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MICHAEL SHORT: So today, I wanted

to give you some context for why we're learning about all

the neutron stuff and go over all the reactor types

that, until this year, the first time you learned

about the non-light water reactors at MIT

was once you left MIT.

I remember that as an undergrad as well.

The only exposure we had to non-light water reactors

is in our design course, because we decided to design one.

So I wanted to show you guys all the different types of reactors

that are out there, how they work,

and start generating and marinating

in all the different variables and nomenclature

that we'll use to develop the neutron transport and neutron

diffusion equations.

The nice part is now, until quiz two,

you can pretty much forget about the concept of charge.

So 8.02 can go back on the shelf,

because every interaction we do here is neutral,

charge neutral.

There'll be radioactive decays that are not the case.

But everything neutron is neutral.

It doesn't mean it's going to be simple.

It's just going to be different.

But in the meantime, today is not

going to be particularly intense,

but I do want to show you where we're going.

And this goes with the pedagogical switch

that we made in this department starting this year.

And you guys are the first trial of this.

We're switching to context first and theory second.

I personally find it much more interesting

to study the theory of something for which I

know the application exists.

Who here would agree?

Just about actually everybody.

OK.

Yeah.

That's what I thought too.

So in the end, we had arguments amongst the faculty about,

well, you have to learn the theory

to understand the application.

And that works really well when you say it behind the closed

office door by yourself.

But the fact is, I'm in it for--

yeah.

I'm in it for maximum subject matter retention,

so in whatever order that works the best.

And sounds like, for you guys, this works the best.

That's what we're doing with the whole undergrad curriculum, not

just this class.

So let's launch into all the different methods of making

nuclear power, both fission and fusion,

and to switch gears since we're dealing with neutrons.

I don't know what happened with the-- oh, there we go.

The idea here is that neutrons hit things

like uranium and plutonium, the fissile

isotopes that you guys saw on the exam,

and caused the release of other neutrons.

And as we come up with these variables,

I'm going to start laying them out here.

It might take more than a board to fill them all.

And I'll warn you ahead of time, this

is the only time in this course that we're

going to have V and nu, the Greek letter nu,

on the board at the same time.

And I'm going to make it really obvious which one is nu

and which one is V.

So this parameter that describes how many neutrons come out

from each fission reaction we refer to as nu,

or the average number you'll see in the data tables as nu bar.

And so as we come up with these sorts of things,

I will start going over them.

And the idea here is that each uranium-235, or plutonium,

or whatever nucleus begets two to three neutrons,

the exact number for which is still under a hot debate,

and I don't think it actually matters,

will make a couple of fission products that take away

most of the heat of the nuclear reaction.

And I just want to stop there, even though you know there's

going to be a chain reaction.

And that's what makes nuclear power happen.

And we can go over the timeline of what actually happens

in fission and what kind of a nuclear reaction it really is.

So in this case, this is a reaction

where a neutron is heading towards,

this time we're actually going to give it

a label, a uranium-235 nucleus.

And it very temporarily, like I showed you yesterday,

forms a compound nucleus, some sort

of large excited nucleus that lasts for about 10

to the minus 14 seconds.

So it doesn't instantly fizz apart.

There's actually a neutron absorption event,

some sort of nuclear instability, at which point

your two fission products break off.

Notice, you don't have-- let's call them fission product one

and fission product two.

Notice, you don't quite have any neutrons yet.

Neutron production is not instantaneous for the following

reason.

If you remember back to nuclear stability, when we plotted,

let's say, I think that was maybe Z and this was N.

And I think this was a homework problem.

And you had to come up with some sort of curve

of best fit for the most stable combination of NZ

for a nucleus.

It was not a straight line.

It was something on the order of like N equals--

what is it?

--1.0055Z plus some constant, something with a rather small

slope.

Well, if you have a heavy nucleus, like uranium-235,

and you split it apart evenly, let's just

pretend it splits evenly for now,

you're kind of splitting that nucleus

along a rather unstable line.

And, as you saw in the semi-empirical mass formula,

a little bit of instability goes a really long way

towards making the nucleus extremely unstable.

So let's say you'd make a couple of fission products

that just cleaved that nucleus with the same proportion

of protons and neutrons.

How would they decay?

Or how can they decay?

There's a couple different ways.

What do you guys think?

AUDIENCE: It can emit neutrons.

MICHAEL SHORT: It can emit neutrons

if it's really unstable, at which point

it would just go down a neutron number.

Or how else could it decay?

AUDIENCE: Alpha decay.

MICHAEL SHORT: Alpha decay.

Let's see, yeah, a lot of those will--

the heavier ones tend to do alpha decay.

What would it do at alpha decay?

For alpha, I guess it will be going that direction, right?

You know what?

I'm not going to rule that out yet.

So let's go with that.

How else could they decay?

AUDIENCE: Through beta decay.

MICHAEL SHORT: Through beta decay,

let's say in that direction.

Pretty much all these happen, just

not necessarily in this order.

When you have a really, really asymmetric nucleus,

a lot of these fission products will

emit neutrons almost instantaneously

in the realm of like 10 to the minus 17 seconds,

some incredibly short timeline.

You will start to decay downwards a little bit.

But you're not quite at the stability

line, which is why a lot of the fission products then go on.

And they deposit their kinetic energy

by bouncing around the different atoms in material

creating heat.

But a lot of them will also send off betas or gammas.

And it may take 10 to the minus 13 seconds for them

to whatever the half-life of that particular isotope is.

And after around, let's say, 10 to the minus 10 to 10

to the minus 6 seconds, depending

on the isotope in the medium, those two fission products

will stop.

And let's just say that they stop there.

So the whole process of fission, it's actually

quite a compound process.

First, the neutron is absorbed, forming a compound nucleus.

Then it splits apart.

Then those individual fission products

undergo whatever decays suit them best.

And that's the source of the neutrons in fission.

Sometimes one of those fission products

might be particularly unstable.

And it might send off two neutrons.

In other cases, though I don't know of one

off the top my head, it might be none.

But this is the whole timeline of events in fission

and the justification for why this happens straight

from the first month of 22.01.

And I wanted to pull up some of the nuclear data

so you can see what these values tend to look like and also

where to find them.

I'm going to do that screen cloning thing again.

There we go.

So I've already pre-pulled up the JANIS library.

I've already clicked on uranium-235.

Thanks to you guys, I have all the data now on my shirt

so you can see a little better.

I also have it on the screen.

So let's look at this value right

here, nu bar total, neutron production.

And I'll make it bigger so it's easier to see.

Did I click on the right one?

Yeah.

So take a look at that.

The total number of neutrons produced during U-235,

for most energies it's hovering around the 2.4 or so.

There's been arguments about whether it's 2.43 or 2.44.

And that's a linear scale.

That's not very helpful.

Let's go to a logarithmic scale.

That's more like what I'm used to seeing.

Most of the fission happens for U-235 in the thermal region,

in the region where the neutrons are at values, let's say,

the cutoff is usually about one electron volt or lower

in average energy.

And nu bar is fantastically constant at that level.

Then as you go up and up in energy,

you start to make more and more neutrons.

Why do you guys think that would be the case?

What are you doing to that compound nucleus

as you increase the incoming neutron energy?

AUDIENCE: It's going to have more energy.

MICHAEL SHORT: It's going to have more energy itself.

You might excite other nuclear states

that can then lead to other sorts of decays

or other neutron emission.

So to me, that's the reason why, once you hit about 1 MeV,

you can start to see a lot more neutrons being given off.

The reason we usually treat this as a constant,

notice I haven't given it an energy dependence,

is because most of the fission that happens

is at thermal energies.

For that, I want to show you the fission cross section.

There are a lot of cross sections.

And it's probably going to be on a different graph,

because it's in different units.

And this gives you a rough measure

per atom, what's the probability of fission

happening as a function of incoming neutron energy?

At those high energies, you have relatively low cross sections,

or low probabilities, of fission happening.

Then there's this crazy resonance region that

looks like a sideways mustache.

But then as you get down to the lower energy levels,

it gets much more, in fact, exponentially more,

likely that fission will happen.

So almost all the fissioning in a light water reactor,

or any sort of other thermal reactor,

happens at thermal energies.