Hi. It’s Mr. Andersen and this AP Physics essentials video 135. It is on the wave model
of an electron. Remember as we look at the level of an electron we see that they do not
behave like particles but act more like waves. And it was this wave model that allowed us
to really understand what was going on at this classical level of a Bohr atom. And so
we realize that electrons could be here or here or here but they did not exist in the
middle. And that was puzzling to scientists. Also why is it when an electron falls down
it emits a photon of light, a certain amount of energy? Well the wave model unlocked that
because we really have a good understanding of how waves work. So if we have waves moving
back and forth and back forth they create something called a standing wave. And so what
scientists started hypothesizing is maybe the electrons, as they are moving around are
interfering with themselves. They are going so fast that they are interfering with the
electrons as they come around again. And so maybe they are wrapping around and creating
standing waves. And so areas out here, we could get a standing wave where the electron
moving around the outside of the atom is interfering with the electron itself. And so what you
get are these standing waves that build up and that is where that energy allows the electron
to be there. But in between these different orbits they do not match up perfectly. And
so they have to be a whole integer of wave length, of de Broglie wave length for the
electron to exist. If it does not match up perfectly then the electron annihilates itself.
And so electrons can only exist in certain energy states. And so the wave model allows
us to understand this at the level of standing waves. And so standing waves occur when the
waves are interfering with themselves. And so the de Broglie wavelength showed us what
that wavelength is and then we can use that to calculate the momentum and even figure
out what is the size of the atom itself. Another important thing it showed us is that as electrons
fall to a lower energy level that energy contained within that standing wave is released and
released in the form of a photon, that we can see in these spectral lines. So to really
understand what is going to with these wave electrons is we could think about fundamentals
and harmonics. And so when you strum a guitar this would be the first fundamental. This
would be the second fundamental. The third fundamental. So using that as a model, if
we are looking at electrons they are moving out from the center with different wavelengths
as well. And so let’s start with the first inner electron. What is really going on is
one wavelength is wrapping around the atom itself. What would that look like? If we look
here at this first orbital it is going to look like that. Now we know something about
the momentum of the electron. We can calculate the de Broglie wavelength. And if we plug
it into this equation, this here is just a circumference of that circle, we can figure
out what is the size of the atom. And it ends up matching up with the Bohr radius that we
measured before. 0.53 angstroms. Now what is the next level going to look like? Well
we have to have two wavelengths in there. So what is that going to look like? It looks
like that. And if we go to three wavelengths we are going to have a different de Broglie
wavelength. And so what are we going to get? It is going to wrap around like that. And
so what is happening is the electrons are racing around, interfering with themselves.
They are building up energy in that one energy level. Now what is interesting about that
is that as they fall back down they release that energy in the form of a photon. How do
they jump back up to a higher level? They have to absorb that photon. And that starts
to explain why we see these spectral lines. And so did you learn to qualitatively link
together the wave model for electrons and then the different energy states in an atom?
I hope so. And I hope that was helpful.