# Hoyle's calculation of 7.65 MeV level of carbon nucleus

1. Apr 30, 2015

### damosuz

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.

2. Apr 30, 2015

### Drakkith

Staff Emeritus
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. May 1, 2015

### damosuz

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. May 1, 2015

### Drakkith

Staff Emeritus
Ah, a valid point. I'll have to see what I can find on the matter.

5. May 1, 2015

### Staff: Mentor

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. May 1, 2015

### Drakkith

Staff Emeritus
Wouldn't Carbon-12's mass be less than 12 amu since it will be fully ionized too?

7. May 1, 2015

### Staff: Mentor

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 resonance is just close enough to be strong, but not that close to the sum of masses.