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Section 59.4 Energy Source of Sun

The energy for most main-sequence stars come from nuclear fusion of protons into helium. For instance, it is believed that the chain of fusion reactions shown in Figure 59.4.1, called the proton-proton chain - I, occur in the Sun.

Figure 59.4.1.

In the first reaction, two protons are fused to make a deuteron, a positron, and a neutrino. In the second reaction, the deuteron fuses with another proton with the production of \(^{3}\textrm{He}\text{.}\) Two \(^{3}\textrm{He}\) then combine to form \(^{4}\textrm{He}\) and release two protons. Thus, two times the first two reactions and one time the third equation forms a full cycle. In the full chain, four protons combine in the first reaction and two in the second reaction, and two protons are released in the third reaction. Thus, a total of four protons combine to yield one \(^{4}\textrm{He}\text{,}\) two positrons, two neutrino, and two photons.

The net energy released as positron, neutrino, and gamma rays over one proton-proton chain will be \[ Q_{\textrm{net}} = \left(4 m_p - m[\ ^{4}\textrm{He}] \right)\: c^2\approx 25\:\textrm{MeV}. \] When the two positrons collide with two electrons in the Sun, they annihilate each other and produce gamma rays with additional energy of approximately 2 MeV. This makes the total energy released from the proton-proton chain plus annihialtion of positron to be about 27 MeV per four proton. The proton-proton chain reaction occurs deep inside the Sun where the temperature is quite high, \(\sim 15\) MK.