S04E17: The Toast Derivation

Tonight Sheldon told us a story.  But by knowing a little physics you can try to adapt it to profit from gold.


Can we use physics to make gold more valuable?

Over 2000 years ago, Archimedes was challenged to find out if a crown fabricated for the King of Syracuse was 100% gold, as paid for.    Gold was the densest and most valuable element known to ancients.  So, the story goes,  Archimedes knew that of all known substances, pure gold would displace the least amount of water than any other substance of equal weight known to man.    A given volume of gold, has a mass nearly twenty times (19.3) that of water.

Had the crown been alloyed with silver, a less valuable metal, the same mass would displace more water.   If the goldsmith had replaced only 10% of the crown’s mass with silver, he stood to keep a lot of valuable gold for himself.  But by volume silver only has a mass of ten times (10.5)  that of water.  The crown would displace 10% more water than the same weight of pure gold.

Now in modern times, gold is no longer the densest metal.  We could choose other materials more dense than gold to fool the king, or whoever is buying our gold.   For example, osmium is the densest known element found in the Earth’s crust, but was only discovered in 1802 and was unknown to Archimedes.  It displaces 10% less water than the same mass of gold.

By mixing an alloy of osmium and silver  and gold (or some other metal) you can remake your jewelry with precisely the same density as gold.   Then go down to your local motel where someone is buying gold and cash in.     But there’s a catch.   Osmium is one of the least abundant elements in the Earth’s crust.  It costs almost as much as gold.     Given that Osmium is rarer than gold, maybe you are better off holding onto the osmium anyway.

Artificial elements have an even higher density than osmium so maybe they will work a little better.  Mix in a little plutonium into your gold and you are good to go.    Except that plutonium is one of the  most toxic substance known to man.   Ingest even a small dose and you will die of radiation poisoning.   Try to store more than about 10o ounces for this purpose in one place–if you could even find it– and you have a critical mass that will produce enough neutrons to kill you.

Don't bother alloying plutonium into your gold.

Unfortunately all the dense artificial elements are radioactive.  If they weren’t then they would be found naturally.

Besides all of this would be illegal, or at least fraudulent, so is unsportsmanlike.   If you represent your jewelery as pure gold, or some purity gold, and it is not, you are just stealing.  You may as well not go to so much trouble and just become a burglar.

All of which leads me to a potential honest and legal version of this manipulation.    The atoms of the basic elements are labeled by how many protons they have in their nuclei.  You can add neutrons to their central nucleus and leave their chemical properties essentially unchanged.  Elements with different numbers of neutrons are called isotopes.  For example, iron has many isotopes, but they are all legally, chemically, and  truly iron.

So what about gold?  Why not take the  gold reserves in Fort Knox and the Manhattan Federal Reserve Bank of New York to Oak Ridge National Laboratory and irradiate them with a neutron flux?   As the gold atoms absorb neutrons they would become heavier, and more valuable.   The weight of gold in atomic units is 197 and adding even one neutron would make it 198.   That’s a 0.5% increase in value in the 8000 tons of U.S . gold reserves alone.    A rate of 0.5% is not a bad overnight return 250 billion dollars.  This achieves a version of the dream of the alchemists: turning gold into gold.

Meanwhile the U.S. national debt is 14 trillion dollars.  Our money supply (M2) is 8 trillion. Compared to that,  a quarter trillion dollars of gold is loose change.   The US holdings in gold could never back our currency 100% and would not even fill an Olympic-sized swimming pool.  To those who lament leaving the gold standard, as someone we know might say:

“Your argument is not with the Federal Reserve System, it is with basic mathematics.”

The idea of turning gold into gold could net the US a billion dollars overnight.   I’d be happy with just a 1% commission for the idea.   But again, there’s a catch.  Unfortunately gold only has one stable isotope.  No other isotope of gold has a half-life of longer than an hour, not enough time to sell it.  Meanwhile some of those neutrons would turn gold into lesser valued elements such as bismuth.

And that’s the nightmare of the alchemists: turning  gold into bismuth.

17 Responses to “S04E17: The Toast Derivation”

  1. CK Rock Says:

    My wife and I laughed through the whole article. Well done!

  2. Arturo Quirantes Sierra Says:

    You’d have to substract many expenses from that billion $ gain: transportation, irradiation, power bill, security …

    “Unfortunately all the dense artificial elements are radioactive. If they weren’t then they would be found naturally.”

    Are they? I’m now thinking about iridium, for example. Or even better: tungsten. It has the same density as gold, so it could perfectly replace it. In fact, there’s a rumor, conspiracy theory, or whatever, that some gold bullion has been found to have a tungten core.

    Didn’t anybody think of that? I mean, when you read the price of gold in the WSJ, does it refer to any particular isotopic ratio? Is there any standard about it, so the people buying and selling gold know exactly with kind of gold they’re talking about?

    • David Saltzberg Says:

      Iridium is the scarcest element, but still it does have some natural abundance in the Earth’s crust (1 part per billion) so I didn’t call it artificial. Its cost is similar to osmium which is about 1/4 the price of gold right now. So technically the would work for the fraud, but probably the price of gold is inflated artificially and the rarity of iridium and osmium means they ought to be more valuable and you might regret it later.

      Tungsten is still a little less dense than gold (19.25 vs 19.3) so in principle the fraud could still be detected. You could probably fool one of those gold buyers in a motel room.

      There is no need to worry about the isotopic ratio of gold you buy, since there is only one stable isotope. All gold bullion is 100% 197-Au.

  3. Lorenz Cuno Klopfenstein Says:

    Great post! :)

  4. Zig zag zug Says:

    Wows! I read a heavy book on this once! It was strange!

    In it, Isaac Newton was big on measuring gold! He was Master of the Mint in England. Gold, being a soft metal, can actually be dented by biting it! So people, to make coins, added lead to harden them. You wanted a very hard toffee so you could tell how pure a coin was by biting it. This was a rough test of the coin’s purity. If pure, the coins could then be circulated around in great currents of currency. To quote the great sage Homer S: Money can be exchanged for goods and services!

    Naturally, everyone then tried to game the system! You melt gold coins down, and add stuff to keep the same weigh! Which lead (hehe) to tasting… err… testing… metals, ever more accurately. In the book, Stephenson wonders if that’s how people started getting suspicions about isotopes! Metals of identical properties but different density messing with the weight of coins! If you could shave even 1/10 of gold off a coin, that’s a good profit!

    For example, by replacing all the lighter lead in the coin with a heavier lead isotope! For every 204 lead atom, we put a 208! That saves us 4 atomic necleuses! Gold has 197, so we need to replace 197/4= 49.25 atoms of lead 204 to swindle 1 atom of gold away.

    Same weight, but less gold. ^w^

    But if that 1st book is too big, you can always read Making Money by Terry Pratchett. In it, Moist von Lipwig, a professional thief/banker wants to make people rich by taking all their gold!

  5. tudza Says:

    Zig Zag, Newton would have been more concerned with silver during his time at the mint.


    You know, I don’t think the toast derivation is correct.

    • Zig zag zug Says:

      omgggg! Imma read that! “Financial engineering”? Oooh. But yeah! Also, be careful about thinking! You might actually be talking about feeling, which we must banish hither to the most hoary of nether regions! In other words, prove it! >:3

      err… some gold half lives are over 1 day, such as with 199 Au. http://en.wikipedia.org/wiki/Isotopes_of_gold
      Or it it the atomic units != weight of atom? That’s just approximation! Like in horseshoes, close is good enough.

      But the real tricky bit is getting people to buy radioactive, lead filled gold. :D

  6. Top 5 Things I Learned This Week… » New Sense Says:

    […] Gold only has one stable isotope and no other isotope of gold has a half-life of longer than an hour – Which is one of reasons why gold is considered as one of the best measures of money – S04E17: The Toast Derivation […]

  7. Zig zag zug Says:

    I think I know who can help with your differentiel eq. app recognizer!!!!
    Maple has a handwriting symbol finder! Sketch a rough symbol, and it gives you a close guess to it. I can’t get it to recognize my pi, but it’s still a good start!
    Ask the Maple people to make a Maple app for handwriting! ^___^
    I will try and email them also, but I am hard to take seriously. ;_;

  8. acrode Says:

    “No other isotope of gold has a half-life of longer than an hour” ?

  9. TBBT第4季17集:祝酒词的来历 Says:

    […] 原文看这里 […]

  10. Robert Q Says:

    So it won’t work for gold because there’s only one stable isotope. But could this practically work for other precious metals with more than one stable isotope? Say turning the common platinum 194 or 195 into the rarer 198? That’s a whopping 2% return on investment! Plus, platinum is worth more per kg than gold, so it’s an even better investment!

    A little math:

    Quick google research suggests there are 6.5 million ounces of platinum in reserve, all of which can apparently fit in an average living room due to its density (so getting a substantial quantity into enough space for a practical neutron bombardment wouldn’t be impossible). At $1800/oz for platinum, that puts the world’s supply at $11.7 billion. A 2% bump then would net us $234 million.

    So back to my original question, can such a procedure be performed on that much platinum and for less than $234 million, making this a profit-making possibility? If doing it for the world’s platinum reserves is possible, what % of that would someone need to hold at one time to do this to be profitable at all? 11% (Russia)? 80% (South Africa)?

    Great blog!

    • David Saltzberg Says:

      Shhh. You are giving away my idea.

      • Robert Q Says:

        Haha. I was actually just curious how much it costs to add neutrons to things, as I have no idea, but I promise I won’t steal your idea, at least until I get my hands on $11.7 billion.

  11. Shaun Says:

    Good luck but the costs of doing this are outrageous, thats why its hasn’t been done, lol

    Not to mention if you get audited and find out its been messed with, you go to jail, not fun.

  12. Galen Pickett Says:

    So, now the plot of Goldfinger makes a bit more sense. Auric invented a neutron bomb, dragged it to Ft. Knox, and was going to detonate it with the intention of contamination the US gold supply with bismuth! Goldmember, on the other hand, is still a deep mystery.

  13. Han-Kwang Says:

    You wrote: “plutonium is one of the most toxic substance known to man.” I think this is an urban legend, although it depends on your interpretation of “one of the most”. For inhalation of dust particles that are small enough to float in the air (which is pretty small for a heavy material), it is, by weight, comparable to nerve gases, and hundreds of times less toxic than anthrax and botulism spores. For ingestion, the toxicity is comparable to caffeine, because plutonium is hardly absorbed by the intestine.

    Source: http://www.phyast.pitt.edu/~blc/book/chapter13.html

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