How Einstein’s Special Theory of Relativity Creates Gold

How Einstein’s Special Theory of Relativity Creates Gold


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!

42 Comments

  1. Umm.. If travelling close to speed of light increases mass… Why the the heck photons are massless!? Plz explain…… 😕.
    This question has been my nightmare since ages😅

  2. What about color of copper? Are relativistic effects seen in copper too? Doesn't copper consist of less protons for relativistic effects to be seen? How can we explain its colour?

  3. This was a brilliant presentation and is nowhere near the level of sophistication I had when I was taking college physics (Mechanics and Electricity, sound, light, and magnetics). This definitely boiled the important points such that I did not feel like my head was going to explode.

    Good Job! 🙂

  4. mercury (HG) is really not in the position to call gold a freak, since it's the only element liquid at room temperature in the whole periodic table. the reason is explained by special relativity as well. hmmm, maybe that's why those two like to stick to gather so much? amagalmation is ruling the nation (of metals, that is).

  5. Can you do a video on the time of the formation of different elements.and also the condtions for their formations…..thanks

  6. You could do a really interesting series on some other colored elements; Br, S, Cu – what's up with those guys?

  7. I know just about enough chemistry to understand what electron orbitals are, but it was a challenge to digest. I'll just take your word for it that the contraction of S-orbitals, because 1/2 the speed of light causes them to be 20% more massive, which will allow gold to absorb blue & violet light and reflect yellow light, and leave it at that.

  8. But as a mass approaches the speed of light it does not get more massive. This is a pedagogic (and bad) way of giving one an intuitive feel for relativistic effects. As Don Lincoln, a physicist, at Fermilab explains, at velocities approaching the velocity of light the momentum approaches infinity, not the mass. When protons were acclerated to 99.999999% the velocity of light in the LHC they did not exert a gravitic force 7500 greater than they did at rest. They were just that much harder to "push".

  9. Gold is actually valuable because it is not affected by rust processes… which is interesting to know why on its own

  10. Hello Jade … I have a question that if a body is accelerated by gravity which is just a curvature in space-time instead of a force then if the body due to gravity approaches the speed of light, the increase in mass of the body will have no effect on decreasing its speed and even greater mass would cause greater gravitational pull and the body could surpass speed of light ??? what say?

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