Relativistic Effects In Your Wedding Ring

Gold wedding ringsBoundaries between academic disciplines are like borders between European countries. They’re crossed without blinking. You can’t understand what’s going on in your gut without knowing its chemistry, and gold’s properties make little sense without considering special relativity.

Gold is in the same periodic table family as copper and silver, but while its siblings form patina and a dark tarnish, respectively, gold retains its characteristic color in the presence of either smog or sea spray. Less known is the fact that gold can actually mimic chlorine’s relatives and forms salts with rubidium and cesium metals.

Some scientific ideas are greater than others. Like loved ones, they can be old but resurface in a different context to enlighten you. Who hasn’t been wowed at least a few times by special relativity? For instance, it has to be taken into account by engineers designing GPS systems. But there are even more tangible relativistic effects happening right now in something as prosaic as a gold ring. In heavy atomic nuclei, the strong coulombic force has a significant effect on the velocity of inner electrons. Close enough to that of light, electrons’ speed increases their mass, enough to contract the Bohr radius. Specifically, gold’s innermost electrons move at 58% of the speed of light, and instead of the typical < 0.01c and ensuing negligible rest mass-increase for a hydrogen atom’s electron, there is a 23% increase in mass for a gold 1s electron. Although the relativistic effect doesn’t affect all types of atomic orbitals, it draws all orbitals closer to the nucleus, including gold’s 6s orbital, where its valence electron resides. If the relativistic radii for various atomic numbers are plotted, we notice that gold is the most affected in the entire periodic table.

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The ratio of the relativistic radius for 6s orbital to the non-relativistic radius. Au is the most affected.


Gold’s 79 electrons are configured as such: [Xe]4f145d106s1. If it wasn’t for relativistic effects, there would be a bigger energy gap between the 5d level and the Fermi band at the 6s orbital. An excited electron would absorb in the ultraviolet. But instead as the 6s orbital is pulled closer to the nucleus and the 5d electrons are shielded and brought closer to the 6s, there’s a strong absorption in the blue and violet, leading to the beautiful blend of red and yellow we perceive as gold.

It takes energy to remove an electron from an atom, so if an electron is instead returned to an atom, energy will be released. The latter is known as electron affinity. With a half-filled orbital that’s more attracted by its nucleus than usual, gold has a high affinity for electrons, sharing something in common with with the halogens(see graph). It explains not only the existence of compounds like RbAu but of a more recently created one like Rb5Au3O. Both of these feature the gold (-1) ion, an unusual charge for metals.electron-affinity-page_4-feb-2013

If you have a conventional mercury(Hg) thermometer, you can also watch special relativity impact gold’s period-6 neighbor. With one more electron than Au, Hg’s 6s orbital is filled and because it’s also tightly held due to relativity, the electrons don’t flow as easily from one mercury atom to the next. This weakens metallic bonds, rendering mercury a liquid at any temperature above -38.4 oC.

Thallium is next to mercury on the periodic table. Although the relativistic effects are a bit less pronounced, as shown in the first graph, the 6s2 electrons are still jealously guarded, so to speak. In most cases only the 6p1 electron is lost, which is why thallium salts, formerly used as rat poisons, are typically in a +1 oxidation state. This makes thallium the black sheep of its family. Other members including aluminum and gallium normally form compounds containing +3 ions. Interestingly, before thallium ions do their mysterious damage, they get through cell membranes by serving as K+ -impostors, thanks to their single positive charge and similar ionic radius.

In 2011, a pharmaceutical chemist who allegedly was more interested in the relativistic effects of thallium than in those of her wedding ring, sneaked a Tl compound out of her lab and poisoned her husband. She was arrested after her flight to China was delayed, not by a relativistic effect but by a snowstorm.

For relativistic effects in Pb see Focus: Relativity Powers Your Car Battery


RJ Hoffman. Thallium toxicity and the role of Prussian blue in therapy. Toxicological Reviews. http://www.ncbi.nlm.nih.gov/pubmed/14579545
Lars J Norrby. Why is Mercury a Liquid. Journal of Chemical Education
http://voh.chem.ucla.edu/vohtar/fall02/classes/172/pdf/172rpint.pdf

Geoffrey Bond. Relativistic effects in coordination, chemisorption and catalysis

M. Concepción Gimeno. The Chemistry of Gold. 

Image from http://exagger-art.artistwebsites.com/featured/albert-einstein-art.html

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Wasp On Deck Applied Physics

Two summers ago, I was eating fruit in the sun when I noticed that a wasp had found a fragment of my pear on the deck. The piece was only about a centimeter cubed in volume but heavy enough to prevent the wasp’s takeoff. Soon after its unsuccessful straight-up takeoff attempts, the wasp dragged the little pear morsel across the deck for about two and a half meters until it reached the edge. Once off the deck, the wasp was able to fly away with its meal.

By observing the wasp, I was reminded that anything trying to take off vertically needs a lot more of its own force to get off the ground than to propel itself in flight. (When flying, the circulating air mass around the wasp helps it overcome gravity.) A study (Dial, Kenneth B. J. exp. Biol. 176, 31–54 (1993)) done on the liftoff force generated by pigeons concluded that the birds had to develop, in using their legs and a clap and fling mechanism, an upward directed force as high as 2 to 3 times their body weight.

I could not find anything on insects, but let’s assume that a wasp is also capable of developing an upward force of up to two to three times its body weight. The mass of the pear is somewhere between 0.6 and 1 gram (the pear is mostly water with a density of 1g/cm3). But the average mass of a wasp is only about 90 mg. Even if it could generate an upward force three or even five times its weight, it would still fall short of the force needed to directly ascend upwards with my pear.

With rotary motion which is more efficient than the mechanism of birds and insects, helicopters also takeoff vertically. The largest cargo helicopter, the Mi-12, has a maximum takeoff weight of 231 500 lbs. But the Antonov An-225 Mriya, which like most planes takes off at an angle slightly raised from the horizontal, has a maximum takeoff capacity that’s about six times bigger.  With the pear, the wasp failed to take off vertically, so it turned my deck into a runway.

It’s interesting how the wasp first tried to takeoff in its usual way, which is a practical strategy when it has to fly off a flower or off a paralyzed insect whose fluids it has sucked away. But what went on its brain as it solved the problem of how to fly off with a heavy meal?

It’s no wonder that parts of their brain grow in size after they are repeatedly engaged in complex tasks. Wasps have also been known to pick up competitors(ants) who were eating their food, fly off with them and then dropping them at a distance. Since the ants are much smaller in size, the wasps, in this case, don’t have to combine their airlift behavior with a runway-strategy.

Other Sources:

http://www.airplanedesign.info/53-vertical-takeoff-and-landing-airplanes-vtol.htm

http://www.gizmag.com/skyhook-and-boeing-team-up-to-build-the-worlds-largest-vtol-cargo-aircraft/9618/

http://www.usnews.com/science/articles/2009/10/16/the-tiny-but-adaptable-wasp-brain

http://www.dailymail.co.uk/sciencetech/article-1371624/Angry-wasps-airlift-ants-away-food.html

Hey, Don’t Disrespect Galileo!

An article about Galileo in io9 makes the tiresome and unoriginal argument that if Galileo had been a little more tactful, his former friend, who later became Pope, would have continued to tolerate Galileo’s heliocentric views. The article is entitled “Did Galileo get in trouble for being right, or for being a jerk about it?” Two years ago an article in Discovery magazine made a similar point, also by using the “jerk” word.

But what you have to understand that one reason we celebrate Galileo’s contributions is because Galileo was very good at self-promotion. He published his drawings, while Harriot did not. Of course, Galileo’s self-image is what got him into so much trouble later in life. He went way out of his way to insult the Pope and the Church, and was pretty much a huge jerk about it.

In the same way that it’s nonsense to tear down effective politicians for infidelity, it does not do the world any good to take shots at the icons of science. If he was an untactful, self-promoting white European male, so what? He may not have been the inventor of the telescope and maybe not the very first to aim it at the moon, but he was the first to make extraordinary use of the instrument by noticing that four little moons were circling Jupiter and not our presumed center of the universe. His mind was analytic and creative enough to think of projectile motion has having a gravity-affected vertical component and a constant horizontal motion. Despite his unsuccessful attempt to disguise his friend’s (and who knows who else’s?) Aristotelian arguments with the “Simplicio” character in his dialogues, they still involved brilliant thought experiments such as:

Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object. But the system considered as a whole is heavier than the heavy object alone, and therefore should fall faster. This contradiction leads one to conclude the assumption is false. Wiki

The io9 author concludes by writing,

The Pope, still smarting, resisted all efforts to end Galileo’s house arrest, even towards the end of the man’s life. He also demanded a public renunciation, during which he probably smiled and muttered, “Who’s Simplicio now?

Nice try, but I still sympathize with a nearly blind and brilliant guy who was at the mercy of a vain leader of a tyrannical organization.
Galileo

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