Video Transcript
In this video, our topic is the
conservation of baryon number. Baryon number is a property that’s
possessed by all subatomic particles. In this lesson, we’ll learn how to
figure out that number for a given particle and we’ll also see how it’s conserved in
nuclear interactions.
Even though this term baryon number
may be unfamiliar to us, we do know a bit about what baryons are. This is a particle that’s made up
of exactly three quarks. And we can remember that there are
six quarks — up, down; charm, strange; and top, bottom — and also that each type of
quark has a corresponding antiquark. We bring up quarks and their
antiparticles because the baryon number of any particle, including a baryon, is
determined by the quarks that compose it.
Now, as we said, baryon number is a
property of particles. In that way, it’s similar to
electric charge. Every particle has some electric
charge, even if it’s zero, and it’s the same with baryon number. For every quark, their baryon
number is positive one-third, while every antiquark has a baryon number of negative
one-third.
Knowing this, we can figure out the
baryon number of any particle, whether it’s a quark or not, by knowing what quarks
make it up. To get the baryon number of some
composite particle made up of more than one quark or one antiquark, we add together
the baryon numbers of the quarks and antiquarks that comprise it.
Here’s an example. Say that we’re working with a
neutron. And a neutron is a particle that’s
made up of an up quark and two down quarks. To solve for the baryon number of a
neutron then, we add together the baryon numbers of the quarks in it. Since all the particles that make
up a neutron are quarks rather than antiquarks, they all have a baryon number of
positive one-third. So for each of the three quarks, we
add together its number of one-third and get a total of one. So this is the baryon number of a
neutron.
And notice how this process is
similar to solving for the overall charge of a composite particle. It works by the same method: add
together the baryon number of each of the parts of a particle to get its total
baryon number.
Now, we mentioned earlier that this
name, baryon number, refers specifically to a class of particles called baryons. A baryon is made of exactly three
quarks, so we see that a neutron is an example of this. Since the baryon number of an
individual quark is positive one-third and every baryon is made of three quarks, we
can conclude that every baryon has a baryon number of exactly one. We know though that there are other
classes of particles besides baryons. Baryons are just one subclass of a
group of composite particles called hadrons.
Hadrons are made up of more than
one quark. And they include a group of
particles called mesons. Mesons differ from baryons in that
they’re comprised of one quark and one antiquark. Knowing what we know about the
baryon number of quarks and antiquarks, what would be the baryon number of
mesons?
Like we said, a meson is made of a
quark and an antiquark. And here is an example of that. The quark, in this case a charm
quark, has a baryon number of positive one-third, while the antiquark, in this case
a down antiquark, has a baryon number of negative one-third. Adding these together for the
particle overall, we get a total baryon number of zero. And indeed this is true for all
mesons since they’re all made of one quark and one antiquark.
For any hadron then, any particle
made up of multiple quarks, we can solve for its baryon number by adding together
the baryon numbers of its constituent quarks and antiquarks. But then not all particles are made
up of quarks. For example, there’s a particle
class called leptons. These include the electron, the
muon, the tauon, and a number of neutrinos, all of which are elementary particles
not made of quarks. That last part, that leptons are
not made of quarks, is the key to understanding their baryon number. The only reason a particle would
have a nonzero baryon number is if it’s made of quarks or antiquarks. So leptons, having no quarks in
them, all have a baryon number of zero.
Earlier, we mentioned that baryon
number, just like electric charge, is a property that all particles possess. If we think about why a given
particle or object has a net electric charge, we know that it comes down to
fundamental positive and negative charges. When we’re talking about baryon
number, we can think of quarks and antiquarks in the same way. These are the basic units, we could
say, of baryon number. So just as any particle that didn’t
have any positive or negative charges would have zero net charge, so any particle
that has no quarks or antiquarks will have a baryon number of zero.
Now, there’s even another
similarity between baryon number and electric charge. To see what that is, let’s clear a
bit of space on screen. And now we’ll write out a fairly
common nuclear decay equation. In this equation, we have a
hydrogen three nucleus, that is, a nucleus with one proton and two neutrons, going
through the process of beta decay so that it becomes a helium three nucleus plus an
electron plus a particle called an electron antineutrino.
Now, we know that in any nuclear
equation that’s valid, electric charge needs to be conserved. That means the total electric
charge on one side must equal that on the other. If we look at the left-hand side of
this equation, we see that the total charge here for a helium three nucleus is
positive one. That’s due to the one proton in the
nucleus. Then, if we look at the product
side, we see we now have a helium three nucleus. So this is a nucleus that has two
protons, which means that the relative charge of this nucleus would be positive
two.
Note though that an electron is
also a product of this decay. And it has a relative charge of
negative one. And then our electron antineutrino
is a neutral particle. It has an overall charge of
zero. If we make an equation out of the
reactant and product sides of this decay, we see that positive one really does equal
two minus one. That is, electric charge is
conserved in this interaction, and this is generally true we know.
Well, in this lesson about baryon
number, we find that the same thing happens. In any valid nuclear equation,
baryon number is conserved. And in fact, we can see an example
of that in this equation. Starting on the left-hand side with
our hydrogen, we know that here we have one proton and two neutrons. Earlier, we saw that the baryon
number of a neutron is positive one. So the two neutrons give us a total
baryon number of two. And then we add to that the baryon
number of the single proton. And a proton, just like a neutron,
is a baryon. That is, it’s a class of particle
with a baryon number of one. All this means that the total
baryon number of this hydrogen three nucleus is positive three.
Then when we look at the product
side of this reaction, we see a helium nucleus now with two protons and one
neutron. But once again, each proton and
each neutron has a baryon number of one. And so the total baryon number of
this nucleus is three.
And then we consider the baryon
number of the electron and the electron antineutrino. These particles though are
fundamental particles. They’re not made up of quarks. And therefore, they have a baryon
number of zero. When we consider baryon number
across this equation then, we find that it is conserved. And as we said, this is generally
true. In fact, if we found a nuclear
equation where baryon number was not conserved, then we would know that that
equation is not a possible one. This fact has helped researchers
figure out what nuclear equations can and cannot take place.
Knowing all this about baryon
number, let’s get some practice now through an example exercise.
A Xi baryon is a particle that is
made up of one up quark and two strange quarks. What is the baryon number of a Xi
baryon?
Okay, so let’s say that this here
is our Xi baryon with its one up quark and its two strange quarks. We want to figure out what is the
baryon number of a Xi baryon. One way to start doing this is to
recall that baryon number is a basic property of particles. In that way, it’s like electric
charge or mass. In the case of electric charge, for
example, we know that a particle is given a charge based on how many positive and
negative fundamental charges it possesses. Baryon number though, rather than
being determined by the number of protons and electrons, is determined by the number
of quarks and antiquarks in a particle.
A quark has a baryon number of
positive one-third, while an antiquark has a baryon number of negative
one-third. So to figure out the baryon number
of a Xi baryon, we can add together the baryon number of its quarks. Each one has a baryon number of
positive one-third, and so they add up to one. This is indeed the baryon number of
a Xi baryon.
But note that there’s another way
that we could’ve gotten the same answer. We could recall that any particle
called a baryon has a baryon number of positive one. This is true because a baryon, by
definition, is a particle made up of three quarks. Either way we look at it, the
baryon number of this particle is positive one.
Let’s look now at a second example
exercise.
A positively charged pion is a
meson that is made up of an up quark and a down antiquark. What is the baryon number of a
positively charged pion?
Alright, so let’s say this is our
pion. It’s made of an up quark and a down
antiquark. And we see that we represent it
with this symbol 𝜋 with a plus sign in the superscript. We want to know the baryon number
of this pion. And to figure that out, we can
recall first that any quark has a baryon number of positive one-third, while any
antiquark has a baryon number of negative one-third. So to get the total baryon number
of our pion, we’ll add together the baryon numbers of the particles that make it up,
in this case an up quark and a down antiquark.
The up quark has a baryon number of
positive one-third. And we add that to the baryon
number of the down antiquark, negative one-third, which we see gives a sum of
zero. This then is the baryon number of a
pion.
Another way we could recognize this
to be true is to note that since a pion is a meson, that is, a particle made of one
quark and one antiquark, it will have a baryon number of zero because that’s true
for all mesons. For all of these particles, we add
a baryon number of positive one-third for the quark to a baryon number of negative
one-third for the antiquark and get zero.
Let’s now look at one last example
exercise.
Which of the following particles
have a baryon number of zero? Proton, top quark, electron, B
meson, down antiquark, tauon, mu neutrino, delta baryon, up quark.
To figure out which of these nine
particles has a baryon number of zero, let’s remember what gives something a baryon
number in the first place. This property comes from the kind
of quarks a particle does or does not possess. What we mean is that a quark has a
baryon number of positive one-third. An antiquark, on the other hand,
has a baryon number of negative one-third. We can determine the total baryon
number of a particle by considering what quarks and antiquarks it possesses.
For example, considering the first
item on our list, the proton, this is a particle that’s made of three quarks: two up
quarks and one down quark. Since each of these three quarks
has a baryon number of positive one-third, the total baryon number of this particle,
the proton, is equal to one-third plus one-third plus one-third. That’s one. So we see a proton does not have a
baryon number of zero, and we can cross it out.
What about a top quark? Well, we see that every quark has a
baryon number of positive one-third. So a top quark by itself will not
have a baryon number of zero. Rather, its baryon number is
positive one-third, so we cross this out as well.
Next, we consider an electron. An electron is a fundamental
particle. As far as we know, it’s not made of
anything smaller. As such, an electron possesses no
quarks. And since quarks are what give a
particle a baryon number, an electron, having none of them, has a baryon number of
zero. We know then that our answer to
this question will include the electron.
Next, let’s look at this particle
called the B meson. Though we may not be familiar with
this particular kind of meson, we can remember that mesons in general are particles
made of one quark and one antiquark. As an example of this, this is a
meson comprised of a charm quark and a down antiquark. Since the charm quark has a baryon
number of positive one-third and the down antiquark has a baryon number of negative
one-third, we can see that the overall baryon number for this particle is zero. And we can also see that this will
be true for all mesons because any quark has the same baryon number of positive
one-third and any antiquark has the same baryon number of negative one-third. So even though we may not exactly
recall what a B meson is made of, we know that since it’s a meson, it does have a
baryon number of zero.
Next, we consider a down
antiquark. All by itself, this antiquark, we
know, will have a baryon number of negative one-third, not zero. And so we’ll cross it off our list,
too.
Next, we consider this particle
called a tauon. A tauon is a fundamental particle
not made up of any particles smaller than itself. As such, it doesn’t possess any
quarks or antiquarks and, therefore, has nothing to contribute to giving it a
nonzero baryon number. So because it doesn’t possess any
quarks or antiquarks, a tauon will have a baryon number of zero.
We next consider this particle
called a mu neutrino, which is actually in the same class of particles as
tauons. They’re called leptons. Just like the tauon, the mu
neutrino is not comprised of any quarks. And so it, too, has a baryon number
of zero.
Next, there’s this particle called
the delta baryon. A baryon, we can recall, is a type
of particle that’s made of exactly three quarks. Our proton over here is an example
of a baryon. And just as the proton had a baryon
number of one, so all particles made of exactly three quarks, that is, all baryons,
have the same baryon number. This means a delta baryon does not
have a baryon number of zero, so we won’t choose this option.
Lastly, this brings us to the up
quark. As we’ve seen, any individual quark
has a baryon number of positive one-third. So the up quark has the same baryon
number and, therefore, does not have a baryon number of zero.
Of all these particles, it’s the
electron, the B meson, the tauon, and the mu neutrino that have a baryon number of
zero.
Let’s summarize now what we’ve
learned about the conservation of baryon number. In this lesson, we saw that, like
electric charge, baryon number is a fundamental property of particles. A particle’s baryon number is
determined by the quarks and antiquarks it may possess. The baryon number of one quark is
positive one-third, and that of one antiquark is negative one-third. This implies that baryons,
particles made of exactly three quarks, all have a baryon number of positive one and
that mesons, particles made of one quark and one antiquark, have a baryon number of
zero.
We saw further that any particle
not made up of any quarks also has a baryon number of zero. Lastly, we saw that in nuclear
equations, baryon number is a conserved quantity. Indeed, we saw that this
conservation is a requirement for a given nuclear reaction to happen. This is a summary of the
conservation of baryon number.
