Proton-proton chain reaction
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Image:FusionintheSun.png Image:Wpdms physics proton proton chain 1.png Image:Wpdms physics proton proton chain 2.png Image:Wpdms physics proton proton chain 3.png
The proton-proton chain reaction is one of two fusion reactions by which stars convert hydrogen to helium, the other being the CNO cycle. The proton-proton chain is more important in stars the size of the Sun or less.
To overcome the electromagnetic repulsion between two hydrogen nuclei requires a large amount of energy, and this reaction takes an average of 109 years to complete. Because of the slowness of this reaction the Sun is still shining; if it were faster, the Sun would have exhausted its hydrogen long ago.
In general, proton-proton fusion can occur only if the temperature (i.e. kinetic energy) of the protons is high enough that they can overcome the mutual Coulomb force repulsion. The theory that proton-proton reactions were the basic principle by which the Sun and other stars burn was advocated by Arthur Eddington in the 1920s. At the time, the temperature of the Sun was considered too low to overcome the Coulomb-force barrier. After the development of quantum mechanics, it was discovered that the tunneling of the wave functions of the protons through the repulsive barrier allowed for fusion at a lower temperature than the classical prediction.
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The pp chain reaction
The first step involves the fusion of two hydrogen nuclei 1H (protons) into deuterium 2H, releasing a positron as one proton changes into a neutron, and a neutrino.
with the neutrinos released in this step carrying energies up to 0.42 MeV.
This first step is extremely slow, because it depends on the weak interaction to convert one proton into a neutron. In fact this is the limiting step, with a proton waiting an average of 109 years before fusing into deuterium.
The positron immediately annihilates with one of the hydrogen's electrons, and their mass energy is carried off by two gamma ray photons.
- e+ + e− → 2γ + 1.02 MeV
After this the deuterium produced in the first stage can fuse with another hydrogen to produce a light isotope of helium, 3He:
- 2H + 1H → 3He + γ + 5.49 MeV
From here three different main branches arise to generate helium isotope 4He. In pp1 helium-4 comes from fusing two of the helium-3 nuclei produced; the other two branches, pp2 and pp3 require the helium-4 produced in pp1, both branches arising from the different paths that Beryllium-7 can follow. In the Sun, branch pp1 takes place with a frequency of 91%, pp2 with 9% and pp3 with 0.1%.
The pp I branch
- 3He +3He → 4He + 1H + 1H + 12.86 MeV
The complete pp I chain reaction releases a net energy of 26.7 MeV. The pp I branch is dominant in temperatures of 10 to 14 megakelvins (MK). Below 10 MK, the PP chain does not produce much 4He.
The pp II branch
| 3He + 4He | → | 7Be + γ | |
| 7Be + e− | → | 7Li + νe | |
| 7Li + 1H | → | 4He + 4He |
The pp II branch is dominant in temperatures of 14 to 23 MK.
90% of the neutrinos produced in the reaction 7Be(e−,νe)7Li* carry an energy of 0.861 MeV, while the remaining 10% carry 0.383 MeV (depending on whether lithium-7 is excited or in the ground state).
The pp III branch
| 3He + 4He | → | 7Be + γ | |
| 7Be + 1H | → | 8B + γ | |
| 8B | → | 8Be + e+ + νe | |
| 8Be | ↔ | 4He + 4He |
The pp III chain is dominant if the temperatures exceeds 23 MK.
The pp III chain is not a major source of energy in the Sun (as the Sun's core temperature is not high enough), but was very important in the solar neutrino problem because it generates the highest energy neutrinos (≤14.06 MeV).
The pp IV or Hep
In this case Helium-3 reacts directly with a proton to give helium-4
- 3He + 1H → 4He + νe + e+
Energy release
Comparing the mass of the final helium-4 atom with the masses of the four protons reveals that 0.007 or 0.7% of the mass of the original protons has been lost. This mass has been converted into energy, in the form of gamma rays and neutrinos released during each of the individual reactions.
Only energy released as gamma rays will interact with electrons and protons and heat the interior of the Sun. This heating supports the Sun and prevents it from collapsing under its own weight.
Neutrinos do not interact significantly with matter and do not help support the Sun against gravitational collapse.
The pep reaction
The so-called pep (proton-electron-proton) reaction is a pretty rare one, that can take place instead of the pp reaction:
- 1H + e− + 1H → 2H + νe
In the Sun, the frequency of pep reaction versus pp reaction is 1:400. However the neutrinos released are far more energetic: while neutrinos produced in the first step of the pp reaction range in energy up to 0.42 MeV, the neutrinos from the pep reaction produce sharp-energy-line neutrinos of 1.44 MeV.
See also
es:Cadena protón-protón fr:Chaîne proton-proton it:Catena protone-protone ja:陽子-陽子連鎖反応 ko:양성자-양성자 연쇄 반응 hu:Proton-proton ciklus nl:Proton-protoncyclus pl:Cykl protonowy