Why does the CNO cycle's final reaction produce carbon-12, not oxygen-16?

[sunrah]

The last reaction in CNO-I sees ¹⁵N + ¹H --> ¹²C + ⁴He

I'm interested why it doesn't produce ¹⁶O, which is also stable.

 

[Ken G]

That does indeed happen, just far less often. So it's a matter of branching ratios.

 

[Matterwave]

Specifically, the CNO cycle uses Carbon, Oxygen, an Nitrogen as catalysts for the reaction 4H->He, the "interesting" branches of the cycle are the ones which produces an alpha particle from 4 protons.

 

[mfb]

Multiple particles fusing to create a single one is a rare process in general. Due to energy conservation, the energy has to be "just right" to produce the particle. It is never exactly right, so you have to hit some excited state that decays to the ground state afterwards.
Carbon-12 has this state for the triple-alpha process, oxygen-16 does not have a state at the right energy.

Specifically, the CNO cycle uses Carbon, Oxygen, an Nitrogen as catalysts for the reaction 4H->He, the "interesting" branches of the cycle are the ones which produces an alpha particle from 4 protons.

Well, our interest does not influence the reaction rates ;).

 

[Matterwave]

Well, our interest does not influence the reaction rates ;).

But they might influence which branches get emphasized in a textbook and which branches are neglected.

 

[Ken G]

I think it's fair to say that the processes that are of most interest are the ones that have the fastest rates. There are states of Oxygen 16 that have the right energy to be obtained from Nitrogen 15 and a proton, they just spit out a gamma ray, but they are just less likely to happen because if you spit out an alpha particle instead, you have a higher momentum particle for the same energy (it's less relativistic), so you get access to more momentum states. There's also different internal processes involved, so they all affect the branching ratio. This means there are just more ways the processes with a higher branching ratio can happen. I'll bet it's not at all uncommon for three alpha particles to come together but then fly apart again before they release a gamma ray and drop into a bound state, it's just that we don't count that as a kind of reaction so it just doesn't show up. But of the reactions that change the nature of the nucleus, the ones that happen the most ways are the ones that we need to track.

 

[Bandersnatch]

Multiple particles fusing to create a single one is a rare process in general. Due to energy conservation, the energy has to be "just right" to produce the particle. It is never exactly right, so you have to hit some excited state that decays to the ground state afterwards.
Carbon-12 has this state for the triple-alpha process, oxygen-16 does not have a state at the right energy.

My understanding of the processes involved is probably a very naive one, but couldn't the extra energy simply go into kinetic energy of the daughter nucleus?

 

[Ken G]

No, if two particles go into one, you can't conserve both energy and momentum unless you can find internal degrees of freedom in the daughter to put that energy. So the daughter can be in an excited state, which eventually de-excites and releases a gamma ray. That can conserve both energy and momentum because you end up having two particles go into two particles.

 

[Matterwave]

I think it's fair to say that the processes that are of most interest are the ones that have the fastest rates. There are states of Oxygen 16 that have the right energy to be obtained from Nitrogen 15 and a proton, they just spit out a gamma ray, but they are just less likely to happen because if you spit out an alpha particle instead, you have a higher momentum particle for the same energy (it's less relativistic), so you get access to more momentum states. There's also different internal processes involved, so they all affect the branching ratio. This means there are just more ways the processes with a higher branching ratio can happen. I'll bet it's not at all uncommon for three alpha particles to come together but then fly apart again before they release a gamma ray and drop into a bound state, it's just that we don't count that as a kind of reaction so it just doesn't show up. But of the reactions that change the nature of the nucleus, the ones that happen the most ways are the ones that we need to track.

Fair enough.

 

[mfb]

My understanding of the processes involved is probably a very naive one, but couldn't the extra energy simply go into kinetic energy of the daughter nucleus?

You can view the reaction in the system of the final product - no kinetic energy.
Alternatively: the kinetic energy is fixed by the momentum, there is no degree of freedom to use here.

 

[Bandersnatch]

Thanks Ken G and mfb. And thanks to the OP for asking the question. I remember wondering about it back in secondary school when I still thought I'd go into astronomy for a career. Coldn't find the answer back then, and completely forgot about it until now.