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Nuclear Fusion
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From the course by Princeton University
Imagining Other Earths
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From the lesson
Stellar Evolution
Like planets, the structure of stars are shaped by the balance between gravity and pressure. Nuclear fusion, the energy source at the star’s interior, converts Hydrogen to heavier elements. This lecture introduces these concepts and shows how nuclear burning drives the evolution of stars.
Meet the Instructors
David SpergelCharles Young Professor of Astronomy on the Class of 1897 Foundation and Chair
Department of Astrophysics
Welcome back.
You should have estimated that the age of the
sun would have been only a million years or so.
Not the billion years we observe, if it's only source was gravitational energy.
This implies there's a new energy source that powers the sun.
This was something that wasn't understood
by 19th century physicists and astronomers.
It was only in the 20th century that we start to understand what powers stars.
And we started to understand a more complete picture of the forces of nature.
Physicists today talk about four fundamental forces.
Gravity, which we've talked a lot about.
Electromagnetism, how electrons and protons are attracted to each
other through electric fields, the affects of magnetic fields.
These ideas were worked out largely by Maxwell
in the 19th century, the ideas of electromagnetism.
But then in the 20th century physicists realized there
were two other fundamental forces the weak nuclear force which
as we'll see is involved with radioactivity changing neutrons into
protons and the strong nuclear force which spines nuclei together.
Most of the course we're going to focus on these two forces.
But today, because we want to talk about what
powers stars, we're going to focus on the nuclear force.
So let's go back to the Periodic Table of Elements and remember that,
all the elements we see in nature are made of protons, neutrons, and electrons.
And they're the basic building blocks.
Of all the atoms we see.
And let's remind ourselves of the structure of an atom.
An atom consists of a sea of electrons orbiting around
a much denser nucleus made up of protons and neutrons.
And a typical nucleus has both significant numbers of protons and neutrons.
Now here are the most common, or some of
the most common and important things we want to talk about.
Hydrogen is made of a single proton typically,
helium two protons and two neutrons bound together.
Carbon, six protons and six neutrons.
Nitrogen seven and seven, and so on.
Now there are two important forces acting on the nucleus of an atom.
The nuclear force wants to bind things together.
It attracts the protons and neutrons, and the more protons and
neutrons you have, The stronger the nuclear force, binds the nucleus together.
This nuclear force, is counteracted by electro magnetism.
The more charges I have, positive charges repel each other.
And in this nucleus I brought together,
say in a carbon nucleus, six positive charges.
And those six positive charges, if
there was only electromagnetism, would fly apart.
And the structure of a nucleus
is basically determined by the balance between
the nuclear force binding it together
and the electromagnetic force driving it apart.
That actually explains this trend we see.
As we get to a heavier nuclear like iron,
you'll notice that it has more neutrons than protons.
That's because you can add neutrons, make the nucleus bigger, more tightly and hence
more tightly bound, without paying the price
of having electro-magnetism try to drive it apart.
Now, if it were not for that balance you
would always end up having the same number of protons
and neutrons because as far as nuclear force is concerned,
this is the most stable, the most tightly bound state.
By the time you get up to uranium, you'll find you've
got 92 protons, and over a, and many more a 146 neutrons.
In, uranium 238.
And that large number of neutrons ends up being the most close to stable situation.
It's actually not quite stable.
Because you've got this balance between electro-magnetism and nuclear force.
We could quantify what's going on with the
nuclear force by measuring the binding energy per nucleon.
Hydrogen is here in this plot.
When we look at helium we brought together two protons and two neutrons.
They're more tightly bound than they were in free space.
Because of that the binding energy proneutron, nucleons.
This is a more tight, helium is more tightly bound than hydrogen.
Carbon is even more tightly bound.
Then oxygen.
As we keep adding nucleons, the material gets more and more tightly bound,
until we reach iron, which is the most tightly bound nucelon around.
Once we move beyond iron, we start paying a price.
We start accumulating so many positive charges in the nucleus.
As we march toward uranium, that uranium is less tightly bound than iron.
There are going to be two important processes.
Driven by this binding energy.
If you have light nuclei, you can gain energy by fusing them towards iron.
If you have heavy nuclei, you can gain energy by having
them split up into pieces and having fission drive them towards iron.
So iron sort of the bottom of the hill.
Left to itself, that's the form in which nuclear matter is most tightly bound.
It's like happiest, it's where it would like to be.
And a lot of the physics in stars is driven by the energy available
in transforming hydrogen, to helium, to carbon, to oxygen, towards iron.
I'll also note these little bumps here, mean that certain odd
nuclei, things like lithium, and beryllium, and boron,
are less tightly bound than a helium or carbon.
And that's the main reason, why these elements are rarer.
And in fact if you work through how nuclear forces behave, nuclear
force, when you have a situation where you have an even number of protons and
an even number of neutrons, that state is typically, particularly in this region
here, more tightly bound than the cases with odd numbers of protons and neutrons.
So if you look at the periodic table, you find the materials made up of even numbers
- carbon, oxygen, silicon, sulphur, magnesium, neon -
Are more common than things like scadnium with odd nuclear numbers.
So these are the two processes we're going to, want to look into.
Let's begin by talking mostly about fusion.
Because fusion's going to be what powers stars.
The idea in fusion is we're going to transform.
Four hydrogens into a helium and release energy.
Now the way that actually happens in the
star, is the star is so hot, temperatures of
about 14 million degrees, that the hydrogen has been
disassociated into a free proton and a free electron.
And what happens in the star, is
four protons Get transformed to a helium nucleus.
So that's four protons going to two protons and two neutrons.
When that happens this is charge four, so to
keep things balance we're going to throw off a positron.
So we have charged four on this side,
energy in the form of gamma rays and neutrinos.
And this process releases a lot of energy, roughly speaking it releases about,
doesn't sound like much, but ten to the minus 12 joules for every hydrogen atom.
And there's a lot of hydrogen atoms in the sun.
So there's a lot of energy available.
Now, I want you to notice a couple elements here.
In order to do this, we have to transform protons into neutrons.
That involves what we call the weak interaction.
And that weak nuclear interaction is weak.
So it's pretty hard to make this happen.
So, we're going to have to bring the
nucleons very close together to make this happen.
And to do that we're going to have to overcome the electromagnetic repulsion.
Now the way this proceeds in stars is typically through multiple steps.
We bring two hydrons together to form duterium a hydrogen and a neutron.
Duterium together often to form helium three,
and then finally end up with helium four.
And as we go through the pull process, this, what's called PP chain, this is one
of the PP chains, converts four hydrogens Ultimately
to four helium and in doing so releases energy.
Fusion needs to be distinguished from fission.
And nuclear fusion by the way is an energy
source which is relatively speaking a very clean energy source.
From nuclear fission, today when people talk about nuclear power
plants they're talking about plants that are powered by fission.
Not by fusion.
Fusion is a very promising energy source because it's
potentially very clean and hydrogen is so readily available.
But we've not yet realized this in laboratories.
There's a big international effort, most noticeably at the international lab.
In France called Iter to make fusion happen.
Fission is something we've been doing in nuclear power plants for a very long time.
And it's physically a very different process.
Fusion is bringing light nuclei together, fission is tearing heavy nuclei apart.
So one of the most,
Famous examples of fission is radioactive decay, starting with uranium,
and working its way finally to the stable state of lead.
And in doing so, uranium keeps throwing off particles.
And there's two prominent forms of decay.
Alpha particles which are helium nuclei and beta particles
which are electrons or the electron's anti-particle the positron.
So when these decays happen, neutrons decay
typically into protons, electrons, and throw off neutrinos.
So uranium itself lives pretty long.
The typical uranium nucleus lives over four billion years before it decays.
But once that happens it sets off a chain
where uranium decays into thorium, then working its way down
the periodic table, producing along the way things like
radon, which is, for those of us who live here
in a place like New Jersey, which has some
underground uranium, something we worry about getting into our
house as a source of radioactive activity was the
decaying uranium produces things like radon and eventually works its
way to stable led but along the way it
emits a lot of radioactive particles and these are of
significant concern potentially if you have some in your house
because its a source potentially of things like cancer.
Stars are not powered by fission, they're powered by fusion.
They're powered by converting four protons into helium.
And not only is the sun powered this way, this
is the dominant energy source for all main sequence stars.
They're all burning hydrogen to helium.
And giving off energy.
Now, in order to make this happen we're going to have
to, overcome the fact that two protons don't like to come together.
That means we're going to need pretty high densities and high temperatures.
So this nuclear fusion process only happens in the center of stars.
So we look at a model of the sun, you should think
of it as having a relatively cold exterior, of only about 5800 degrees.
And this very hot interior of 14 million
degrees where all the nuclear fusion takes place.
Now, the light we see from the sun.
It's ultimate energy source was in the center, but as we know it already.
It took thousands of years for that light to diffuse out to the outside.
So by the time it gets to the outside the energy of the typical photon we see.
It's not the high x-ray energies associated
with the center, but the optical light, typically
yellow light, that we see from the outside when we look out and see the sun.
We can probe directly to the sun's
center though, because when this nuclear fusion takes
place It produces not only these high energy
X and gamma rays, it also produces neutrinos.
And these neutrinos, as they head towards us, can be detected.
These neutrinos can travel directly out of the center of the sun,
and as they travel to us they can be detected in big detectors.
And here's a famous underground detector
in Canada called the Sudbury Neutrino experiment.
And deep down in an underground mine where
we get away from all other sources of radiation.
Neutrino's are [UNKNOWN] so weakly than can travel through the Earth.
Scientists have been detecting neutrinos from the sun,
and they've done this in several different experiments.
And one of the things we've learned from these experiments is that the sun
is behaving as our models predict, very
high temperatures of about 14 million degrees.
And in the center of the sun we are seeing nuclear fusion taking place.
Now as an aside it turned out that, the neutrino
was a little more complicated than we thought, and one
of the things that we learned from the solar neutrino
experiments, is that neutrinos have masses and different flavors that oscillate.
There's very rich physics there, but it's
not really the center of our conversation today.
But if you'd like to learn more about neutrinos, go to the websites
of one of these neutrino experiments and they offer a lot more information.
Right.
Stars like our sun burn hydrogen
to helium, but eventually they're going to exhaust
all the helium, sorry, eventually they're going to exhaust all the hydrogen.
Once they've exhausted the hydrogen, they need a new fuel.
The next fuel that's available is helium.
Remember our binding chart.
You can get energy out of burning helium to carve it.
And that's the next step.
Once you've burned all your helium to carbon
You then start marching through the periodic table.
You burn carbon to oxygen, oxygen to neon, neon
to magnesium, magnesium to silicon, ultimately to iron.
And massive stars are powered by burning
their way through the periodic table to iron.
Now that we've discussed nuclear fusion you can now answer Kelvin's question.
I'd like you to make an estimate of the lifetime of the sun.
For this estimate, we'll be generous.
We'll let the sun burn all the hydrogen that's available, it
actually doesn't do that but that makes the estimate easier to do.
Take the sun's mass, work out the number of hydrogen nuclei in the sun,
take the energy available per nucleon and work out how much energy is available.
In the sun, divide by the luminosity and you should be able
to figure out how long the sun can burn at its current rate.
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