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Roger's Equations

This blog is all about science and technology (with occasional math thrown in for fun). The goal of this blog is to try and pass on the sense of excitement and wonder I feel when I read about these topics. I hope you enjoy the posts.

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Gold: The Noble Metal by Roger Pink

Posted February 03, 2014 5:47 PM by Bayes

"...as my eyes grew accustomed to the light, details of the room within emerged slowly from the mist, strange animals, statues, and gold - everywhere the glint of gold. For the moment - an eternity it must have seemed to the others standing by - I was struck dumb with amazement, and when Lord Carnarvon, unable to stand the suspense any longer, inquired anxiously, 'Can you see anything?' it was all I could do to get out the words, 'Yes, wonderful things."

― Howard Carter, Tomb of Tutankhamen

King Tut

What British archaeologist Howard Carter was gazing upon when he uttered those now famous words was the intact Tomb of Tutankhamen, 11th pharaoh of the 18th dynasty of ancient Egypt. The tomb consisted of the mummified remains of a 17 year old boy-king surrounded by priceless artifacts, most of which were made of gold.

In 1922 when this discovery was made, it quickly became a worldwide sensation. People couldn't get enough of the boy pharaoh and his magnificent treasure. How was it that the tomb had escaped grave robbers for 33 centuries? Who was Tutankhamen? Why did he die so young? Of course the one thing no one asked was "Why was the pharaoh surrounded by gold?". Everyone understood that.

It's simply understood that gold was/is valuable. Of course someone powerful like a Pharaoh would be surrounded by gold. But that raises an interesting question. Why do we take for granted that gold is valuable? Why has it always (as far as we can tell) been a symbol of wealth? Is it because it's easy to work with? Is it because it shines and is rare? Is it arbitrary?

I think ultimately the answer has several parts. It doesn't hurt that it's relatively scarce on the Earth's surface. It doesn't tarnish or corrode, so in an impermanent world, it lasts. It can be combined easily (melt it). It's malleable, and so can be worked to produce jewelry (humans have been adorning themselves with jewelry for 100,000 years). It's shiny (high luster). In short, it has a lot of properties humans find appealing.

So where do these properties come from? And why haven't metals with similar properties been embraced like gold?


Noble Metals

The electron configuration of Gold is [Xe]4f145d106s1. Let's ignore the [Xe] and concentrate on the last part. 4f14 means that there are 14 electrons in the f subshell of the 4th electron shell. 5d10 means there are 10 electrons in the d subshell of the 5th electron shell. Finally 6s1 means there is 1 electron in the s subshell of the 6th electron shell. The subshells s,p,d, and f can respectively hold 2, 6, 10, and 14 electrons. So if there are 14 electrons in an f subshell, it is considered "full". We'll come back to that in a minute, but first let's look at that [Xe] in the front of the configuration and try to understand what it means.

Xe is the symbol for the noble gas Xenon. [Xe] is a way of truncating the notation for an electron configuration. It basically means that the orbitals are filled up completely to Xenon's electron configuration (see on left). That symbol [Xe] represents the inner electrons and everything after it (in the configuration) are the valence electrons.

In chemistry the inner electrons are far less important than the outermost (valence) electrons. The six elements displayed on the left have completely filled subshells and are known as the noble gases. Noble gases don't react much at all except under extreme conditions. This is because they are perfectly happy with their filled shells and have nothing to gain through a reaction. You see, reactions happen because an atom is trying to fill a valence subshell.

Think of it this way. Imagine you're spinning and wobbling and you see someone else spinning and wobbling. You two reach out and clasp hands and suddenly neither wobbles anymore! Now imagine you are not wobbling and any time you reached out and clasped hands you started wobbling. Obviously you wouldn't want to clasp hands but rather keep to yourself (the goal here is to minimize wobbling). That's a huge simplification of why the outermost shells of an atom want to be filled*, but hopefully it gives you a little intuition. To put it in more scientific terms, a filled valence subshell, even if it means the atom has to share it's valence electrons with another atom, is a lower net energy arrangement for the system of atoms then just standing around with unfilled electron subshells next to each other. Since nature loves to minimize the energy of a system (when it can), atoms with unfilled valence subshells will react to fill them. Atoms with filled valence subshells will not react.

Back To Gold's Configuration

So there is gold, [Xe]4f145d106s1, filled f-subshell, filled d-subshell,...but wait! What about its s-subshell? That's one short of being full! Why doesn't gold react with other atoms to try to get rid of that electron so that it only has filled valence subshells, like an Alkali metal would? The answer is simple (and very complicated). Basically it is harder to remove an 6s electron from gold than it is a 5d electron due to screening effects. So all any other atom trying to react with gold has to work with are the 5d electrons, and that subshell is full (and thus wants to be left alone). As far as other atoms are concerned, gold looks chemically like a noble gas!

What is screening, you may ask? I'll try to explain electron screening in a basic way (avoiding the quantum rabbit hole). Just picture an atom as a positive nucleus surrounded by shells (1,2,3,4) of electrons that orbit it. These shells aren't really nice, well defined circular shells, but more like average orbital distances for the electrons which get really close to the nucleus and really far away too.**

The shape of the orbits that the electrons follow depend on their subshell type. For instance s-subshells get closer to the nucleus than p-subshells. The closer an electron gets to the nucleus, the less electrons there are in between that electron and the nucleus. Since electrons are negatively charged, the more electrons between an electron its nucleus, the less strongly charged the nucleus appears to that electron (the negatively charged electrons in between are "screening" the positive charge of the nucleus). Now without screening it's simple. The closer the electron is, on average, to the nucleus, the harder it is to remove the electron from the atom. So all other things being equal, pulling an electron from the 6 shell should be easier than pulling an electron from the 5 shell. HOWEVER, since 6s electrons get closer to the nucleus than 5d electrons, they experience less screening and thus "feel" the positive charge more, making them harder to remove even though they are slightly farther (on average) from the nucleus. This screening versus average radial distance competition for electron binding to an atom is why a 6s electron in Gold is harder to remove than a 5d electron. In fact, the larger the noble metal, the more powerful the screening effect, the less reactive it is!

Silver has an electron configuration of [Kr]4d105s1 and is also a noble metal. Once again, atoms from the outside see only a nice full 4d shell and move on thinking they've met a noble gas. Copper, [Ar] 3d10 4s1, is another noble metal.

It's important to remember that all noble metals are not created equal. Since electron screening is the key to making that single s subshell electron difficult to remove, the larger the atom, the more dramatic the screening effects (more electrons to screen the nucleus), the more noble the noble metal. Gold has the most electrons and thus the most screening effects on its valence electrons. It therefore is the most resistant to reaction (among the noble metals).

The Value of Gold

The ancient Egyptians of course didn't know all this chemistry. They simply noticed that over time gold tended not to react. Also gold tended to be more scarce, not being able to bind with lighter elements to keep it floating on the Earths crust, most of the gold (and precious metals in general) were pulled down to the core by gravity while the Earth was forming. In fact, there is a school of thought that believes that most of the gold and other precious metals found on Earth's surface were brought here by meteorites after the crust cooled.

However it may be that Gold made its way onto the Earths surface, once found, gold was prized by humans. For thousands of years it has been coveted and fought over. Gold and Silver discoveries have shaped the fate of nations, from ancient Athens to age of discovery Spain to the modern Unite States. This is not likely to change anytime soon. The value of gold is in its chemistry

Notes

*Filled subshells are spherically symmetric and have a total angular momentum of zero.

**If you're having trouble visualizing how something with an average orbital distance further away from the nucleus can sometimes be closer to the nucleus, picture the classical orbits of a comet and a planet. A comet has a very elliptical orbit, so it gets very close to the Sun and also very far from the Sun. A planet generally has a near circular orbit and doesn't vary too far from it's average orbital distance. A planet (Earth) can have an average orbital distance much closer to the Sun than a comet (Halley's Comet) and yet be further away from the Sun at times. Got it? Great! Now forget it, because Electron orbitals are quantum mechanical.

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#1

Re: Gold: The Noble Metal by Roger Pink

02/04/2014 9:35 AM

Thanks for this thoughtful blog.

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The curiosity of gold seems to go far beyond the relatively high price it commands. Anything with sufficient demand perceived as critically limited in supply can command high prices.

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The ubiquity of gold use across cultures throughout recorded history is interesting. An interesting exception were native North Americans who considered it close to worthless.

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Until recent times, the choice to use gold was almost exclusively a preference rather than a requirement. This substitutability makes it all the more puzzling that gold could be so consistently highly valued throughout history (with the exception of one extended period in ancient Egypt resulting from the Malian Emperor giving away so much gold as he traveled through on his way to Mecca, that prices were severely depressed for a decade) yet existing in sufficient abundance across the world to be widely used in so many different cultures.

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It turns out the estimated total amount of gold humans have since we began pulling it out of the ground is around 165,000 metric tons. That is a little over 3/4 of a troy ounce per living person currently. I have no idea how correlated population and total mined gold have been over time, but that does seem to be an amount that would be sufficiently rare (high pricing) and still allow use to be widespread.

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The blog touched on the idea that being malleable might factor into the value we place in gold. Pure gold does not work harden appreciably and is the most malleable metal. I find it interesting that pure silver, also enjoying ubiquitous high value, is also very malleable. It seems to be a common trait among metals valued and used for coinage, even though it is necessary to alloy with other metals to reduce that very trait when minting coins.

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One part of the blog stirred some thoughts that didn't settle. I'm hoping an explanation might help me out of my mental predicament....

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....The explanation of low reactivity of large nucleus noble metals due to variation in screening effects is a good one, but it raises a big question. If the 6s electron is so difficult to remove, and the shell-full 5d electrons aren't budging, why is gold shiny and why does it conduct electricity with low resistance?

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"All that glitters is not gold, but at least the electrons are free"

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So which is it? Are the electron relatively free....floating around in a sea of their brethren all shiny and conductive? Or are they held close to the vest, not all that sea-shiny or free? Or have I introduced a false dichotomy?

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#11
In reply to #1

Re: Gold: The Noble Metal by Roger Pink

02/06/2014 3:15 PM

So no one is taking a stab at an explanation, not even any guesses?

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"....The explanation of low reactivity of large nucleus noble metals due to variation in screening effects is a good one, but it raises a big question. If the 6s electron is so difficult to remove, and the shell-full 5d electrons aren't budging, why is gold shiny and why does it conduct electricity with low resistance?

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"All that glitters is not gold, but at least the electrons are free"

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So which is it? Are the electron relatively free....floating around in a sea of their brethren all shiny and conductive? Or are they held close to the vest, not all that sea-shiny or free? Or have I introduced a false dichotomy?...."

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#2

Re: Gold: The Noble Metal by Roger Pink

02/04/2014 5:02 PM

One thing that we were never taught, but I found out in recent years is that an "s" electron has a finite chance of passing right through the nucleus. The shape of the s-orbital is "solid spherical" and not just a simple sphere as we were taught. Therefore an "s" electron can be anywhere in that solid sphere, including the nucleus.

Perhaps this explains the "K-electron capture" mode of radioactive decay, where an inner electron is captured by the nucleus and combines with a proton to form a neutron, this become the next element down, although keeping the same atomic weight.

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#3
In reply to #2

Re: Gold: The Noble Metal by Roger Pink

02/04/2014 8:41 PM

".... electron ......combines with a proton to form a neutron and an electron neutrino, this become the next element down, although keeping the same atomic weight mass...."

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#5
In reply to #3

Re: Gold: The Noble Metal by Roger Pink

02/05/2014 3:58 AM

Yes, I knew about the various radiations involved having spent a large part of my working life in x-ray fluorescence spectroscopy, but wanted to keep it simple. One of the standard x-ray sources for a simple benchtop xrf analyser is Fe-55, which decays to Mn-55 by K-electron capture, with the emission of the Mn K-alpha and K-beta lines. These are used to excite the lighter elements.

Furthermore, I have carried a piece of it my pocket on a number of occasions, suitably housed in a lead container, of course. We used it to set the zero and gain of the pulse processor, so that the x-ray photon energies measured were put into the appropriate memory location in the computer.

P.S. The term "atomic weight" is still used. Are we getting a bit nit-picky?

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#6
In reply to #5

Re: Gold: The Noble Metal by Roger Pink

02/05/2014 4:48 AM

I'm familiar with Fe-55 from a different perspective, as it is one of the major activated corrosion products of concern during shutdown maintenance. In practice precautions necessary for Co-60 gammas always overshadowed everything else.

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I don't really consider correcting 'atomic weight' to 'atomic mass' picking nits. It was really just a friendly reminder that these are distinct terms. 'Atomic weight' refers to the weighted average of the atomic masses of the various isotopes as they naturally occur (or as is prepared). 'Atomic mass' was the appropriate term to use in the description you provided as you were referring to a process occurring in a specific isotope.

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In actuality, I worried that both my comments were on the nit-picky side.... So I am relieved to find that you are someone with some working knowledge of the subject..... doesn't seem like I was picking nits in the least to me now.

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#4

Re: Gold: The Noble Metal by Roger Pink

02/04/2014 11:12 PM

Roger, you've set a new gold standard for CR4 articles.

"It doesn't tarnish or corrode, so in an impermanent world, it lasts."

The Egyptians were looking for imortality. The gold, because it doesn't tarnish, may have been part of their religion superstition.

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#7

Re: Gold: The Noble Metal by Roger Pink

02/06/2014 10:08 AM

One of the things that makes gold, silver, gems, etc. have a higher value is that they are not easily produced and therefore the supply is more constant and predictable.

Unlike the fiat money we now are using as the U.S. Dollar. It is decreasing in value because the only reason it has value is because we say it does. Since FDR took the US off the Gold Standard in 1933 our money has gradually become less valuable because our illustrious government can print "money" willy-nilly as they see fit. It therefore becomes "fiat" money since there is no backing for it's value, other than that we say it has value.

It is like the "Bitcoin" scam that has begun here in the US or when Ghenghis Khan moved into some country he had overthrown and declared that some item/paper/bead, etc. had value and that was the only way commerce took place. Another example of this is the Continental Dollar during the Civil War. The Continental Congress decided they would issue the "Continental Dollar" as payment for goods and services, since they didn't have enough hard currency to pay their obligations. They increasingly printed more and more, driving the value down. Hence the term, "not worth a Continental". Sound familiar in these days? Our buying power is dropping like a rock because the current government of bho and like-minded liberals on both sides of the political aisle have no concept of economics.

We need to return to the Gold Standard for the economic well-being of our country. This would also place a limit on the government to spend without boundry.

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#8
In reply to #7

Re: Gold: The Noble Metal by Roger Pink

02/06/2014 12:30 PM

"....Since FDR took the US off the Gold Standard in 1933..."

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...wait 1933, FDR? Why would you point at FDR?

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Oh, okay, I think I understand. It is because he is a Democrat oh wait, I mean, liberal:

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"...the current government of bho and like-minded liberals on both sides of the political aisle have no concept of economics..."

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How positively slippery of you. Really quite clever. Similar to the way some people will defend their use of a racial slur by claiming that any ethnicity (even their own!) might be properly described by the slur... yet your version is much more high class.

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The really clever part is that it demonizes all the Democrats by the strong correlation and yet protects itself against the obvious rebuttal using the myriad of examples demonstrating similar Republican propensity, as each Republican example can not be conveniently thrown under the bus as 'a like minded liberal' who just happened to leak over the aisle.

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I have actually pretty much given up on my effort to maintain the useful original definition of 'liberal'. I understand that to a huge block of the population it now means something along the lines of "gay urban tree-hugging effeminate communist-sympathizing hippy socialist neo-euro puppy-hating fetus-eater". Sad.

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Just because I am admitting a lost cause for that term, doesn't mean I'm throwing the towel in on all definitions. Lets look at one in particular:

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Gold Standard: a monetary standard under which the basic unit of currency is defined by a stated quantity of gold.

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Hmm. I bet even a belly-slithering, fetus-eating liberal could figure out the problem with claiming FDR took the US off the Gold Standard in 1933....especially since the actions taken in 1933 required the exchange of gold for currency at a stated quantity of gold.

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It was in fact the right honorable Republican Richard "I am not a crook" Nixon who took the US off the gold standard.

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Okay, here is the funny part. I believe a move back towards the gold standard could be beneficial. In an of itself, it doesn't necessarily provide further constraint to government spending without limit (We can discuss this if you want. Consider financing based on future tax revenue). It may provide some cushion against the massive devaluation looming that will result from the US dollar loosing de facto status as world reserve currency.

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Another funny part is that I tend to agree with more of the Republican party claimed ideals than those claimed by the Democratic party. Of course, 'claimed ideals' don't seem to be a very consistent predictor of action these days. I hesitate to call myself a 'conservative' because with the convenient rapid redefining of 'liberal', I can't shake the feeling I'm leaving myself wide open unfortunate associations (One example would be related to the common misconception that Rush Limbaugh is a conservative, when he is not. Rush is the quintessential buffoon, which is a political ideology at odds with much of true traditional conservatism.)

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Still, I can't help but speak up when the facts are being so clearly distorted.... It also makes me question my preference of those political ideals.... have I really analyzed things properly if I find myself more aligned with the group who cannot resist/refrain continually making vilifying ad hominem attacks and engaging in shameless factual/historical distortions?

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#9
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Re: Gold: The Noble Metal by Roger Pink

02/06/2014 2:32 PM

The "axe that I have to grind" is with any politician who does things that hurt the freedom in this great country of ours. It isn't a Repulican, Democrat, Libertarian ideology that I am a proponent of. There is hardly a dimes worth of difference between most of them. We don't have Statesmen anymore, we have politicians who have forgotten what they are to be doing in their positions of power. There are precious few leaders for "We the People".

I am a proponent of conservative ideology in regard to Constitutional Law, economics, Natural Law, free enterprise, the judiciary doing what the Constitution has established. When there are the proper checks and balances and divisions of power and responsibility between the 3 branches of government the citizenry will have a fighting chance to succeed for the long run.

I wasn't throwing rocks at FDR when I said he discontinued the Gold Standard, I was just relaying history. "The gold standard effectively came to an end in 1933 when President Franklin D. Roosevelt outlawed private gold ownership (except for the purposes of jewelery)." It could just as well have been someone else who did it as well. What Richard Nixon did was take away the ability to trade currency for gold. That is also wrong action.

The rest of my comments about fiat money, i.e. Genghis Khan, the "Continental Dollar", Bitcoins and what our, OUR, government is doing are correct. They say something has value but there isn't anything to back it up, to hardly any degree at all. We have little gold, precious metal to back up our currency. There certainily is no "reserve".

I have no idea how you construe any comment I made into some "racial slur". Good economic principles of economics have no race, gender or creed. "How positively slippery of you. Really quite clever. Similar to the way some people will defend their use of a racial slur by claiming that any ethnicity (even their own!) might be properly described by the slur... yet your version is much more high class."

Like I said earlier I am not a Republican, Democrat or Libertarian. I am an American who only wants to see us survive as a great nation. Part of the way that happens is through sound economic principles that give all of our citizens a fighting chance without government jackboots on our necks.

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#10
In reply to #9

Re: Gold: The Noble Metal by Roger Pink

02/06/2014 3:08 PM

In retrospect, relating your comment to a racial slur was inappropriate. I apologize.

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I probably over reacted to your use of the term 'liberal'. So often, that term is thrown around as a slur by people who on closer inspection have trouble providing a decent explanation of how the values of someone deserving that description might differ from their own.

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I misjudged your comment as veiled partisanship. You are clearly someone who hasn't fallen for the 'no we are really two different parties, come get emotionally vested with us by hating them' trick foisted on so many.

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Giving your original and follow up comment a fresh read without the burden of thinking you were someone parroting the 'evil dem lib' AM talk radio conditioning, I don't disagree with any of your points.....with the exception of what exactly defines the gold standard (and the end thereof), which, in the grand scheme, isn't critical.

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