Hello! I'm Jade lovely to meet you. So we
usually think of relativity as like this
super abstract thing that only happens
in bizarre scenarios like trains being
hit by lightning or rockets traveling at
the speed of light so today I just
wanted to share with you a more
down-to-earth phenomenon and it's that
relativity is actually the reason behind
Gold's beautiful yellow shine. Here we go
and I hope you enjoy it. This is gold. All
the other metals made fun of gold
because he was different.
You see most other metals reflect all
wavelengths of light equally. Objects get
their colors because their electrons
resonate most strongly with certain
wavelengths and they absorb these
wavelengths and reflect all the others
back into our eyes. An orange looks
orange because it absorbs all
wavelengths of visible light except
orange. Orange. Most metals electrons
resonate most strongly with ultraviolet
light and so reflect all wavelengths of
visible light back equally. This makes
them silvery and reflective, but not gold.
"You don't reflect all the colors evenly, you don't reflect all the colors evenly", the metals chanted. Gold was tired of
being teased. "Why am i different?" He
questioned. So he did some digging and
found something quite special... relativity.
You see according to Einstein's special
theory of relativity, as an object
approaches the speed of light it gets
heavier and heavier eventually becoming
infinitely heavy. This is why nothing can
move faster than the speed of light,
you'd need an infinite amount of energy
to move something infinitely heavy. In a
light atom like hydrogen which has just
one proton and one electron the
electrostatic force is weak so the
electron orbits the nucleus pretty
slowly. But gold has 79 protons in its
nucleus so the electron feels an
enormous electrostatic attraction. To
avoid spiraling into the nucleus the
innermost electrons need to travel at
over half the speed of light. When things
get that fast relativistic effects
become critical increasing the electrons
mass by around 20% which has a direct
impact on the atomic radius of the
electrons orbit. See the radius of an
atomic orbital is given by this equation,
where a0  is the radius of the
electron's orbit, otherwise known as the Bohr
radius. This m is the mass of the
electron and because it's in the
denominator if it increases, a0, the
radius of the orbit, shrinks. Gold
couldn't wait to tell the other metals
that he was special because of
relativity. But the heavier metals like
Lead and Mercury were like, "So what? We
have even more protons than you do. Our
electrons feel relativistic effects too.
You're not special, you're just a freak."
Gold had to admit that this was a good
point, so he dug deeper. So far Gold had
been using the Bohr model of the atom
which assumes that electrons are like
particles which orbit around the nucleus,
just like planets orbit around the Sun.
But to get to the bottom of things he
needed to use the more accurate but more
complicated quantum model. This model
replaces the orbiting electrons with
probability clouds which show where the
electrons are most likely to be. The
electron closest to the nucleus is said
to be in the 1s orbital and we can say
that with high probability the electron
will be found somewhere within this
sphere. If we were to take a series of
snapshots it would look something like
this. The next closest electrons are in
the 2s orbital. They can be found with
high probability anywhere within this
larger sphere. I know this looks like a
circle and that's because I'm drawing on
a 2d surface and want you to see all of
the orbitals so just imagine it's a
sphere cut open or something.
Anyway Gold found out that he has six s
orbitals, but not all electron orbitals
are spheres. Other orbitals, like the p
orbitals, look like two identical
balloons, and the d and f orbitals look
even weirder. If you look closely at the
s orbitals you'll see that the
probability distributions aren't equally
spread out. The electrons are more likely
to be found closer to the nucleus
because they like to be in lower energy
states. The closer they are to the
nucleus the lower their energies are. The
areas where the electron is most likely
to be found are called probability peaks,
and the probability peaks of all the s
orbitals are fairly close to the nucleus.
As we discussed earlier the closeness to
the nucleus means the electrons travel
at super high velocities which means
that all six s orbitals of the gold atom
are relativistically contracted. But
the d-orbitals have their probability
peaks further away from the nucleus.
Because they don't feel as strong an
attractive force they don't reach high
velocities so they're unaffected by this
relativistic contraction. What's more is
that as the electrons in the s orbitals
become more tightly bound to the nucleus
they act as a kind of electrostatic
shield, so the electrons in the farther
out d orbitals feel an even weaker force
from the nucleus and expand out even
further. In this quantum model the
absorption of wavelengths occurs between
orbitals as well. Most metals have their
peak absorption wavelength in the
ultraviolet spectrum meaning that they
reflect all visible light back. For gold
this absorption occurs between the 5d
and 6s orbitals. An electron in the 5d
orbital will absorb a photon of a
certain wavelength and jump to the 6s
orbital. Without accounting for
relativity, the energy needed to jump
from the 5d orbital to the 6s orbital
would correspond to frequencies in the
ultraviolet spectrum, just like the other
metals. But because of relativistic
contraction the 6s and 5d orbitals
shift closer together. This lowers the
energy needed for an electron to jump
the gap bringing it from the ultraviolet
into the visible spectrum. Scientists
have measured this energy to be around
2.3 electron volts which corresponds to
the frequencies of blue and violet light.
An object that absorbs blue and violet
light and reflects the rest of the
visible spectrum will appear... yellow. Why
this didn't occur for the other heavy
metals like mercury and lead is because
their peak absorption wavelengths didn't
lie in the Goldilocks zone. I'm so sorry.
Gold ran to the other metals to tell
them the good news. He was yellow because
of relativity and therefore they should
make him the ruler of all metals. The
other metals didn't quite get the logic
but decided to go along with it anyway.
And that's why gold is recognized as one
of the most valuable metals on earth. So
next time you see a piece of gold
remember it got its place at the top of
the metals by being curious and
following the scientific
method - and being bullied by the other
metals... Thanks for watching guys! I tried
something a bit different this week with
the format, I hope you liked it but also
let me know if you didn't because, you
know, I want to make videos that you guys
want to see! If this is your first time
here make sure to subscribe for new
videos every week. I do math physics and
computer science. A big thank you to my
patrons as always, you guys are the best
in the world and I will see all of you
in the next episode. Bye!
