Answer to your question if fusion. Sun generates energy through fusion, but first in order for fusion to start we need some gravitational shrinking to kick in on a big molecular cloud - that will form a star. Now that is completely different topic but when we have thermal equilibrium and a star on main sequence, just like Sun is fusion is main source of energy.
I will try to be short and concize with this answer, in order to do this we need to start with Einstein's equation. ΔE = Δmc2.
For fusion to happen two nuclei must overcome repellent Coulomb force.
Fusion of two protons requires energy of above 1 MeV, these energies come from thermal velocities as a result of high temperatures. Inside the Sun we have thermal equilibrium at T = 15×106 K.
In theory, 4 hydrogen nucleons are fused into nucleus of helium, and one helium nucleus is lighter than 4 separate nucleons this is known as defect of mass. According to Einstein theory mass defect ( Δm = 4mH1 - mHe4 = ) is transformed into enormous energy of about 26.72MeV, and most of it is released by radiation as a γ quantum, small fraction leaves the star as a neutrino, and the rest provides more kinetic energy for produced particles. (Bethe and Weizsäcker)
Nuclear transmutation () are happening through chains or cycles of several nuclear reactions.
Proton - proton (p-p) chain
Main reactions of this chain are given below, but there are several variations of it.
1st reaction has very low probability to happen but there are so many protons in the sun that it happens quite often.
2nd recion: shortly after deuteron is made it collides with a proton which gives us helium isotope and releases a gamma quantum.
final step is collision of two helium isotopes which produces stable helium nucleus (alpha particle) and two protons and releases huge amount of energy (12.86MeV).
Total energy produced in one proton-proton chain is E = 2(1.18 + 0.26 +5.49) + 12.86 = 26.72 MeV. To produce two helium isotopes first two reactions must happen twice.
Proton-proton chain is most efficient at the temperatures of about 15 million K and densities of 100 g/cm3, so it is considered as main source of energy in the Sun and Sun-like stars.
CNO – Bethe’s Cycle
According to stellar evolution theory, chemical composition of the star is changing as a result of the nuclear reactions, hence composition of stellar atmosphere shows initial material the star was made of. The fact that we observe stars with heavy elements in stars atmospheres (C, N, O) means that they are not first generation stars. These stars have another possibility to form helium nucleus out of 4 hydrogen nucleus which releases energy equal to 26.72 MeV (Bethe 1939). For this reaction we need carbon, but it acts only as catalyst.
Nuclei of N13 and O15 are unstable due to excess of positive charge, so they decay (2nd and 5th reaction).
Bethe's CNO cycle becomes important and dominant source of energy when the temperatures in the stars are higher than 20×106 K.
Dominance of p-p chain or Bethe’s cycle effects the stellar structure and its physical conditions. While physical conditions influence ratio of these two energy sources, combined with stellar structure it also determines where will be established convection zone, in the central or peripheral zone of the star.
So in the above text we presented two ways that stars produce energy in their interiors. Sun and Sun-like stars do have dominance of p-p chain but Bethe's cycle is also active and producing heavier elements.
For the end one information regarding our Sun and life on Earth: Chandrasekhar calculated that Sun has enough hydrogen fuel for life of 10 × 10 9 years. Current amount of helium in the Sun, determined in the studies of Solar spectra, tells us that our Sun is old about 5 × 10 9 years.
If you have any additional questions I will gladly answer them.
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