Hi Keith: 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. The problem with crystal lattices is that the constituent atoms are usually the same -- e.g., diamond or graphene. In the case of crystals like NaCl, there is no hope of exchanging a Na for a Cl, and if a Na<->Na happened or a Cl<->Cl happened, we'd not notice. In the case of a metal, the electrons become smeared all over the crystal, so they can't be localized at all. In the case of a diamond crystal, the location of "a" carbon nucleus is localized to within the distance to its 4 (?) nearest neighbors. https://en.wikipedia.org/wiki/Diamond_cubic Delocalizing a carbon nucleus would make diamond look a lot more like a liquid. Diamond won't melt at 1 atmosphere, as 1 atmosphere is below its triple point at 107 atmospheres and 7820 degrees F. 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. However, if we heat up diamond at 1 atmosphere, past about 3500F it first turns to graphite before finally melting at ~7600F. So somewhere in the vicinity of 3500F and 1 atmosphere, the localization of the carbon atoms must start to break down, and the exchange probability must rise sharply. So the real question is: what is the falloff in exchange probability as we lower the temperature from 3500F to 100F ? https://en.wikipedia.org/wiki/File:Carbon_basic_phase_diagram.png At 02:13 PM 6/5/2016, Keith F. Lynch wrote:
Henry Baker <hbaker1@pipeline.com> wrote:
Re adjacent C12/C13 swapping: in a quantum universe, never say "never". The probability & half-life of such swapping should be calculable.
The atoms are locked into a rigid lattice. It's enormously more likely that the lattice will break down than that atoms will swap in an intact lattice. So it's the half-life of the lattice that you should calculate.