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!

Channel: Up and Atom

Views: 118,250

Keywords: up and atom, einstein, relativity, special relativity, albert einstein, gold relativity, relativity theory, physics, physics video, theory of relativity, special theory of relativity, albert einstein relativity, length contraction, general relativity, science, simultaneity, inertial reference frame, general theory of relativity, albert, time dilation, speed of light, spacetime, space time, observer, relative, mass, dark matter, equations, classical mechanics

Id: p_4zihzPClY

Length: 7min 11sec (431 seconds)

Published: Fri Jul 13 2018