Quantum Mechanics and the shape of atoms as
discovered by Schrödinger.
We all know about Quantum Mechanics, which
is of course the physics theory that describes
atoms and elementary particles, how they move
around like slushy little waves, and interestingly,
it predicts what they look like.
What shape they have.
It was invented in the first couple of decades
of the 20th century by a lot of people all
working together.
Amongst them were Planck, Heisenberg, Bohr,
Davisson, De Broglie, Einstein and of course
Schrödinger.
These guys already knew a lot about atoms
from the scientists who came before them.
For instance, they knew that there are about
a hundred different atoms in nature and that
these atoms join in larger structures such
as molecules, metal lattices and salt lattices
to make everything we see around us.
But what they didn't know – what exactly
was going on on the inside of the atom.
What it was made of, what shape it has.
So they were doing experiments on that.
And pretty soon they found out that atoms
themselves are composed of smaller particles.
They found the proton and the electron and
they were theorizing the neutron.
And with the protons and neutrons they almost
immediately knew what the deal was.
They realized that they were clumped in a
very tiny core at the center of the atom.
That core was really small, a typical atom
is about 300 picometers across, whereas that
core is typically 0.01 picometers.
So this leaves this big open space in an atom,
and they realized that this open space was
going to be the domain of the electron.
But what they didn't know was exactly how
the electrons are filling this space.
If they are spinning around, or orbiting,
or...what.
So, they made an initial sketch.
They called it the planetary model of the
atom.
Basically the core at the center and the electrons
spinning around in big orbits.
It was their first idea of what an atom looks
like.
It proved to be incorrect, but it was a fine
enough starting point.
It made some very nice predictions, and it
allowed them to start doing experiments.
And they did.
One man who was looking at these experiments
was a Frenchman called De Broglie, and he
was noticing something very interesting.
He found that when electrons were forced to
interact with matter, either through some
physical process, or by hitting a detector,
that the electrons presented themselves as
particles.
As hard little balls of matter.
Kinda what you expect them to do.
But when the electrons were allowed to move
on their own, either by being shot through
a crystal or allowed to wander through a vacuum,
they always propagated as if they were waves.
It was almost as if, when you stopped messing
around with the electron, it would suddenly
fall apart into some sort of wave function,
some sort of probability wave that sloshed
around all of space and predicted where the
electron was likely next to be found.
This was the first time they encountered particle-wave
duality in matter and it spelled disaster
for their planetary model.
Because this model really assumed that the
electron stays a particle during the entire
orbit and doesn't fall apart into a wave halfway
through.
So, they needed a new model.
But they realized that this model couldn't
come from classical mechanics, because classical
mechanics makes the same assumption, that
particles stay particles.
In fact, they would need entire new mechanics,
something, some new theory that included the
wavelike nature of particles.
And this is when Schrödinger entered the
picture.
He had looked at the experiments as well,
and he found one common theme running through
all of them.
In his insight, he saw one law of nature,
one equation that seemed to hold no matter
what you did.
He called it: the wave equation.
Nowadays, we simple know it as the Schrödinger
Equation, because it was the rock-solid core
onto which all of Quantum Mechanics was build.
Schrödinger realized that with this equation
he was now in a very interesting position.
What he could do, is take an atom – any
atom – take its properties (stuff like its
mass, and its charge, all those numbers),
put that in that equation, do the math on
it and what he would end up with would be
a series of pictures that show what that atom
looks like.
He went on and did it, for hydrogen.
Which is the easiest atom, its just one proton
and one electron, and that one proved to be
crucial into unlocking the shapes of all the
other atoms.
And when he had worked his way through the
math, these are the pictures he found.
Ladies and gentlemen: the shapes of hydrogen.
So this then is how an electron fills the
empty space in an atom: not by spinning around,
but instead with its blobby-shaped wave function
(which we call the orbital).
What I've drawn here each time is just the
same hydrogen atom, with the proton at the
center.
And the electron has been allowed to go into
a different orbital each time, by giving it
energy for instance.
And if you look at this one: these three blobs
together form that one orbital, they house
that one single electron.
And this one makes a fine example, we can
look a bit at its properties.
What you can do in an experiment is, take
a hydrogen atom and prepare it in this orbital
(by giving it some energy for instance).
And if you leave it undisturbed, then the
electron takes this shape, it becomes this
wave function, this blobby shape.
And if you then were to take a measurement
of the electron, find out where it actually
is, what would happen is this wave function
suddenly collapses.
It condenses into a single point, which we
call the electron.
If you then were to re-prepare your hydrogen
atom in the same orbital (maybe give it some
new energy).
Then you can do a new measurement, and you
can find that electron in the same blob, or
in any of the other blobs.
And if you were to repeat this thousands of
times you would end up with a picture very
much like this.
Notice that there's a high probability of
encountering the electron at the center of
a blob; there the probability wave function
becomes more dense.
But there's something interesting about these
pictures of course, something that is, well,
staring us in the face.
The fact that these blobs are not connected.
There's an area in between where you cannot
encounter the electron.
So it kinda begs the question: how on earth
is the electron traveling from one blob to
another?
Is it...teleporting?
Or...what?
This was one of the important questions that
led to 40 years of heated debate that ended
up with Einstein saying very angry things
about dice.
But, who cares.
Schrödinger had made an important discovery:
he had found the shapes of hydrogen.
And, using that as a basis, those that came
after him were able to find the shapes of
all the other atoms.
They are very much based on hydrogen, they
use the same orbitals.
It's just that the higher atoms consist of
more electrons, therefore they require more
orbitals to house all of them.
So you end up with a situation where the orbitals
all get stacked on top of one another.
Overlapping, but not mixing.
They do however repel, because, that's what
electrons do, they repel one another.
So the orbitals begin distorting each other
according to some very complicated math.
But these guys were also good at what they
were doing.
And, combined with Schrödinger's discovery,
they had now made a link between physics and
chemistry.
A link which in fact led to an entire revolution,
in both of 'em.
So, with that I would like to conclude by
just saying: Mr. Schrödinger...
Thank you very much
