Coulomb’s Law

Coulomb’s Law

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Hi. It’s Mr. Andersen and this
is chemistry essentials video 4. It’s on Coulomb’s Law which is a physics law but also has huge
ramifications when it comes to chemistry. And so if we look at a simple atom. This right
here is helium. It’s going to have 2 protons, 2 neutrons and 2 electrons. What’s holding
those electrons around that nucleus is going to be Coulomb’s Law. And so if we were to
look at the charges, the positive protons are going to have a positive charge. And the
negative electrons are going to have a negative charge. And those opposites attract. That’s
Coulomb’s Law. And so that’s the first thing that he discovered. If we have opposite charges
there’s going to be an attraction between the two. Now the other things he learned is
that if you have two like charges they’re going to repel each other. And so those 2
protons don’t want to be next to each other. They’re going to be really unstable. And the
neutrons and the strong nuclear force actually hold them together. Now did you see what happened
to the arrows? The arrows got larger when we looked at the protons. And that’s because
according to Coulomb’s Law, as those charges get closer and closer and closer, then the
forces get larger and larger and larger. And so it’s sometimes referred to as the inverse
square rule. And so let’s get to Coulomb’s Law. And why is it important? Well again it
shows us that positive and negative attract. And it also tells us that if we have two like
charges they’re going to repel. But the closer they get, the bigger that charge is going
to be. And so Coulomb’s Law tells us the force between charged particles is proportional
to their charges. So all you do is just multiple the two charges. And that’s going to give
you the magnitude. It also tells us that it’s inversely proportional to the square of their
radius. In other words how far they are apart. So if things are far apart, it’s going to
be less charge. As they get closer and closer and closer that charge is going to get greater.
It’s very similar to the gravitational, Newton’s Law, universal gravitation. This just deals
on the small level with charges. Now in chemistry it’s important because we can use Coulomb’s
Law to predict ionization energy. Ionization energy is the amount of energy required to
create an ion. And so what’s an ion? It’s when you’re either losing or gaining an electron.
And so ionization is the energy required to remove an electron. And in chemistry, in science,
we can actually measure ionization energy using something called photoelectron spectroscopy.
Or PES. Now that seems confusing, but it’s actually a really simply concept and has huge
implications when it comes to understanding what an atom actually looks like. So we can
use the data to predict the shell’s structure. So how do we know if we have these shells
and orbitals? A lot of that is predicted through Coulomb’s Law but it’s also verified through
PES. So who was Coulomb? We has a French physicist. And what he was doing was studying charges.
A lot of people thought that there was some law that could be applied to charges. And
he was the first one to really quantify that. So essentially if we have two like charges
they repel. And if we have two unlike charges there’s going to be an attraction. And here’s
the equation right here. You have a Coulomb’s coefficient. And then we’re going to have
multiplying the charges. And then we’re going to take the radius square. Now how did he
discover this before we had electronics and even electricity had really been discovered?
He used something called a torsion balance. And this is one of his sketches of a torsion
balance. It looks a little complex. But it’s really simple. All he would do is he would
take a sphere. And he would charge that sphere. And so we’re talking about electrical, static
electrical energy. And so that was suspended by a fiber that went all the way down here
in the torsion balance. So he’d give this a positive charge. And he would give this
a positive charge as well. And so if we have two like charges what’s going to happen when
I bring this one, you can see it right here. As I bring this closer, what’s it going to
do? You can see that it’s going to push it away. It’s going to repel. And so it would
twist this fiber and he could measure it. You can kind of see the scale on the side.
He could measure how far it went. He would then move it away. And he would touchy his
sphere to another sphere that didn’t have a charge. And what it would do is would transfer
half of its charge to that uncharged sphere. He would then bring it back again. And it
wouldn’t move as far. And so he was able to quantify Coulomb’s Law using a not super sophisticated
torsion balance. And so why is this important in chemistry? We can use it to measure ionization
energy. And so what is ionization energy again? It’s the amount of energy required to remove
an electron. And so think of it as just a little hand that has to come in and grab this
electron and pull it off. So that’s the ionization energy. And so it’s going to depend on Coulomb’s
Law, how big that ionization energy is going to be. Because that proton wants to hold it
in place. And so let’s say we were to look at something that’s a little larger. So this
is lithium. And so lithium is going to have this outer electron out here. And since the
distance is greater, in other words that radius is larger, you’re going to require a smaller
amount of ionization energy to pull it off. And so that Nobel Prize was awarded to Albert
Einstein for his discovery of the photoelectric effect. And what that means is if you hit
metal with photons or hit metal with light what it will do is it’ll eject these electrons.
And we call those photoelectrons. And so hold on to that idea. It’s going to become really
important in just a second. But let’s build an atom for a second. And this is a simulation
from PHET. What you can do, you could go to the website right down here. What you can
do is you can just start dragging things in. And then it will actually build that atom
for you. So let’s do that. So let’s say I drag a proton in. I’ve now created hydrogen.
You can see on the periodic table that’s going to be H. It’s going 1 atomic number. But let
me just throw an electron in there. And where does it go? It goes right there. What’s holding
it in place is going to be Coulomb’s Law. They’re opposite in charge and so they’re
going to be held together. Well what happens if I throw another proton in? Now we’ve got
helium. But look how unstable it is. Why is it so unstable? It’s because those are like
charges and so they want to repel each other. Luckily if we, and it would never exist like
that, luckily if we add some neutrons to it, then we can stabilize it. And so that’s not
going to decay. Now let’s add another electron. It’s going to sit in this shell. And so we’ve
got 2 electrons in this first shell. Let’s make it from helium, let’s move up. Make it
a little bit of unstable lithium. We’ll stabilize that with a neutron. Now let’s add another
electron. What happens? Well, it sits right there. In other words it’s in the outer shell.
And this is in the outer shell. And this is in the outer shell. So why is it that those
first two electrons are going to be on the inside shell? And the outer electrons are
going to carry, or excuse me, those additional electrons that we add are all going to be
thrown to the outside? That has to do with quantum mechanics and quantum physics. And
so it’s quantum numbers that are determining that. But how did physicists figure this out?
How did chemists figure out that there’s going to be 2 in the first. And then we’re going
to have 8 in the next. And we’re going to have all these orbitals? Well we owe it to
the photoelectric effect. And so going back to that again, that’s Einstein’s theory. That
if you hit matter with light, it’s going to eject these photoelectrons. And so let me
show you photoelectron spectroscopy. And so what is that? You basically have a photon
source on one side. So you’re going to have a source of light on one side. And so that
could be infrared light. It could be UV light. It could be X-rays. The energy of those photons
is determined according to the equation where energy is equal to hv. Where h is Plank’s
contestant and v is going to be the frequency of the light. So basically in this machine
you can vary the energy of those photons that are coming out. They’ll strike the matter
that you want to study. That’s sitting inside a vacuum. And that’s going to eject electrons.
So photoelectrons. And those photoelectrons will be captured up above so we can measure
them. And so this is a pretty simple set up. What are you doing? You’re hitting matter
with light. And then you’re measuring electrons that come out of it. And so let’s look at
hydrogen. If we’re looking at a sample of hydrogen we’re going to create a spectrum
or a photoelectron spectrum. And so we’re going to have energy across the bottom. That’s
the amount of energy that we’re introducing with the light. And then we’re going to have
the number of electrons on the side. And so what happens when you turn on the machine
is you can just vary the energy. And eventually you’ll hit the point where you get a bunch
of electrons coming out. So why is that? Well, what we’re doing is we’re changing the amount
of energy to the point where we hit ionization energy. And then, boom, we’re going to release
all of those electrons from hydrogen. And so we’re going to get a peak at, we’ll just
all this 1.3 and think of it as an amount of energy. Now let’s go to helium. What do
you think that’s going to look like? Well helium has 2 protons on the inside. So it’s
going to have a different amount of ionization energy. And so if we hit that with light,
watch what happens. Okay. It’s different amount of energy. You can see that we need more energy
to eject those electrons, but look how big the peak is. Now let’s compare that back to
hydrogen. Hydrogen had a peak like this. Helium had a peak like that. Why is this twice as
high this one? It’s because it has twice as many electrons. It’s because we’re ejecting
two electrons when we tune that frequency to the right ionization energy. Okay, you
think you’ve got that? Let’s go to the next one. What do you think will happen with lithium
then? If we hit lithium with energy? Well we’ve already talked about this outer one
is going to have a low amount of ionization energy. So let me show you the spectrum for
lithium. Wow. What do we get here? Well we get one peak that’s going to be one electron
that’s going to have low ionization energy. And that’s going to be this one right here.
But then we’re going to have a double peak, in other words two electrons, that’s going
to be way more energy. Why is that? Lithium is going to have way more protons. And so
what’s cool about photoelectron spectroscopy is we can actually verify the predictions
that we made with Coulomb’s Law. So could you fill in this concept map? Coulomb’s Law
is the force between charged particles. And how is that related to their magnitude and
radius squared? Could you fill in those two blanks? And what is that technology, do you
remember that measures ionization energy? And then what is ionization energy? It’s the
energy required to do what? Let’s see. So it’s the force between charged particles is
proportional to the magnitude. In other words it’s just multiply the charges, inversely
proportional to the radius squared. That technology is called photoelectron spectroscopy. And
then ionization energy remember is the amount of energy required to remove an electron.
So what did you learn? You should have learned that we can explain the distribution of electrons
in an atom or ion based on data. And so we can predict data using Coulomb’s Law. And
we can also verify it using PES. We can analyze the data and we could look for patterns and
relationships. And we’re going to get more into those patterns and relationships in the
next video. But I hope that was helpful.

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