors, but the type we used on Friday is one of the
simplest and most effective - the Geiger-Müller tube. The
diagram on the screen shows a schematic of a GM tube.
The tube consists of a sealed chamber, filled with a
rarefied noble gas, and enclosed by a metal casing.
There is a metal wire suspended in the chamber and
insulated from the casing. The casing and the wire are
then used as electrodes - they are connected to either
end of a high-voltage power supply which maintains a
potential difference of more than 500V between them.
Since there is no conducting material, just a rarefied inert
gas, between the electrodes, there is no complete circuit
and current cannot flow. However, when an ionizing
particle enters through the detector, it may ionize one of the
atoms of gas. This will result in a positive ion and a free
electron, which may attach to another neutral atom or
remain free. In either case we get two oppositely charged
particles inside the detector. These charged particles are
influenced by the strong electric field, and each accelerate
towards the oppositely-charged electrode. As they
accelerate, they build up their own kinetic energy; so if they
happen to hit another atom of gas, they will have enough
energy to ionize it. This results in more ions being
produced, which then accelerate and may produce more
ions, etc. In this way a cascade proceeds, of positive
particles towards the cathode and negative particles
towards the anode. When they eventually hit the
electrodes, a net transfer of charge takes place from the
anode to the cathode, meaning that a small net current has
flown around the circuit. This causes a brief pulse, which
can be detected and amplified by other electronics. This
pulse is the telltale signature of some kind of ionizing
radiation passing through the detector.
Slide: Example: decay chain of U-238
We have discussed how all of the three types of radiation
arise from just a few underlying principles, and seen how
they can ionize matter. Let’s use this knowledge to
understand some well-known examples of radioactive
decay.
Uranium-238 is the most common isotope of uranium on
Earth - it is a relatively common element with an
abundance of roughly 1.8 parts per million in the Earth’s
crust. This means there are probably at least a few
grams of uranium, if not more, in the soil in the school
grounds. Uranium-238 is a very long-lived isotope with a
half-life of around 4.47 billion years. But it does decay, and
we can understand its decay chain.
Uranium-238 has a very large nucleus, so it will decay by
alpha decay. This causes it to jump down to thorium-234.
But this now has too many neutrons, so it undergoes betaminus decay twice to eventually reach uranium-234 again.
… [equations on slide] … Finally, we get to lead-208, which
has the largest stable nucleus of all known isotopes. Lead
is a sort of boundary element, in that all elements with
higher atomic numbers will eventually decay to either lead
or elements lower than lead. Decay chains similar to this
one are all present in the nuclide chart from earlier for all
radioactive isotopes.
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Slides: Example: fission of U-235
Uranium-238 is the most common naturally occurring
isotope of uranium, but it isn’t very commercially useful.
A different isotope, uranium-235, is what is used in
nuclear power plants. This isotope naturally undergoes
alpha decay, but can be made to undergo nuclear
fission and rapidly liberate large amounts of energy.
Nuclear fission is a different reaction to the three types of
decay, but it is governed by the same principles. The
first step is to hit a uranium-235 nucleus with an
energetic neutron. This results in a nucleus of
uranium-236, but in a high-energy, unstable state. In fact,
it is so unstable that it spontaneously breaks into two
large fragments - nuclei of barium-141 and krypton-92.
Crucially, these atomic masses don’t add up to 236 - three
free neutrons are also ejected at high speeds. The fission
process also releases some of the potential energy of the
nucleus. We can summarize this process in an equation:
n + ^235_92 U —> ^236_92 U* (* means excited) —>
^141_56 Ba + ^92_36 Kr + 3 n
The three neutrons may go on to hit other uranium-235
nuclei, causing them to undergo fission in the same way.
So a chain reaction can proceed. If it can be arranged that
on average, even fractionally more than 1 of these neutrons
goes on to cause another fission reaction, then a runaway
chain reaction occurs: so much energy is released so
quickly that a nuclear explosion takes place. However, if
we can carefully control the number of neutrons that cause
another fission to be exactly 1 out of the three, then a
controlled chain reaction occurs, releasing energy at a
constant rate. These sorts of arrangements are used in
nuclear power plants.
Slide: Thank you for listening
Thank you for listening!