Astrophysics - triple alpha core Temp

[supersam]

Homework Statement

Explain why stage 1 and 2 of the triple alpha process will not being until the core Temp of the star is around 10^8K.

Homework Equations

4He+4He = 8Be (step 1)
8Be+4He = 12C (Step 2)

The Attempt at a Solution

I "think" I need to work out the nuclear energies... However I am a little stuck on how to do this. This is a marked assignment so I'd appreciate a nudge in the right direction, rather than any form of a solution.

I have a suspicion that I need to use T^v, where v = (EG/4kT)^1/3 - 2/3; where EG is the gammon energy. However I would like just a heads up if this is the right idea.

Thanks

 

[SteamKing]

Homework Statement

Explain why stage 1 and 2 of the triple alpha process will not being until the core Temp of the star is around 10^8K.

Homework Equations

4He+4He = 8Be (step 1)
8Be+4He = 12C (Step 2)

The Attempt at a Solution

I "think" I need to work out the nuclear energies... However I am a little stuck on how to do this. This is a marked assignment so I'd appreciate a nudge in the right direction, rather than any form of a solution.

I have a suspicion that I need to use T^v, where v = (EG/4kT)^1/3 - 2/3; where EG is the gammon energy. However I would like just a heads up if this is the right idea.

Thanks

Perhaps you should review some of the basics of the triple alpha reaction first before going down the rabbit hole:

http://en.wikipedia.org/wiki/Triple-alpha_process

It takes a while before a star with a hydrogen core eagerly fusing away accumulates enough helium to interfere with that reaction. And when hydrogen fusion is interrupted, what happens in the core?

 

[supersam]

Okay - looks like I might have been getting ahead of myself. So the Helium "burning" starts due to huge temperatures when the core of the star collapses. Which in turn creates Beryllium and then Carbon. However I am still not exactly sure how the 10^8K value is determined. I can understand that the energy comes from the Gravitational Potential energy - but how do you show that 10^8K is the magic number?

 

[SteamKing]

Okay - looks like I might have been getting ahead of myself. So the Helium "burning" starts due to huge temperatures when the core of the star collapses. Which in turn creates Beryllium and then Carbon. However I am still not exactly sure how the 10^8K value is determined. I can understand that the energy comes from the Gravitational Potential energy - but how do you show that 10^8K is the magic number?

Look at the conditions necessary for helium fusion to take place after hydrogen fusion is no longer able to support the core against collapse.

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

 

[paranormal]

I can explain why the triple alpha process, which is the fusion of three helium nuclei to form carbon, does not begin until the core temperature of a star reaches around 10^8K.

The first step of the triple alpha process involves the fusion of two helium nuclei (4He) to form beryllium-8 (8Be). This reaction has a very low probability of occurring due to the repulsive forces between the positively charged nuclei. In order for this reaction to occur, the helium nuclei must have enough energy to overcome this repulsion and fuse together.

The energy required for this reaction is related to the temperature of the core of the star. At lower temperatures, the particles in the core have less kinetic energy and therefore a lower chance of overcoming the repulsive forces and fusing together. As the temperature increases, the particles have more kinetic energy and a higher chance of fusion occurring.

However, even at high temperatures, the formation of 8Be is not stable and it quickly decays back into two helium nuclei. This is where the second step of the triple alpha process comes in, which involves the fusion of 8Be with another helium nucleus to form carbon-12 (12C). This reaction also has a low probability of occurring and requires even higher temperatures to overcome the repulsive forces.

Therefore, the triple alpha process will not begin until the core temperature of the star reaches around 10^8K, which is the temperature at which the particles have enough energy to overcome the repulsive forces and initiate the fusion reactions. This temperature is also high enough for the reactions to proceed at a significant rate, leading to the formation of carbon in the star's core.

In terms of the equations, you are correct in thinking that the temperature plays a crucial role in the triple alpha process. The equation you mentioned, T^v, is known as the Gamow factor and is used to calculate the probability of nuclear reactions at a given temperature. It is related to the energy required for the reaction and the temperature, as you suspected.

I hope this explanation helps guide you in the right direction for your assignment. Remember to always consider the physical processes and concepts behind the equations, rather than just plugging in numbers and solving for a result. Good luck!