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MARKUS KLUTE: Welcome
back to 8.701.

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So in this video, we
talk about stability

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and, the opposite of stability,
the decays of nuclei.

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OK, so let's look
at this diagram

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first, which shows the
number of protons--

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the number of protons and
the number of neutrons here.

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And you find that
the stable elements

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sit in this so-called
Valley of Stability.

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So there's a certain part of
our nuclei which are stable.

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This valley follows directly
out of the discussion

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of the binding energy, where
you can calculate the optimal Z

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value such that the
mass is minimal.

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It's about A half in this
area here at low masses,

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and about 40% of A the higher
part-- at high value of mass.

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We already discussed that the
binding energy has this form

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here, with a maximum
around the mass of iron,

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which is like somewhere here--

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50 some.

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OK, so it's
energetically favorable

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for some unstable
nuclei to break apart

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in so-called fission processes.

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And it's also
energetically favorable

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to fuse together
to create energy.

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And we'll talk about the
applications of those processes

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later on.

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But for now, we
want to just look

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at a radioactive nuclide, which
can decay in various ways.

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And so the first, most prominent
decays we want to discuss

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here-- and then we'll
follow up a little later--

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is an alpha decay,
which is splitting up--

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a mother particle splits up
into daughter particle nuclei

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and helium-- which is
an alpha particle--

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or the emission of electrons,
positrons, or the capture of

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electrons as well.

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It is also possible,
but rather rare,

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that a nuclei just spits out a
proton, or spits out a neutron.

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So this is possible,
but it's rather rare.

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All right, so let's look
at the alpha decay first.

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As I said, we start from a
rather large, heavy nuclei.

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And it seems possible
for it to spit out

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helium or an alpha particle.

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So the first thing we want to--
the view we want to have here

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is of the potential in which
the alpha particle sits.

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So the alpha particle
sees a really deep well

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of the nuclear potential.

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And it also sees this
boundary here, this barrier,

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of the Coulomb potential.

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So for the alpha
particle to be emitted,

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it needs to break through
this Coulomb potential here.

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And you can calculate the
likelihood using quantum

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mechanics-- the quantum
tunneling likelihood--

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in order to figure
out how stable

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an individual particle is.

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Here, I just wanted
to show you something.

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This plot here shows you the
lifetime of an unstable nuclei,

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for various sorts, as a
function of the energy.

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And what you see here is it's
very strong energy dependent.

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This is a logarithmic plot.

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And what you see is
the lifetime seems

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to be rather, rather short
when the emitted particle has

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a lot of energy.

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And that can be explained by
this plot here very easily.

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In order for this particle--
the energy of this particle,

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when it goes here, is dependent
on where this particle sits

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in this potential, right?

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So particles which sit
at very high values here

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will have a high likelihood to
tunnel through this barrier,

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and therefore a short lifetime.

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Hence, this particle
has a lot of energy

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after it's been emitted.

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So we see lifetimes in the
range of 10 nanoseconds to 10

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to the 17 years
for some examples.

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So there's this huge
variation depending

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on where the alpha particle
sits in this potential.

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We can have a discussion
of the energetics involved.

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And we use our very same
formula for the binding energy.

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So you write this down
here, including your helium

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here, and then just
figuring out what

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are the contribution of
the individual terms.

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And since we observe
experimentally

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alpha decays only for heavy
particles, in this discussion

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here, we can assume that
Z is approximately 0.041

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times the mass number.

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And so the energy of the
emitted alpha particle for this

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to be able to occur
has to be positive.

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And so we find this to be
possible for A values starting

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from about 150.

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Experimentally, you
observe this to start

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happening at about 200.

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All right, the next thought we
want to discuss is beta decay.

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So this is shown in this
diagram here, where--

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starting from carbon-14
decays, for example--

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carbon-14, you will see
this in the next recitation,

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is very useful probe in
order to date living things,

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and date when they were
not living anymore.

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And you will discuss why and
how you can actually do this.

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But for now, carbon-14
can decay via beta decay.

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And what you find is
nitrogen, an anti-electron,

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and an electron.

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This is a beta decay,
or beta minus decay.

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And using our particle
physics discussion,

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we can easily understand this.

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The neutron is transformed
into a proton via electroweak

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processes with a W.
The electron comes out,

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the anti-neutrino comes out.

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And similarly, we can
look at carbon-10 here.

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Into boron is a
neutrino and a positron.

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And again here, we have
a W plus in the decay.

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So now, we can, again,
use our binding energy

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in order to understand this.

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So what we want to do here,
for constant mass numbers,

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you want to plot the binding
energy for the individual atoms

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or nuclei.

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And so if you do this for odd
A, those as where the pairing

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term doesn't contribute, you
find this nice quadratic term.

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And you can find beta decays in
each of those instances here.

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For A even, you have the
question whether or not

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Z is odd or N is odd--

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oh sorry, Z and N are
odd, or Z and N are even.

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So you have two
quadratic functions here.

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And you find the beta decay
between one and the other.

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And so that's interesting
you find those decays chains,

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based on where you
start in the chain,

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you have the possibility
to go back and forth.

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And because of the
even and odd pattern,

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the lifetime of the decay
can vary quite tremendously

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between those individual states.

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Last but not least,
election capture--

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if you have a very
massive nuclei and atom,

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and the electrons-- you know,
thinking about a cloud around

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this--

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some of the electrons can
come very, very close,

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and be captured into the nuclei.

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And you find this here.

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The time direction
goes up, proton

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captures via the
weak interaction.

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The electron becomes a
neutron and emits a neutrino.

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And an example is the electron
capture of krypton into boron.

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All right, so we start to get
some sort of understanding

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of nuclear decays.

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We find this Valley
of Stability here.

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We find, in a large
range for lower numbers

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of Z, beta decays.

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For higher numbers of Z,
we find beta plus decays.

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And for very heavy nuclei,
we find alpha decays.

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Proton decays, seen at
the very boundary here,

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and nuclear fission processes
where the nuclei spontaneously

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breaks up, we haven't
discussed in detail.

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But you can think about
them very similarly

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to the alpha decay.

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As you already kind
of probably saw

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from the discussion
of the beta decay,

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it's possible to have
rather long decay chains.

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So you start from
radioactive nuclei,

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which then decays, and
decays, and decays, and decays

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in those kind of chains.

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So this is two examples
here-- the thorium chain

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and the uranium chain--

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creating all kinds of
other new elements.

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And on the uranium chain,
it's very interesting

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to say uranium is
part of our core.

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If you build a house
and you build--

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if you build-- the
foundation is concrete,

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you probably have
some uranium in there,

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which then, in this decay
chain, generates radium.

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And therefore, if you build
a house with concrete,

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you want to have a measure to
get rid of the radium which

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is just floating around.

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All right, so this
is it for now.

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We continue the discussion with
more detailed understanding,

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or detailed discussion,
on how those decay

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processes are possible, and
what we can learn from them.