# Triple Alpha Reaction: DE's for He4, C12, O16, Ne20

• t_n_p
In summary, the conversation discusses the triple alpha reaction in astrophysics and the resulting production of C12, O16, and Ne20. The rate of production and destruction of each element is given by specific rate coefficients (e.g. λ3α). The equations for the abundances of each element as a function of time are also provided.
t_n_p
Hi guys,
I posted this in the homework subforum but since its more intensive on the astrophysics side of things I thought I'd give it a shot here. Hope this isn't a problem mods.

Helium is burnt via the triple alpha reaction: 3He4 -> C12 at a rate of λ(He4)3, where He4 denotes the number abundance of He4. Once there is some C12 present then we can get C12(α,γ)O16 which occurs at the rate λ12αHe4C12. Then, once O16 has been produced, we also get O16(α,γ)Ne20 which occurs at the rate λ16αHe4O16.

Write down DE's for He4,C12, O16, Ne20 abundances as a function of time.

Basically here's what I did.
d(He4)/dt = production - destruction = - λ(He4)3
d(C12)/dt = production - destruction = λ(He4)3 - λ12αHe4C12
d(O16)/dt = production - destruction = λ12αHe4C12 - λ16αHe4O16
d(Ne20)/dt = production - destruction = λ16αHe4O16

This is most likely wrong, but I'd thought I'd just give it a shot.
Any thoughts?

.Your equations look correct to me. The only thing I would add is to make sure that you include the rate coefficients for the reactions (e.g. λ3α) as constants in your equations. You will also need to add a source of He4 if it is not being produced.

## 1. What is the triple alpha reaction?

The triple alpha reaction is a nuclear fusion reaction that occurs in stars with high enough temperatures and densities. It involves the fusion of three alpha particles (helium nuclei) to form a carbon-12 nucleus.

## 2. What is the significance of the triple alpha reaction?

The triple alpha reaction is important in the production of heavier elements in stars. It is responsible for the formation of carbon, which is essential for life on Earth. It also provides the energy that allows stars to shine.

## 3. What are the reactants and products of the triple alpha reaction?

The reactants of the triple alpha reaction are three alpha particles (He-4 nuclei). The product is a carbon-12 nucleus (C-12). In some cases, additional helium nuclei may be produced in a chain reaction.

## 4. What are the conditions required for the triple alpha reaction to occur?

The triple alpha reaction requires very high temperatures (around 100 million Kelvin) and densities in order for the alpha particles to overcome their mutual repulsion and fuse together. This typically occurs in the core of a star.

## 5. How does the triple alpha reaction contribute to the energy production in stars?

The triple alpha reaction is an exothermic reaction, meaning it releases energy. This energy is in the form of photons (light) and is what allows stars to shine. The energy produced by the triple alpha reaction also helps to maintain the high temperatures and pressures necessary for the reaction to continue.

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