What is an unstable Carbon-12?

[MTd2]

I just noticed that Boron-11 gets a proton and becomes Carbon – 12, which is the most common stable carbon isotope. So, how can a carbon – 12 be unstable and give 3 Helium – 4?

[DerekShannon]

The carbon-12 has less mass than the proton and boron-11 did–That mass became ENERGY, so even though regular carbon-12 is stable, this transitory carbon-12 nucleus has too much energy and breaks apart into three alpha particles.

Wolfram Alpha is a easy tool to look at this.

It actually is possible in a small fraction of pB11 reactions for the energy to be released as a gamma ray instead of in the break-up into alpha particles, and when that happens you are indeed left with a carbon-12. A friend in astrophysics at Caltech suggested it might be interesting to look for the gamma ray signature as part of our diagnostics.

The comments here go into slightly more detail: https://focusfusion.pmhclients.com/index.php/site/article/are_you_sure_pb11_fusion_isnt_fission/

[jamesr]

Another way to look at it is that nuclei have excited states just like atoms do.

You can excite a nucleus to a higher state where the neutrons an protons vibrate more. Often the most efficient way for it to release the energy is not necessarily via photon but via an interaction through the strong force, whereby an alpha particle it emitted. (interaction via the weak nuclear force are far less likely, by far I mean 20 orders of magnitude less likely)

So where the Boron and proton overlap and have a total energy greater than the rest mass of the carbon 12 they combine resulting in an excited C-12 state. The excess is released, on average, as with any radioactive decay, by the most probable route. ie. the C-12 emits one alpha, then shortly after the Be-8 left splits again into to more alphas.

[MTd2]

Thanks Derek, but I did the calculation provided by jamesr and the result is closer to the 8.7 MeV provided by wikipedia:

http://en.wikipedia.org/wiki/Aneutronic_fusion

http://www.wolframalpha.com/input/?i=mass+of+proton+++mass+of+Boron-11+-+mass+of+Beryllium-8+-++mass+of+Helium-4

The result is 8.07 MeV

The decay of beryllium 8 to helium – 4 gives ( http://www.wolframalpha.com/input/?i=mass+of+Beryllium-8+-+mass+of+Helium-4+-+mass+of+Helium-4+)

0.09 MeV

The total is 8.16MeV

There are still 0.540MeV missing…

Maybe there’s a rounding error? Or are there still decay chains missing?

[jamesr]

You have the mass of a proton, but the atomic masses of the others. Atomic masses include the electrons in a bound atom, ie the rest mass of all the electrons minus their binding energy in the ground state.

http://www.wolframalpha.com/input/?i=mass+of+proton++++mass+of+Boron-11+-++3*++mass+of+alpha+-5*electron+mass
Gets closer at 8.68MeV – but still ignores the binding energy of the 5 electrons in atomic Boron-11

The ionisation energies to strip each of the electrons from the boron are: 8.30, 25.15, 37.93, 259.37, and 340.22eV = 670eV = 0.00067MeV (ie an insignificant correction)

[DerekShannon]

Yes, here is the follow-up all the way the to helium that I tweeted from @LPPX but didn’t get around to posting here: http://bit.ly/cxJGck

Not meant to be super-exact, but always amazing when Wolfram Alpha turns out to be useful for something!

[vansig]

DerekShannon wrote:
It actually is possible in a small fraction of pB11 reactions for the energy to be released as a gamma ray instead of in the break-up into alpha particles, and when that happens you are indeed left with a carbon-12. A friend in astrophysics at Caltech suggested it might be interesting to look for the gamma ray signature as part of our diagnostics.

does the probability of a gamma change with the velocity of the collision? if so, it becomes a way to measure reaction temperature.

[Lerner]

That reaction occurs only at energies above 7Mev and even at 14 Mev is about a million times less likely than the tri-alpha one is at 600 keV.

[DerekShannon]

OK, we’ll let him look for the gamma ray signature himself, then ;-P

[Brian H]

Back in August there was some discussion of diborane as a possible fuel, and Eric was going to talk to the poster Alchemist about decaborane, etc., handling issues. Did Alchemist manage to make a case for diborane? It sounded a lot safer and cheaper.

[vansig]

cheaper, yes. but, safer? i really doubt that

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