Relativity and the color of gold

Relativity and the color of gold

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Einstein's theory of relativity is good for more than H-bombs; it keeps your fiancé's fingers on her hand when you get engaged, and Lil Wayne's head on his shoulders.

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WASHINGTON, June 3, 2015 – Einstein’s general theory of relativity is 100 years old this year, and special relativity is 110.

Big deal, you say. What’s relativity done for me recently? Well, it’s probably kept your fingers on your hand, and it’s certainly kept Lil Wayne’s head on his shoulders.

Relativity isn’t important just to physicists. Its effects are incorporated into systems from GPS to CRTs. It gave us the bomb and the Cold War.

You don’t need to know physics to work a GPS receiver, and you may not love the bomb, but relativity is still important in your life, and it turns out that its effects were obvious and important long before Einstein came along. We might even say that relativity has given millions of people their heart’s desire.

Special relativity is the reason that the Forty-niners went west and settled California. It’s because of special relativity that the Spanish came to the New World and enslaved or slaughtered the people living here. It’s the reason that the Vikings thought of taking on Byzantium and that Archimedes ran naked through the streets shouting “eureka!”

Special relativity is why gold is golden and why it’s a “noble metal.”

Metals, like silver and gold, are shiny; they absorb photons across the spectrum, then immediately re-emit them as reflection. Silver reflects every color of light that we can see, so when white light hits it, white light is reflected back. In white light, you can look at yourself in a silver mirror and see the colors of your eyes and hair and clothes as they look to anyone who sees you.

Silver doesn’t reflect every color you can’t see. It doesn’t reflect ultraviolet.

The electrons in an atom are located in orbitals. Grade school science books sometimes depict atoms as little solar systems, the “Bohr model,” named after Niels Bohr, the physicist who came up with it. The nucleus is like the sun, with the electrons orbiting like planets, though bound to the nucleus by electromagnetic force rather than by gravity. The farther out those electrons are from the nucleus, the faster they travel and the greater their energy.

Orbitals aren’t really quite like planetary orbits. Instead, they represent regions of probability. Quantum mechanical calculations tell us where an electron in an atom’s 1s orbital is most likely to be or where its 2s and 2p electrons are most likely to be. Those orbitals aren’t circular orbits, but for now we can pretend that they are.

The orbitals are numbered and lettered: 1s, 2s, 2p, 3s, 3p, 3d and so on, and the p, d and f orbitals all have sub-orbitals. Each sub-orbital can contain two electrons, no more. An electron can move from one orbital to another if there is an empty spot for it. To move an electron from a lower orbital to a higher orbital, say from 4d to 5s, takes energy, photons of a specific color or wavelength.

Silver has a single electron in its 5s orbital, but several electrons in its 4d orbital. To move a 4d electron to the 5s orbital takes a photon of a specific energy–ultraviolet. When you shine white light on silver, all the colors that you can see are reflected, but ultraviolet is absorbed to move 4d electrons to 5s orbitals.

Gold has a solitary electron in its 6s orbital, and several electrons in its 5d orbital. When you shine white light on gold, it reflects back every color except one: blue. The energy required to bump an electron from 5d to 6s in gold is less than the energy required to bump one from 4d to 5s in silver; it’s the energy of blue light, not ultraviolet. And if you subtract blue from white light, the remaining colors—red and orange and green—combine in your eye and brain into one color–golden yellow.

So why does it take less energy to make that jump in gold than it does in silver? Special relativity, of course. That outer 6s electron is moving at fearsome speeds—relativistic speeds, in fact. Because of that, it has more mass than electrons at rest or the lower energy electrons in lower orbitals. And because of that greater mass, it has greater momentum, and in quantum mechanical calculations, that translates into an orbital that is contracted inward toward the nucleus. That means that the jump from 5s to 6d is “smaller” than it would be, and gold is golden.

Gold’s lone 6s electron should make gold highly reactive. After all, cesium has a lone 6s electron that is responsible for its high reactivity. Toss a piece of cesium in a cup of water and it will explode. Give your fiancé an exploding engagement ring and see what happens to your romance. In fact, give her a ring that turns her finger green and you may as well call off the wedding.

But gold doesn’t react. It doesn’t turn funny colors when your fingers sweat on it (of course, your fiancé doesn’t sweat; horses sweat, men perspire and ladies glow). It’s a noble metal. So why isn’t that 6s electron blowing newly engaged fingers and rappers’ heads into kingdom come?

Because it’s slumming with the s electrons in lower orbitals. Because its orbital is contracted inward, the probability (quantum mechanics is all about probabilities) that gold’s 6s electron will be found consorting with 5s and 4s electrons is much higher than it should be, so that 6s electron is shielded from having to interact with electrons in the molecules of air and water.

It’s relativity that makes gold golden, and relativity that keeps it pure.

We might also add that it’s relativity that makes gold even denser than fruit cake. Gold’s electrons are contracted inward, so a gold atom (element 79) is about the size of a cesium atom (element 55). It packs a lot more mass into the same space. Relativity isn’t the only reason for this contraction; something called the “lanthanide contraction” and “de-shielded” f electrons plays a role. So we’ll say that relativity is responsible for the fact that gold is beautiful and pure and pretend that blame for its substantial weight lies elsewhere.

By the way, the golden color of gold can help explain the color of the sky and the sun and why, if you hold a fine sapphire over a piece of white paper on a sunny day, the light that hits the paper will be golden. But that’s an explanation for another day.

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Jim Picht
James Picht is the Senior Editor for Communities Politics. He teaches economics and Russian at the Louisiana Scholars' College in Natchitoches, La. After earning his doctorate in economics, he spent several years doing economic development work in Moscow and the new independent states of the former Soviet Union for the U.S. government, the Asian Development Bank, and as a private contractor. He has also worked in Latin America, the former USSR and the Balkans as an educator, teaching courses in economics and law at universities in Ukraine and at finance ministries throughout the region. He has been writing at the Communities since 2009.