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.