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- [Voiceover] In the last
video, we talked about

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the helium nucleus, which contains

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two protons and two neutrons.

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Protons and neutrons in the nucleus

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are called nucleons, and so I'll

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use that term a few times in this video.

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Here's a picture of the nucleus,

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with two protons and two neutrons,

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and we know it's stable,

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even though we know like charges repel.

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And so these two protons are repelling

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each other, and that's
the electrostatic force.

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So let me go ahead and write that here.

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The electrostatic force
says like charges repel.

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We know that this nucleus is stable,

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so there must be something else

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holding the nucleus together,

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which we call the strong force.

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So the nuclear strong force is

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stronger than the electrostatic force.

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The strong force acts only over

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short distances though, but it does act

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between all nucleons.

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For example, a proton-proton interaction

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is the same as a
proton-neutron interaction,

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which is the same as a
neutron-neutron interaction.

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You can get into much more detail

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about the strong force.

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That's not really the point of this video.

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The point is that this nucleus is stable.

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And let's think about why.

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We have equal numbers
of protons and neutrons,

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and so that's interesting.

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So let's think about the atomic number,

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which tells us the number of protons,

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which we represent by Z.

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And the number of neutrons
we could say is capital N.

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So if we're concerned with the ratio,

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the ratio of neutrons to protons,

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so the N to Z ratio.

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In this example, we have two
protons and two neutrons.

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So two neutrons over two
protons is equal to one.

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We have N to Z ratio of one.

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It turns out that nuclei
that have small numbers

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of protons, so if we're talking
about Z is less than 20,

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they have stable nuclei

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when the N to Z ratio is equal to one.

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So when N over Z is equal to one,

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you can say you have a stable nucleus,

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so equal numbers of protons and neutrons

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turns out to be stable.

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So for this example, the
helium-four nucleus is stable.

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Thinking about that, let's
look at carbon-14 next.

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We have carbon-14, so let's get

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a little space right down here.

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So carbon-14 atomic number of six.

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Therefore, carbon has six
protons in the nucleus.

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So there are six protons.

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Number of neutrons will be 14 minus six,

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so eight neutrons.

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So what's the neutron to proton ratio?

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So what's the N to Z ratio here?

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Well the N to Z ratio would be

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eight neutrons and six protons,

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and obviously that number
is greater than one,

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so we have an unstable nucleus.

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The carbon-14 nucleus is unstable,

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it's radioactive, it's going to

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undergo spontaneous decay.

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It's going to try to get a better

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neutron to proton ratio.

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So let's look at the nuclear equation

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which represents the
spontaneous decay of carbon-14.

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So here is our nuclear equation.

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And when you're writing nuclear equations,

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you're representing only the nuclei here,

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so for example, on the left side

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of my nuclear equation, I have carbon-14,

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we're talking about only the nucleus,

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so we're talking about six protons

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and eight neutrons in the nucleus.

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And so let's look and
see what happens here.

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So carbon-14, the nucleus,
the carbon-14 nucleus

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is actually going to give off an electron,

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and so that's pretty weird,

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and we'll talk about more
why in the next video.

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It's a conversion that's governed
by the weak nuclear force.

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But we know that an electron
has a negative one charge,

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and so that's what we're
talking about here.

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Here for carbon, we have six protons,

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let me go and write
that, six protons here.

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An electron has a negative one charge,

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let's write a negative one
charge here for the electron.

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The carbon-14 nucleus is turning into

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the nucleus for nitrogen here.

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Let's look at what we have.

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Our atomic number is seven,

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so we have seven protons,

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let's go ahead and write that here.

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Seven protons, and 14 minus
7 gives us seven neutrons.

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So we look at the mass number here,

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so 14 minus seven gives us seven neutrons.

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And so that ratio, the ratio of neutrons

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to protons is seven over seven,

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which is equal to one.

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That implies that we have
a stable nucleus here.

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That's the reason why carbon-14
undergoes radioactive decay.

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Let's look at more details
about a nuclear equation,

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because that's really what
I'm most concerned about

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here in this video.

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The number of nucleons is conserved.

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Let's use a different color here.

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We have 14 nucleons on the left.

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We have six protons and eight neutrons.

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And on the right, we
also have 14 nucleons,

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seven protons and seven neutrons,

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so obviously an electron is
not a proton or a neutron.

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Nucleons are conserved,
so we have 14 on the left,

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and we have zero plus 14 on the right.

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Also charge is conserved,

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and so that's what we see down here.

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We have six positive
charges on the left side.

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On the right side, we
have one negative charge

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and seven positive charges,

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so negative one and
seven give us plus six,

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so we have plus six.

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So nucleons are conserved

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and charge is conserved
in a nuclear equation.

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And notice what happened here.

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We changed the identity.

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We went from carbon to nitrogen,

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because we changed the number of protons.

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We went from six protons to seven protons,

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and so that's the idea of transmutations,

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of changing one element
into another element.

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For nuclei with small numbers of protons,

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the N to Z ratio, the
ideal one is one to one.

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For nuclei with more protons,

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it turns out the ratio
changes, so let's look at that.

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As you increase the number of protons,

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the ratio changes for a stable nucleus.

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The N to Z ratio turns out to be 1.5,

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so as you increase in Z,

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so as you go above Z is equal to 20.

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As you get more and more protons,

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you need more neutrons.

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You need more neutrons,

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and let's think about why.

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If I have a bigger nucleus here,

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so this is a very poor
representation of a nucleus.

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I think about two protons, let me use,

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I'll use magenta here.

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So I'll have two protons
really close to each other.

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We know that there is a weak
electrostatic repulsion here,

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and there's a strong nuclear force.

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There's a strong nuclear
force between those protons.

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The strong nuclear force wins,

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but this is only when you're
talking about short distances.

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Remember the strong force acts
only over short distances.

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So if you have protons that
are far away from each other,

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so these two protons here
are far away from each other,

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there's still a repulsive force.

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The electrostatic force is still present,

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so they're still repelling each other.

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But you don't have the
strong force any more.

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And because you don't have
the strong force any more,

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eventually as you keep
increasing the number of protons,

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you're increasing in
the electrostatic force,

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and you get to a point where you need more

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of the strong force, and so you need

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to add in more neutrons
to balance things out.

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So you need to add in more neutrons here,

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and that's the reason
for this increased ratio.

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You need more neutrons as you increase

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the number of protons here.

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When you get beyond approximately 83,

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so let me go ahead and
write this down here,

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so once you get an atomic

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number greater than 83, so bismuth,

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the repulsive force of the protons,

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this electrostatic repulsive
force that we talked about here

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is so great that pretty much all

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of the nuclei are unstable,

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and will undergo radioactive decay.

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We'll talk in the next video about

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the types of radioactive
decay that you might see.