Why is quantum mechanics important?
Why do we have to talk about it for orgo?
Because maybe you guys remember that the smaller
particles get, the more that they're going
to function as both particles and as waves.
What that means is that in regular physics,
if you have a ball and it hits something and
it collides, that's what we can Newtonian
physics.
But as these particles get very, very small,
for example, electrons, they're not just going
to behave as particles anymore.
They're not just going to have collisions.
They're also going to behave as waves and
interfere with each other.
There are these mathematical equations that
make this – the math is very confusing.
We don't need to know all that, but we do
need to know a few things.
For example, the Heisenberg Uncertainty Principle,
what does that mean?
Well, what that says is that because these
are acting as waves, we can't simultaneously
know an electron's speed and it's position.
We can know one or the other.
We can know where it is, but not how fast
it's going or we can know how fast it's going,
but not where it is.
What that means is that instead of focusing
so much on where the electron is at a given
moment, what we're going to do is we're going
to focus more on probabilities.
We're going to say, “Okay, what are the
chances that an electron is in this space?”
That's actually going to be a lot more important
for this course.
Remember that I was just talking about these
mathematical equations.
Well, the reason that these equations are
complicated is because these aren't just particles;
these are acting as waves.
There's a lot more complexity to it.
The way that we describe these is through
wave functions.
So you can think of a function in math.
It's just an equation that's going to describe
the energy state of an electron at a given
time.
There is a Greek letter that we use to symbolize
the wave function, so go ahead and circle
that.
It's the Greek letter psi, so I kind of drew
a bad psi, but whatever.
That's a psi.
The psi is my letter to substitute for this
wave function that I'm not going to teach
you because it would be way too long and way
too tedious.
But it turns out that if I take a derivation
of that equation and in fact, if I square
it, so the psi squared, what that's going
to give me is the relative probability of
finding an electron in a certain space.
That's really important because now if I can
take that equation and square it, that's going
to tell me what are the chances that an electron
is in a certain place and that's what's important
to me as an organic chemist.
Finally, where does this all go?
Finally, if you take the 3D plot of this psi
squared, because remember this is just an
equation, so if I take a 3D representation
of it, so just right here of the psi squared,
what I'm going to get is a region of space
called an atomic orbital.
That's where this all comes together.
Basically, I'm using these really fancy equations
to describe where our electron is going to
be.
That is what we call the atomic orbital.
So the atomic orbital is just a mathematical
representation of where these electrons might
be at a given time.
That's a place where the chances of finding
an electron are high.
So now let's go ahead and talk a little bit
about what these orbitals look like.
I know you guys might remember this from gen
chem, but let's just go over it really quick.
The simplest type of orbital is the 1s orbital.
The 1s orbital is just a sphere.
It's kind of small.
That's it.
Remember that the first shell can hold two
electrons and the 1s orbital – each orbital
can hold how many electrons?
Two.
So that's it.
There's really nothing more to know.
That first shell only has one orbital and
it's 1s.
Then once we get into the second shell, the
second shell we're going to learn can actually
hold eight electrons.
I'll just put e's.
Eight electrons.
What that means is that it consists of four
different orbitals that can hold two electrons
each.
The first one and the lower energy one is
going to be the 2s.
Now the 2s looks a lot like the 1s, it's just
bigger because these electrons are now a little
bit further away from the nucleus, so they
have a little bit more energy.
So that one can also hold two.
Then finally, we have these three orbitals
that are of a little higher energy state and
they're all the p orbitals.
The way that I think of it is they kind of
look like peanuts.
Your professor might have said dumbbells or
whatever.
Whatever the case is, I just think they look
like peanuts.
So there's three of these.
They go in different directions.
The important part to know is that they all
have the same energy and they can hold two
electrons.
Good.
What if we were, for example, trying to draw
the atomic orbital diagram for carbon.
Let's say we're doing carbon right here and
trying to figure out where the electrons are
going to go.
So first of all, you guys have to tell me
how many electrons would a carbon atom have.
It would have six.
So let's go ahead and write six electrons.
That's because carbon has an atomic number
of six, so it would have the same amount of
electrons.
So where do we put these electrons?
Well, the first two should definitely go in
the 1s.
So now I have my two first electrons at the
lowest energy state possible.
Now, that energy state is full.
That shell is full, so now I have to jump
up to the next higher energy and that would
actually be the 2s.
Remember that I said 2s is a little bit more.
I would then put two more electrons in the
2s.
Now I have four electrons that are filled
in orbitals, but I still have two left.
Where do you guys think I should put those?
This one's a little trickier.
I should put one in one p orbital and one
in another p orbital.
Now just so you know, all three of these p
orbitals are mathematically equivalent, but
it's just normal convention to use x and y
first.
If you really wanted to be a rebel, you could
use z first, but your professor would just
think what are you doing.
Also, notice that I drew them with an up spin.
If you drew them with a down spin, that would
also be fine as long as you're consistent.
Don't draw one up and one down.
That would be bad.
But if you draw them both down, that's fine.
Cool.
Just so you know this little meme that I drew,
I made this because it's like Schrodinger's
cat is a thought experiment to talk about
that a cat could be half alive or half dead
at the same time.
It's used to talk about how electrons could
be in one place or they could not be in one
place.
It's interesting.
Whatever.
This meme did not go viral, so I should probably
just stick to organic chemistry because I
guess it wasn't that funny.
