Hoyle's calculation of 7.65 MeV level of carbon nucleus

In summary, the conversation discussed the calculation of the mass of helium-4 and beryllium-8, which combined to give 12.0068 u and 6.38 MeV. However, there seemed to be an error in the calculation, with the correct value being 7.37 MeV. The conversation then considered the effect of fully ionizing the particles and the inclusion of electrons. Finally, the answer was found in a 1954 paper, which identified a resonance level at 7.68 MeV above ground level.
  • #1
damosuz
72
0
Mass of helium-4 (4.0015 u) plus mass of beryllium-8 (8.0053 u) gives 12.0068 u, which is 6.35 MeV above fundamental level of carbon-12. For triple alpha process T= 100 MK, which corresponds to a kinetic energy of 2 x 3/2 kBT = 0.03 MeV for the particles. This amounts to 6.38 MeV, way below 7.65 MeV. I would like to know what is wrong with my calculation.
 
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  • #2
From wiki, Helium-4 is 4.002602 amu's and Beryllium-8 is 8.00530510 amu's. Doing some back of the envelope calculations, I get 7.4135 MeV prior to including kinetic energy.
 
  • #3
4,002602 u is helium-4 including mass of electrons, but at 100 MK, helium-4 must be completely ionized, so I guess you should take mass of alpha particle...
 
  • #4
damosuz said:
4,002602 u is helium-4 including mass of electrons, but at 100 MK, helium-4 must be completely ionized, so I guess you should take mass of alpha particle...

Ah, a valid point. I'll have to see what I can find on the matter.
 
  • #5
Beryllium will be fully ionized as well.
If we neglect binding energies of electrons (<1 keV), we don't have to care about them - we remove 2+4 electrons from the left side and 6 electrons from the right side of the reaction, which does not change anything.
4.002602 u + 8.005305 = 12.007907 u or 7.37 MeV above 12.00000. Hmm, still wrong, but much closer.
 
  • #6
Wouldn't Carbon-12's mass be less than 12 amu since it will be fully ionized too?
 
  • #7
Electrons are included on both sides in my calculation. Removing them does not change the difference, it just makes calculations more complicated
I found the answer in the original 1954 paper, page 130:
The important energy level of the C12 nucleus in the present problem is one very recently identified by Dunbar, Pixley, Wenzel, and Whaling (1953). This level occurs at about 7.68 mev above ground level, which corresponds to a value of E_R of about 0.31 mev (It will be recalled that E_R is measured relative to the sum of the masses of Be8 and alpha-particle, this being about 7.37 mev above the ground level of C12
The resonance is just close enough to be strong, but not that close to the sum of masses.
 

Related to Hoyle's calculation of 7.65 MeV level of carbon nucleus

1. What is Hoyle's calculation of the 7.65 MeV level of the carbon nucleus?

Hoyle's calculation refers to the work of astrophysicist Sir Fred Hoyle, who predicted the existence of a specific energy level in the carbon-12 nucleus. This calculation is significant because it explains the abundance of carbon in the universe, which is essential for life as we know it.

2. How did Hoyle calculate the 7.65 MeV level of the carbon nucleus?

Hoyle used nuclear physics principles and mathematical equations to predict the existence of the 7.65 MeV energy level. He based his calculations on the concept of nuclear resonance, which occurs when particles within a nucleus align in a specific way to create a stable energy state.

3. Why is the 7.65 MeV level of the carbon nucleus important?

The 7.65 MeV level is significant because it is the first step in the process of nucleosynthesis, the formation of elements in the universe. This energy level allows carbon-12 to efficiently fuse with other elements to create heavier elements, such as oxygen and nitrogen, which are crucial for life.

4. Has Hoyle's calculation of the 7.65 MeV level been confirmed?

Yes, Hoyle's calculation has been confirmed by various experiments and observations. In 1953, Hoyle's prediction was supported by the discovery of the 7.65 MeV energy level in the carbon-12 nucleus. Since then, further studies have validated his calculation, solidifying its place in modern astrophysics.

5. How does Hoyle's calculation impact our understanding of the universe?

Hoyle's calculation of the 7.65 MeV level plays a crucial role in our understanding of the universe. It explains the abundance of carbon, which is necessary for life as we know it. Additionally, it provides insight into the processes that occur within stars, helping us understand how elements are formed and distributed throughout the universe.

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