This episode is sponsored by brilliant. From ripples in the sand to the stripes
on a zebra, all the way down to the sodium and chlorine atoms in a crystal
of salt, repeating patterns in nature remind us how even the most chaotic
systems can produce their own form of order. While the patterns we see around
us are cool to look at, things become very interesting when we go down to the
atomic level. The combination of these patterns and quantum mechanical effects
give rise to the beautiful colors we see in butterfly wings, peacock feathers, and
the way a chameleon changes color when it's... excited. In this video we're going
to see the exact quantum physics involved, and how our chameleon Bernard
here uses it to his advantage to find love. Or at least to woo a girl
chameleon. To understand this we first have to understand this salt crystal. If
we zoom into the atomic level we see a very neat and periodic arrangement of
atoms with electrons orbiting around them. This structure is called a crystal
lattice because it's common to all crystals. Now the key idea is that these
electrons can't have just any energy level. Okay guys things are about to get
real. This is the infamous Schrodinger wave equation and it's kind of the holy
grail of quantum physics. I did a whole video about it, but quickly this equation
tells us everything we can possibly know about a quantum particle, like an
electron. Now this funny-looking pitchfork here is the Greek letter psi
and it stands for what's called the wave function of the electron. See electrons
are a bit elusive in that you can't pinpoint exactly where they are like
regular objects, you can only predict where they might be with more or less
probability. This probability is modeled by a wave, hence the name wave function.
Now the thing is only certain wavelengths can exist in a confined
space. If you imagine a string on a guitar only
certain wavelengths are allowed because the ends need to be attached to the
guitar. For example this wavelength is fine but this one doesn't work. This one
is fine, this one, nope. That's why two strings of different lengths can't
produce the same sounds. It's the same thing going on with our electrons in the
crystal lattice. Only certain wave functions are allowed
while others are banished because of the fixed lengths within the lattice. The
energy of an electron is intrinsically linked to its wave function, so if only
certain wave function values are allowed only certain energy levels are allowed,
and indeed when we solve the Schrodinger equation that's exactly what we get. This
equation gives us the energy levels allowed for an electron. Notice how all
the terms are constant values except one. h-bar is Planck's constant on 2 pi, M is
the mass of the electron which doesn't change, L is the length of the lattice
spacing which doesn't change, and pi is a constant. n is the only value that
changes and needs to go up in whole numbers, therefore if n can only increase
in whole numbers and the rest of the values are fixed the energy levels must
also increase in discrete chunks. But what's the point of all this math if it
doesn't result in a happy chameleon? These calculations apply to just one
particle but things get pretty interesting when we have a party of
particles. The periodic structure of the crystal lattice means the atoms are
really close together so the electrons are all whizzing around and interacting
and their energy levels start overlapping, forming into kind of energy
bands. These energy bands and the gaps between them decide which electron
energies are and are not allowed inside the crystal. Now let's imagine everything
blown up one or two hundred times. Instead of atoms say we have some
periodic structure and instead of electrons we have particles of light,
photons. It turns out that similar band structures appear when we have
microscopic patterns which have a period in the range of the wavelength of
visible light. These are called photonic crystals because of their similarity to
regular crystals. This structure leads to the formation of optical bands just like
electronic bands which allow some wavelengths of light to pass and others
to get reflected. This makes objects appear a certain color and different
structures allow for different colors. Now you might be wondering how is this
different from regular colors? How is it gonna help our boy Bernard here impress
his date? The big difference is that with photonic crystals the color is dependent
on the structure of the material, while the regular colors that we see around us
are dependent on the chemical composition of the material. Take leaves
for example. Leaves look green because the electrons in the shaded region of
the chlorophyll molecule get excited when light hits them and due to their
chemical bonding they absorb blue and red light and
reflect green. Fun fact: if you ever want to grow plants inside and use indoor
lighting try using a purple light. Purple is a mixture of blue and red which the
plants need to grow. Shining green light on leaves does little to their growth
because it's reflected and wastes energy so purple light is energy efficient for
plant growth. So that's how color usually works but in photonic crystals the color
comes from the interaction of light with the physical structure of the material,
not the chemical bonds. Take for example this CD. Now I don't know if this is
considered vintage these days but it's basically something that plays music.
Notice the beautiful colors that we have. The multicolored pattern isn't caused by
a colorful coating, it happens because of the underlying pattern or tracks where
the data is written. The track spacing is comparable to the wavelength of visible
light and so different wavelengths of different light diffract at different
angles giving multicolor patterns.
Chameleons, butterfly wings and peacock feathers all have photonic crystals in
them, and these microscopic interactions manifest themselves in a pretty cool way
at the macroscopic level. For one thing the color can be tuned. Chameleons change
their body color by adjusting the crystal patterns to indicate when
they're excited. By stretching or compressing the lattice they can change
the color of light which is reflected, going from a dull camouflage to a
vibrant hue, and what girl wouldn't be impressed by that! Another cool thing is
that photonic crystals reflect different colors depending on the angle you look
at them. This is why you see those cars that go from green to purple as you walk
by them. They have special paint with photonic crystals. Today lots of research
is being done to mimic the bio photonic crystals found in nature for a range of
applications from camouflaging and even optical communication. In fact one of the
main technologies of solar energy, solar panels, use the same physics of
structural color we find in Bernard and peacocks. By engineering the thickness of
the glass layer we can control what colors of light are reflected and
absorbed, just like Bernard. This is an interactive cartoon from today's sponsor,
brilliant org. You can adjust the wavelength of light and the thickness of
the glass to control which colors are reflected, then use what you've learned
to answer today's problem about creating anti-reflective coating in a solar panel.
If you find that this excites in you a passion for solar energy you can talk
about it with the other engineers discussing the problem or check out a
whole course about it. This is just one of brilliants daily problems, which range
from vector calculus to computational biology to quantum physics, and every
problem has an accompanying course to go with it. Signing up is free but I
strongly recommend their premium membership which gives you unlimited
access to all their courses. I use brilliant pretty much every day to
deepen my understanding about the video topic I'm working on. I've used it for a
bunch of my quantum physics videos and pretty much whenever I need to brush up
on math, and I find it to be an invaluable tool. For a 20% discount
be one of the first 200 people to sign up using this link which is in the
description of this video. Just go to brilliant.org/upandatom.
okay bye