Now, if all this particle physics sounds a little bit like magic trick
mumbo-jumbo,, we'll become a little bit more comfortable with it, hopefully, as
we go along and use it. the point to be taken away, is that, you
don't just invent, oh, maybe this happens.
The good thing is that protons and neutrons are things that exist on earth
and upon which we can do experiments and people did and they could measure the
energies involved. The energies involved in nuclear physics
are higher and we understand that exactly why the energies involved in atomic
physics are essentially the electric attraction between a proton and an
electron at a distance of ten to the minus eight centimeters or ten to the
minus ten meter the size of an atom. The nuclear forces are approximately the
right strength, to hold together two protons.
The charge is the same as the charge of the electron and the proton only that the
signs different. And a distance a 100,000 times closer.
Remember the force decays like one over R squared, so this is a factor of ten to
the ten, in the magnitude of the force. The nuclear force, and the energies
involved, are therefore, much, much larger.
And this is, the source, of solar energy that became clear, and.
as I said before, E=mc squared, is really tangential to the entire exercise.
We'll deal with that, when that becomes important.
And then it is in the early decades of the twentieth century that physicists
finally figure out the mechanism that allows the sun to produce such copius
amounts of energy and, by extension, stars.
And one can imagine, the sense, in fact, I think it was [INAUDIBLE] who writes
about it. of looking up at the stars and being able
to say, and I understand why they shine. And that's an emotional high that we want
to share. So, the following animation will help us
follow the process by which the sun generates it's energy.
The process by which the sun generates its energy is called the pp chain, and
we'll animate it here in a minute. The end result is that one starts with
four protons, and through a sequence of collisions ends
up with a helium nucleus. The helium nucleus has a lot of binding
energy. This liberates energy.
That is what lights the sun. And understanding the process again, by
doing experiments on Earth. It took a long time.
We're going to follow through the stages for a minute.
So here we have up here at the top, two protons collliding.
most of the time when protons collide electrostatic repulsion just pushes them
apart. If they're moving fast enough and aim
directly enough right at each other then they crash into each other,
and they sometimes form this unstable bound state of two protons,
which is called helium 2. Now helium 2, as I said, is very
unstable. It decays very rapidly.
we don't find helium 2 anywhere, but once in a long while and this is the insight
of Hans Betten that really told us how the sun produces it's energy.
once in a long while, right here, while this ephemeral helium 2 nucleus
exists, one of the protons is able to beta decay
or positive beta decay, becoming a neutron and emitting a positron and an
electron neutrino. So, the proton is undergoing the decay
proton, goes to neutron plus positron, conserving
electric charge, and since this has negative electron number, it produces an
electron neutrino. This is an important decay for us.
Now this process cannot happen with just a free proton flying around, because the
neutron is more massive than the proton. That's why the decay of a neutron works
but the decay of a proton doesn't. The free proton, a hydrogen atom, is
stable, but in the context of a nucleus, this helium 2 nucleus, this process is
possible. The extra energy needed to create the
neutron is borrowed from the binding energy of deuterium,
hydrogen 2. So this is, this converts helium 2 to
hydrogen 2, because one of the protons was converted to a neutron, this is
deuterium. That's a bound state.
And so there's nuclear binding energy, and that provides the excess energy.
Now this positron goes off and, of course.
There's a sea of electrons floating around, finds an electron, annihilates,
and we get some extra energy. Now we have this nucleus of deuterium
flying around, and we need another hydrogen nucleus, another proton, to
crash into that, and that, if the conditions are just right, will form
helium three, another isotope of Helium. And we need that process to happen again,
the whole process, with all its stages, to happen again elsewhere.
And then we need these two helium 3 nuclei to crash into each other just
right. And if the collision is just right, then,
they merge, they form some unstable beryllium isotope or something.
And the net result is that they emit two protons and form a helium matter, or an
alpha particle. in the process we've had two separate
weak decays. And remember weak decays are rare.
So the stakes are wild. every, an average proton in the sun has
to wait 10 billion years before it's, it's turn to weakly decay.
And we've liberated energy at several stages.
these protons come off with kinetic energy.
These positrons go off and annihilate. There's some gamma rays emitted that
carry energy and this heats the surrounding.
This is how the sun produces energy. and it was the insight into this.
The understanding that this process could happen, that explain to us how stars
work. So this is
the way the sun produces energy. This reviews the exact same process we
just saw. The net result is that you, we had six
protons involved, but two were re-emitted.
So you started with four protons, you produced an alpha particle, two
positrons, two electron neutrinos, and in the process liberated nuclear binding
energy to the tune of 4.3 times ten to the minus twelve joules.
Note this is a factor of ten to the seventh, ten million more than was
available in Chemical interactions.
And so, chemical interactions would power the sun for 10,000 years at a power of
10,000,000. And you realize that if the sun converted
all of its hydrogen to helium, it would be able to let
produce energy at its current luminosity for 100 billion years.
Of course, as we'll see, the sun will never convert all of its hydrogen to
helium. But this at least is consistent with that
being the energy source of the sun and, indeed, that's what it is.
Now, why won't the sun convert all its hydrogen to helium?
Well, it's not that easy to generate fusion.
There are two crucial steps. One is, I need pairs of protons to get
close enough to each other to actually experience nuclear forces.
Remember, protons are positive. They don't like to come close to each
other. What that means is that they need to be
moving fast enough that their kinetic energy carries them close to each other
despite the electric repulsion. This requires temperatures of at least a
million, probably ten million kelvin. Only in the core of the sun are
temperatures this high. as we will see the sun is cooler out
there, so that the outer envelope of the sun does not produce, Helium in, in large
quantities. There's no fusion going on except in the
interior of the sun where the temperatures are high.
Moreover, we need these protons to crash into each other many times because, on
average, most of the time when they crash into each other nothing happens.
And so we need very high density, again, the density obtaining in the core of the
sun. We'll talk about the density, when we
review our models. But only in the core of the sun, only
about 10% of the sun, is available for converting, to helium.
That reduces our estimate from 100 billion years to 10 billion years, which
is roughly the lifetime of the sun. So maybe we found something.
And then, the other bottleneck is that the rate of fusion is restricted by the
fact that 2 in fact, protons must beta decay before helium 2 breaks up and this
slows down the process. And that is what prevents the sun from
essentially blowing itself to smithereens.
The reaction rates inside the sun are controlled,
and we'll see how it maintains a stable equilibrium.