So, what we discovered is that the power of the sun requires a source of energy
that we have not discussed yet. It is not electromagnet energy in the
internal structure of an atom. It is not gravitational energy.
Where else can you mine potential energy? This was a puzzle until the twentieth
Century and the answer, of course, is nuclear energy and so we'll have to learn
a little bit about the structure of the nucleus and we talked, when we mentioned
the nucleus and it's contruction out of Protons that are positive and neutrons
that are neutral. That there's a big puzzle.
That's a collection of positive charge without any negative charge.
And there's a very strong electrostatic repulsion between all these charges.
Remember electric forces like gravitational forces decay with distance
like one over R squared. These are the forces at distances of ten
to the minus fifteen meters. The size of a nucleus,
these protons are very close up against each other.
There's a huge repulsive force between them but nuclei I don't fall apart.
Something must hold them together. So it's natural to conjuncture and later
to verify the existence of a very strong attractive force, that binds the nucleons
to each other. And over comes this electrostatic
repulsion. How strong is the force?
Well, strong enough to over come the electrostatic repulsion between protons
and the nucleus. And that's a very strong force indeed.
on the other hand, we know that this force cannot extend beyond the confines
of the nucleus too far because if it did then the the nuclei of two neighboring
atoms would attract each other and collapse on top of each other and so
unlike gravitation and electromagnetic ray interactions that are long range
interactions, volumes interact, every parts of the universe attracts every
other part gravitationally the nuclear force is a short range force that ranges
larger than the size of the nucleus, it effectively decreases to zero.
and so there's no interaction between neighboring nuclei.
We don't have a problem. We have this very strong force.
And this brings up the idea, that maybe just as rearranging electrons lead to the
liberation of electrostatic potential energy.
Maybe rearranging nucleons inside a nucleus can liberate nuclear energy.
And we've learned a lot about nuclear energy.
the way, they have parameterized the amount of potential energy liberated at
creating a nucleus similar to the way we computed the gravitational energy
liberated in creating the song. Is to say imagine starting with a bunch
of nucleons, put them together. Of course, you'll have to input a lot of
energy to get them close to each other because at large distances the
electrostatic repulsion will dominate. But once they get close there's a strong
attractive force. They'll crash into each other and
liberate a lot of energy producing the nucleus.
The question we want to ask is if we have a whole bunch of nucleons, what's the
most efficient way to pack them together. To do that, we measure the total
liberated energy. nuclear minus electrostatic.
The total difference, the total energy gained by constructing nuclei out of nu,
a bunch of nucleons, and that's, we want to do that energy per nucleon, so that if
you have a, some fixed number of nucleons what's the most efficient way to pack
them. And one would think that because we have
this very strong attractive interaction, that certainly a hydrogen atom is not a
good way, to produce efficient packing. A hydrogen atom is a proton it's not
interacting with anybody it hasn't, liberated any potential energy.
but one would think that very heavy elements like uranium.
Big nuclei, where there is a lot of nuclear interactions would be the ones
that liberate the most energy and what this plot shows us, we have here atomic
number or number of nucleons running mass number running to the right and the
average energy liberated per nucleon going up.
And we see that the most stable configuration is not a bunch of uranium
nuclei, but a bunch as many as you have nucleons for of iron nuclei, the sort of
intermediate range, intermediate size nucleus is the most efficient packing.
And the explanation for this is an important one, the explanation for this
is very close to the discussion we had of the cross over between short range
chemical forces that are short range but are very strong and enact on the surface
and ling range gravitational forces at about a size of kilometer in the solar
system. A similar thing happens with nuclei.
What goes on is that if you have a great big uranium nucleus, then a proton that
is located on this side of the nucleus and a proton on that side of the nucleus
basically are too far apart to really interact through the strong force, so
they do not attract each other. Remember, the attraction falls to O.
in some sense each of these protons on the edge of a very large uranium nucleus.
Interact only with his neighbors what that means on the other hand the electric
forces between these protons decay only as the distance squared those are long
range forces so these guys definitely do repel each other through electro static
forces. And therefore the sort of efficient way
to arrange the energy just as we saw this is really analogous to the discussion
what holds a mountain together is to cleave this nucleus in two, perhaps.
we now have, lost all the nuclear energy that was involved in the bonds along the
place we cut. But when these two positive sub-nuclei
are created, they are two positive charges very near
each other. They repel with the great electrostatic
repulsion. That produces a lot of energy as they
accelerate away. And the net result is a gain of energy
and so what we see indeed is that the most efficient way to pack is iron and
nuclei. Heavier than iron are not efficient
packing, and by rearranging their nucleons, they can re-liberate energy
well known case is the case of fussion. This is the case exactly, where this
nucleus of californium breaks into cadmium and tin and some debris, some
extra neutrons flying around. And in the process, liberates essentially
the electrostatic repulsion that, once these two nuclei are free, they are
repelled and proceed at great energy to move away from each other.
Another popular mode of breaking up, if you're a heavy nucleus, is, we see here,
rutherfordium, emitting, an alpha particle.
Remember, an alpha particle is a nucleus of helium, two protons and two neutrons,
and the rutherfordium decays to seaborgium.
so both of those modes occur in heavy nuclei.
They liberate a lot of energy. This was the radioactive energy that
powred heated up the, the interior of Earth.
Remember that was the 89 watts per liter squared or 87 watts per liter squared
that were bubbling up from nuclear reactions in the core but
it's not going to be enough to power the sun, because in the sun we don't have
rutherfordium or californium or uranium. We have hydrogen and hydrogen remember is
way on the other side of the divide. a hydrogen atom nucleus is just a proton.
It's not bound to anything. Of course if we could make bound states
of protons, maybe we could gain. But there are no bound states of protons
only. helium 2 is not a stable nucleus.
If you put two protons together, they may bind for a short time but the
electrostatic repulsion will break that nucleus apart very quickly.
And so the first really stable nucleus and it's a very stable nucleus indeed, is
helium 4, that alpha particle. If you can make a helium nucleus out of
the hydrogen, you will have gained all this energy.
that's very good. The problem is that to make a helium
nucleus you need two protons, two neutrons.
The sun is full of protons but there's no neutrons essential where do you get the
neutrons we can't using the srong force, convert photons to neutrons but we know
that somebody can. And the reason we know that somebody can
is because we talked about beta decay of nuclei and we see here some of the decay
of oxygen to fluorine. And what's going on here is, since this
is a positive beta decay, you can look at the atomic number and see that in fact,
one of the protons in the fluorine is being converted to a neutron.
So, fluorine is decaying to oxygen with the emission of a positron and there's
also the inverse reaction, in which here carbon-14 converts one of its neutrons to
a proton becomes nitrogen-14. And emits an electron and so we know
about these decays. In fact, the free neutron decays to a
proton within about fifteen or sixteen minutes.
And so there is this thing called the weak nuclear force, probably better
called the weak interaction, which mediates these decays.
It is possible for one elementary particle to be converted to another
elementary particle. And this is a very confusing thing.
So we have to sort of stop. We're not going to discuss the physics of
the weak interactions, fascinating though it is, in detail.
But we need to have, set some ground rules.
So what is this kind of force? Magically convert one particle into each
other. We understand that a force can cause a
rearrangement of the constituance of a particle.
So one could image maybe that a neutron is really just a very, very tiny hydrogen
atom. There already were a proton and an
electron inside the neutron and then they just fell apart.
The answer is no, it's a very bad idea to think of a neutron as a hydrogen atom.
there was no proton inside the neutron. The neutron honestly decayed to a proton
and an electron. and yes the weaker interactions can
change one particle to each, to another. But, there are going to be some rules
that we need to understand. And then there was this third object
there. it's called an anti electron neutrino.
So the Greek letter nu stands for neutrino.
The bar says anti, and the subscript E makes it an electron neutrino.
And what all that means, we'll have to understand.
so lets set the rules. What can, interactions do, what can they
not do, they cannot do anything they want.
The rules, basically it turns out, are restricted to a good old fashion
conservation loss, that's why we made such a big deal about it, when we were
learning. Now,
there's a tricky business here, we're getting into the, stepping into the
beginnings of relativity, where you allow the particles to decay.
We will spend almost an entire week understanding relativity, later in the
class. for now, I'll just say the words we had
in Utonian physics of conservation of energy, and of course, conservation of
mass in relativistic theories, those are
combined in the conservation of the sum of energy and mass.
Mass is a form of energy. There's the famous conversion ratio
square of the speed of light. We will talk about this.
it is not that relevant to the processes that take place in the sun despite what
you may have heard. And so when it's important we will talk
about relativistic physics. But mass and energy are conserved.
momentum is conserved just as it always was.
angular momentum is conserved if you are dealing with elementary particles you
need to remember that elementary particles carry intrinsic angular
momentum it's called spin. You could imagine that a proton always
spins and there's a. This, the rotation.
Is at a constant rate and points in some particular direction.
And, then there are the other kinds of conserved quantities, that are not to do
with motion. We talked about electric charge.
Electric charges conserve. No matter what processes go on
the total electric charge in any region of the universe doesn't change unless a
charge is flowing in our out. And then, there's a new one that we
discover as we start to develop particle mechanics.
And that is, Property called electron number.
An electron carries electron number. A proton obviously has zero electron
number, as does a neutron. An electron number will see its
conserved, and this restricts what can happen in interactions involving
electrons. And the interactions we are going to
study. Weak interactions.
What make them weak is that they're not really a force.
They are things that happen. the strength of the interaction
essentially measures, how frequently a reaction will happen.
Weak interactions. Occur very slowly, they are rare.
One out of many, many attempts will generate a reaction.
The example is the neutron that survives as a free particle for fifteen minutes.
By particle standards, that's a very long time.
So, who are the players? Well, here's a list, we're into particle
physics now, of all of the particles we have or should be discussing.
and they include well, I'll start at the bottom.
We have our friend Photon denoted by gamma, its gamma rays
and I have written the quantities of their conserved charges, of course their
momenta and energy depends which way they are moving but a photon is a neutral
particle, it carries no electric charge, it is not an electron carrier, zero
electron number and then here we have our proton, neutron and electron with their
known electric charges and with the fact that the electron carries a charge not
carried by any of the others. And then.
There is this other interesting object called the neutrino.
And the neutrino was discovered because when neutrons decayed.
Studying the conservation of energy mass it was discovered there was missing
energy. it was Enrico Fermi's idea, I believe, to
think that maybe there was a neutral particle.
It doesn't interact with anything. It is not detected by any of our
detectors. Sails right through the detectors.
And produces and carries off our remaining energy since it was
electrically neutral and didn't interact with anything, it was called a neutrino.
We now know that these particles exist and indeed are part of this.
And, in fact an electron neutrino carries a electron charge, electron number one.
Travis will become important in what follows, because the weak interactions of
electrons and protons conserve electron number.
What that means, in particular, is that when a reaction occurs we need to balance
all of these quantum numbers. They're all conserved so, for example,
the decay of a neutron into a proton plus an electron conserves electric charge.
Because the neutron is neutral. And the total electric charge of the
products is zero. But it does not conserve electron number.
Electron number was magically created. And indeed this means that if you have a
neutrino and an electron. And they react, that can produce a proton
and an electron. Now, I was about to write something on
the right hand side, because of course a free neutron decays without anything
hitting it. this brings up the fact that there's this
whole bottom line of the table. And it turns out to be another important
principal of physics, that for every particle there is an antiparticle.
An antiparticle is not something mystical or mysterious or a particle moving
backward. It's simply another kind of particle.
Which has the same mass as the original, and all the opposite charges.
So, for example, there is an antiproton, which has the same mass as a proton but
is negatively charged. And of course, carries the same zero
electron charge. There's an anti-neutrino, which is
neutral. There are anti electrons, they're called
positrons. That was what was emitted in positive
beta decay. They carry the same mass as an electron.
But electric charge positive and negative electron number charge.
And the neutrino has its own anti-particle.
And the anti-electron neutrino is neutral like the electron neutrino but has the
opposite sign of electron charge. And so, the decay can proceed if an empty
electron neutrino is produced over here. This conserves all the charges.
Now these neutrini are very hard to understand.
They interact only through this weak interaction which as I said, makes for
rare events. So mostly, mostly, they don't interact at
all. In the time I've been talking about this
slide, some millions of neutrinos have penetrated each and every of your
fingernails. You have not felt them because they don't
interact with anything. In fact, the great majority of them will
sail right through the Earth and come out the other end, and keep going through the
universe. they carry very little mass if any.
In fact for a long time they were thought to be massless.
And they don't interact which makes detecting them a very difficult
proposition as we will see. But they're important because they
balance the charges in weak decays. And as we'll see they have some other
important role in our story. I didn't bring them up just to tell you
about particle decay and there's a the property that if you take a particle and
an antiparticle so you have an electron and a positatron.
That combination has total charge zero with respect to all the concerned charges
except for energy momentum. And so if you bring an electron or
positron near each other, and they're addressed, there's just energy.
That's in their mass, and that can indeed be converted to straight radiation.
The electron and positron annihilate, and a burst of gamma radiation flies off in
both directions and the energy is essentially the mass of the disappearing
electrons. This is a process that does occur and you
will have to understand how that happens, as I said, when we talk about relativity
for now, we recognize that if you have an electron and a positron, you can liberate
energy. We'll take all this information, and see
what it tells us about, how the sun works.