Veit Elser <ve10@cornell.edu> wrote:
Not sure what?s driving this discussion, or the fascination with carbon isotopes, ...
Perhaps it's slightly off-topic here, but I for one find it fascinating because it could hold all the world's knowledge (books, journals, movies, TV shows, newspapers, web pages, databases, letters, emails, security videos, genomes, paintings, etc.) in a crystal smaller than an ant, a crystal that should last for at least billions of years even with no special storage precautions. The longevity of the world's information is currently a major concern, everything from nitrate-based movie films from the early 20th century to computer tapes and diskettes from the late 20th century. Not to mention much older stuff. Henry Baker <hbaker1@pipeline.com> wrote:
Although I don't know enough quantum physics to do the calculation, my gut still tells me that the probability of exchanging an adjacent C12 for a C13 nucleus is non-negligible.
My gut tells me otherwise. :-) How do you think it would happen? Thermally? Without disrupting the extremely rigid lattice? Each carbon atom is at the center of a regular tetrahedron, with a covalent bond at each vertex. In general, the Arrehenius equation predicts reaction times of much more than trillions of years when applied at absolute temperatures that are small fractions of the temperatures at which the reaction proceeds at a reasonable rate. Quantum tunneling? The distance between the centers of adjacent atoms in a diamond is 1.54E-10 meters. That's 57,000 times the 2.7E-15 meter radius of a carbon nucleus. And for it to happen, two nuclei would have to simultaneously tunnel into each other's positions. It could happen, but for diamond to spontaneously turn into graphite is far more likely -- and has never been observed, even though most natural diamonds are billions of years old. None of this has anything to do with *electron* delocalization, but there's little of that too. Pure diamond is an excellent electrical insulator, with a breakdown voltage of more than a million volts per millimeter. (It's a good conductor of heat, but that's due to phonons, not electrons.)
So I would guess that the probability of an adjacent C12<->C13 exchange would be dramatically improved with 100x atmospheric pressure, and floating on top of molten tungsten at 6500-7000 degrees F.
I agree. Of course the lattice would cease to exist first.
So the real question is: what is the falloff in exchange probability as we lower the temperature from 3500F to 100F ?
Apply the Arrhenius equation to find out.